Splitting Approach Research Articles

On derivations of evolving surface Navier–Stokes equations

In recent literature several derivations of incompressible Navier–Stokes-type equations that model the dynamics of an evolving fluidic surface have been presented. These derivations differ in the physical principles used in the modeling approach and in the coordinate systems in which the resulting equations are represented. This is an overview paper in the sense that we put five different derivations of surface Navier–Stokes equations into one framework. This then allows a systematic comparison of the resulting surface Navier–Stokes equations and shows that some, but not all, of the resulting models are the same. Furthermore, based on a natural splitting approach in tangential and normal components of the velocity, we show that all five derivations that we consider yield the same tangential surface Navier–Stokes equations.

Holistic opto-thermo-electrical analysis of a novel spectral beam splitting-based concentrating photovoltaic thermal system

The spectral beam splitting (SBS) approach decouples the dependence between photovoltaic and photothermal conversions in a traditional photovoltaic thermal (PVT) system. And hence, it overcomes the inherent limitation of obtaining a low-quality thermal output from a conventional PVT system as the operational cell temperature limits the maximum attainable thermal output. However, the energy transfer and transformation are complex operations in an splitting-based PVT system. In the present work, a 2.3× concentration ratio compound parabolic collector (CPC) is truncated from a 2.8× concentration CPC. For the solar spectral splitting, a nanofluid-based optical filter inside a transparent borosilicate glass tube is used. Deionized water and ZnO nanofluid are employed as optical filters. A linked optical–thermal–electrical framework is developed and implemented to assess the performance of the devised physical model. The optical analysis used a Monte Carlo ray-tracing routine to determine the heat flux distribution on the cell and glass tube units. The average heat flux is then used in a quasi-dynamic thermal model to numerically solve for the cell temperature and temperature rise of the optical filter. Furthermore, for analytically calculating the electrical performance with cell temperature and incident solar radiation as known parameters, a five-parameter (1-diode/2-resistor) electrical model is utilized. The stated optical, thermal, and electrical models are validated against the experimental and numerical findings for a simple conventional collector. The developed model demonstrated optical filter’s prowess by transmitting solar rays within the spectral response range to the PV array while absorbing the remainder of the spectrum. Without splitting, average array temperatures are recorded as high as 360 K and 375 K during solar noon in January and June, respectively. However, when using the spectral splitting, the corresponding temperatures are 310 K and 328 K, respectively. Therefore, it is observed that while employing the splitting, the cell temperature is kept near the standard test temperature without using any additional passive or active cooling strategy. Moreover, the greatest cumulative temperature rise of deionized water and ZnO nanofluid at 1600 h in January is reported to be 35.62 K and 43.59 K, respectively. However, for the month of June, it is found to be 58.76 K and 71.88 K for deionized water and ZnO nanofluid, respectively.

Solar‐Driven Co‐Production of Hydrogen and Value‐Add Conductive Polyaniline Polymer

AbstractTo reduce the reliance on fossil fuel, H2, as a clean fuel, has attracted substantial research and development activities in recent years. The traditional water splitting approach requires an applied bias of more than 1.5 V and the use of ion‐selective membranes to prevent the formation of a potentially explosive H2–O2 gas mixture, resulting in increased cost and system design complexity. Here, a solar‐driven H2 production process requiring a much lower applied bias of 1.05 V is reported whereby aniline (ANI) is oxidized to polyaniline (PANI) at the anode with a yield of 96% and H2 evolution reaction occurs at the cathode with a faradaic efficiency of 98.6 ± 3.9%. The process has multiple advantages including the elimination of ion‐exchange membrane as PANI is a solid product that also is of substantially higher value than O2. For demonstration, a single junction perovskite solar cell and low‐cost earth abundant CoP catalyst are successfully applied for this process. This process contributes to the advancement of solar‐driven low‐cost H2 generation coupled with co‐production of a high‐value product expediting the transition to a hydrogen economy.

Unconditional error analysis of a linearized BDF2 virtual element method for nonlinear Ginzburg–Landau equation with variable time step

We consider a virtual element method in space for the nonlinear Ginzburg–Landau equation, while a linearized time-variable-step second order backward differentiation formula (BDF2) is adopted in time. The error splitting approach is used to prove the unconditional optimal error estimate of the derived scheme under the mild restriction on the ratio of adjacent time-steps ratios (similarly proposed in Liao and Zhang 2021, Zhang and Zhao 2021). By using the techniques of the discrete complementary convolution (DOC) kernels and the discrete complementary convolution (DCC) kernels, we obtain the boundedness and error estimates of the solution of time-discrete system. Moreover, the optimal convergence in L2-norm for the fully discrete scheme is finally derived. Numerical examples on a set of polygonal meshes are given to validate our theoretical results.

Permafrost modelling with OpenFOAM®: New advancements of the permaFoam solver

Permafrost, i.e., soil that is year-round frozen in depth, is covering a quarter of the continents of the northern hemisphere. It currently experiences fast changes due to climate change at global scale and technogenic perturbations at local scale, and the assessment and anticipation of these changes are of primary importance for many environmental and engineering applications in cold regions. To these ends, permafrost modelling is required, while the strong couplings and non-linearities involved in the physics at stake make it highly challenging, especially from a computational point of view. In this work we present a new solver for permafrost hydrology developed in the framework of OpenFOAM®, allowing to benefit from its advanced high-performance computing capabilities. The solver is tested for realistic, field-based cases, and its parallel performances are characterized up to ∼16000 cores on IRENE supercomputer (TGCC, CEA). Program summaryProgram Title: permaFoamCPC Library link to program files:https://doi.org/10.17632/swp88cvpwb.1Developer's repository link:https://develop.openfoam.com/Community/hydrology/Licensing provisions: GPLv3Programming language: C++Nature of problem: This software solves the coupled equations that govern water flow and heat transfer in variably saturated and variably frozen porous media, for transient problems in Three-dimensional, heterogeneous domains. The equation for water flow is Richards equation, which is a very popular model for water transfer in variably saturated porous media (e.g.: soils), and the equation for heat transfer is a Fourier equation including advection and the freeze/thaw of the pore water. The solver is designed to take advantage of the massively parallel computing performance of OpenFOAM®. The goal is to be able to model natural hydrosystems of cold regions on large temporal and spatial scales.Solution method: For each equation a mixed implicit (FVM for Finite Volume Method in the object oriented OpenFOAM framework) and explicit (FVC for Finite Volume Calculus in the object oriented OpenFOAM® framework) discretization with backward time scheme is embedded in an iterative linearization procedure (Picard algorithm). The coupling between the two equations is performed through an operator splitting approach. The implementation has been carried out with a concern for robustness and parallel efficiency.Additional comments including restrictions and unusual features: This version of permaFoam has been tested with OpenFOAM_v1912, v2106, v2112 and v2206, thus everything might not work with other (especially older) versions of OpenFOAM®. When using permaFoam, one should be careful to use fine enough spatial and temporal discretisations where and when steep fronts (freeze/thaw fronts, imbibition/drainage fronts) occur, otherwise numerical stability problems might arise.

SnTe nanomaterial decorated over graphene nanosheet for robust OER activity

Hydrogen production via electrocatalytic water splitting has fascinated great attention because of its eco-friendly nature and will be used as a renewable energy resource for the next decade. Despite marvelous efforts, we report the novel GO/SnTe nanocomposite fabricated via a simple chemical reduction approach for electrocatalytic water splitting. All the synthesized electrocatalysts are analyzed via different techniques. Furthermore, the electrochemical performance of fabricated electrode material employed on fluorine-doped tin oxide was investigated with linear sweep voltammetry, cyclic voltammetry, chronoamperometry, and electrochemical active surface area to analyze the kinetics mechanism, active sites, and stability of the material using 1.0 M potassium hydroxide. The electrochemical result of the nanocomposite indicates a remarkable overpotential of 226 mV at 10 mA cm−2 current density with a Tafel slope of 53 mV dec−1. Also, the nanocomposite has a 1.55 V lower onset potential vs reversible hydrogen electrode, and high stability of 180 hours. All these characteristics suggest that the electrocatalyst has potential for the oxidation reaction.

Comprehensive Performance Analysis based on Classical Machine Learning and Deep Learning Methods for Predicting the COVID-19 Infections

The COVID-19 (coronavirus disease) has been declared as pandemic throughout the world by the WHO (World Health Organization). The numbers of active COVID-19 cases are increasing day by day and clinical laboratory findings consume more time while interpreting the COVID-19 infected result. There are limited treatment facilities and proper guidelines for reducing infection rates. To overcome these limitations, the requirement of clinical decision support systems embedded with prediction algorithms are raised. In our study, we have architect the clinical prediction system using classical machine learning, deep learning algorithms, and experimental laboratory data. Our model estimated that which patients likely infected with COVID-19 disease. The prediction performances of our models are evaluated based on the accuracy score. The experimental dataset has been provided by Hospital Israelita Albert Einstein at Sao Paulo, Brazil, which included the records of 600 patients from 18 laboratory findings with 10% COVID-19 disease infected patients. Our model has been validated with a train-test split approach, 10-folds approach, and AUC-ROC curve score. The experimental results show that the infected patients with COVID-19 disease are identified at an accuracy of 91.88% through deep learning method (CNN) and 89.79 % through classical machine learning (Logistic Regression), respectively. We can observe that our prediction model could be used as clinical assistance for predicting the COVID-19 infections. We would like to invite medical experts to recommend our model for clinical studies.

Endoscopic anterior cricoid split with dilation

Endoscopic anterior cricoid split may be performed as an adjunct to balloon dilation in select patients with subglottic stenosis. It offers the possibility for the treatment of more significant, mature subglottic stenosis, as well as congenital subglottic stenosis with cartilaginous anomaly endoscopically whereas previously these patients could only successfully be treated with an open procedure. Here the indications, preoperative workup, operative technique and post-operative considerations are outlined. In certain situations, an endoscopic anterior-posterior cricoid split or open approach may be better suited. Endoscopic anterior cricoid split may be performed as an adjunct to balloon dilation in select patients with subglottic stenosis. It offers the possibility for the treatment of more significant, mature subglottic stenosis, as well as congenital subglottic stenosis with cartilaginous anomaly endoscopically whereas previously these patients could only successfully be treated with an open procedure. Here the indications, preoperative workup, operative technique and post-operative considerations are outlined. In certain situations, an endoscopic anterior-posterior cricoid split or open approach may be better suited.

Systematic scoping review on moral distress among physicians

BackgroundConcepts of moral distress (MD) among physicians have evolved and extend beyond the notion of psychological distress caused by being in a situation in which one is constrained from acting...

FedBERT: When Federated Learning Meets Pre-training

The fast growth ofpre-trained models(PTMs) has brought natural language processing to a new era, which has become a dominant technique for variousnatural language processing(NLP) applications. Every user can download the weights of PTMs, then fine-tune the weights for a task on the local side. However, the pre-training of a model relies heavily on accessing a large-scale of training data and requires a vast amount of computing resources. These strict requirements make it impossible for any single client to pre-train such a model. To grant clients with limited computing capability to participate in pre-training a large model, we propose a new learning approach,FedBERT, that takes advantage of the federated learning and split learning approaches, resorting to pre-training BERT in a federated way.FedBERTcan prevent sharing the raw data information and obtain excellent performance. Extensive experiments on seven GLUE tasks demonstrate thatFedBERTcan maintain its effectiveness without communicating to the sensitive local data of clients.

Wireless powered cognitive radio networks with multiple antenna sources and hardware impairments

In this paper, a radio-frequency (RF) energy harvesting enabled cognitive radio network (CRN) is considered in the presence of transceiver hardware impairments (HIs). Herein, one of the secondary nodes (SNs) exploits simultaneous wireless information and power transfer (SWIPT) technology to harvest energy from the primary signal and provides relay assistance for the primary transmission. We consider multiple antennas at the primary nodes (PNs) to ensure better link reliability and spectrum sharing to mitigate the spectrum scarcity. In the first phase, relaying SN uses non-linear energy harvester circuit to harvest energy from the RF signals received from PN using the power splitting approach. In the second phase, the same SN adds its own signal intended for the other SN along with the primary signal and broadcasts the combined signal. Assuming the network to operate in a Nakagami-m fading environment, the performance of the considered CRN is evaluated in terms of outage probability and system throughput. Also, we formulate two optimization problems to minimize the OP and maximize the system throughput. The Karush–Kuhn–Tucker conditions are used to obtain the closed-form solution of the constrained convex optimization. Numerical results are provided to examine the performance impact concerning different system and channel parameters.

Energy-Efficient beyond 5G Multiple Access Technique with Simultaneous Wireless Information and Power Transfer for the Factory of the Future

In the Industrial Internet of Things (IIoT), non-orthogonal multiple access (NOMA) has emerged as a viable multiple access method due to its superior efficiency. In this paper, a new power allocation technique for NOMA-enabled IIoT devices is presented with trade-offs between increasing energy efficiency and decreasing power consumption. We present a joint optimization of transmission rate and energy harvesting in simultaneous wireless information and power transfer (SWIPT) NOMA-enabled IIoT devices. With the power splitting (PS) approach, we examine how to improve overall transmission rate and harvested energy, simultaneously, while fulfilling the minimum rate and harvested energy needs of each IIoT device in a SWIPT-enabled NOMA system. An objective function is established by adding transmission rates obtained from information decoding and the transformed throughput from energy harvesting. The combination of management approaches with Industry 4.0 technology provides a viable strategy to decrease industrial production’s energy use. Several performance metrics may be utilized to study manufacturing process optimization. The efficiency of production equipment may be measured by looking at the overall effectiveness (OE) of the equipment in use. We divide the non-convex optimization problem into two sub-problems, based on the Lagrangian duality method, and solve them to find the optimal solution for the non-convex problem. The approach is validated based on physical layer parameter settings that represent potential factory of the future scenarios. Simulation results confirm the effectiveness of the presented method in a SWIPT-enabled NOMA system, provide considerable performance gains over the classic rate maximization strategy, and demonstrate the energy efficiency of the presented method compared with the conventional system. The results show huge potential of our solutions to reduce the future huge energy demand related to factory automation.

A critical review of the impacts of split injection strategies on the performance, combustion and emissions characteristics of a diesel engine fueled with low carbon alcohol fuels

This paper reviews the impacts of split (pilot/main) injection tactics on the exhaust pollutants, performance, and combustion of compression ignition (CI) engines operated with low carbon alcohols fuels. For the past several years, scholars have been attempting to simultaneously reduce NOx and soot emissions by enhancing combustion, which is accomplished by optimizing the fuel injection technique by using high amount of EGR or low carbon alcohols fuels. Split injection tactics are used in the diesel engines to accomplish the partially premixed combustion (PPC). The prolonged ignition delay (ID) in PPCI engines improves air/fuel mixing, resulting in lower soot and NOx emissions. Furthermore, due to the more substantial charge cooling effect of low carbon alcohol fuels reduce the combustion temperature, resulting in lower NOX emissions. Thus, combining a split injection approach with low-carbon alcohol fuels in a modern CI engine might be a promising option to satisfy stringent exhaust pollution regulations as well as reducing dependency on fossil fuels. The present paper focuses on the work done in the area of split injection strategies with various low-carbon alcohol fuels and the effects of injection pressures on engine performance.

A Multicomponent Reactive Transport Model for Integrated Surface‐Subsurface Hydrology Problems

AbstractDespite the widespread use of integrated hydrology models in a variety of applications, consideration of multicomponent reactive transport is still not common. The implementation of these processes requires coupling transport at the surface‐subsurface interface and efficient solution of the non‐linear geochemical model that is consistent with the integrated hydrology solution. The Advanced Terrestrial Simulator provides a flexible multiphysics framework that facilitated this process. In this work, the integrated reactive transport process kernel (PK) was weakly coupled to the integrated hydrology PK. In turn, integrated transport and reactions were coupled using an operator splitting approach. This splitting enabled an explicit solution of the integrated transport problem, including a novel algorithm to calculate exchange fluxes across the surface‐subsurface interface and a point‐by‐point solution of the geochemical problem. Geochemical capabilities were added using well‐established external codes, but rather than using a custom interface to each, a generic interface was used that clearly specifies the variables and operations used by the chemistry PK. The implementation is demonstrated with two example simulations: transport of a tracer in a soil column as it saturates over time and water ponds on the surface and reactive transport in a hillslope driven by successive wet‐dry cycles that result in infiltration, runoff and exfiltration processes.

A Second-Order Accurate, Operator Splitting Scheme for Reaction-Diffusion Systems in an Energetic Variational Formulation

A second-order accurate in time, positivity-preserving, and unconditionally energy stable operator splitting scheme is proposed and analyzed for reaction-diffusion systems with the detailed balance condition. The scheme is designed based on an energetic variational formulation, in which the reaction part is reformulated in terms of the reaction trajectory, and both the reaction and diffusion parts dissipate the same free energy. At the reaction stage, the reaction trajectory equation is approximated by a second-order Crank--Nicolson type method. The unique solvability, positivity-preserving property, and energy stability are established based on a convexity analysis. In the diffusion stage, an exact integrator is applied if the diffusion coefficients are constant, and a Crank--Nicolson type scheme is constructed if the diffusion part is nonlinear. In either case, both the positivity-preserving property and energy stability could be theoretically established. Moreover, a combination of the numerical algorithms at both stages by the Strang splitting approach leads to a second-order accurate, structure-preserving scheme for the original reaction-diffusion system. Numerical experiments are presented, which demonstrate the accuracy and the energy stability of the proposed scheme.

Item Response Theory Analyses of Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) Criteria Adapted to Screen Use Disorder: Exploratory Survey.

BackgroundScreen use is part of daily life worldwide and morbidity related to excess use of screens has been reported. Some use of screens in excess could indicate a screen use disorder (ScUD). An integrative approach to ScUD could better fit the polymodal reality of screens, and concurrent problems with screens, than a split approach, activity by activity. In that paradigm, a pragmatic and operationalized approach to study a potential ScUD requires the use of common criteria, for all screens and activities done on screens, in a single questionnaire.ObjectiveOur goals were (1) to describe screen uses in a general population sample and (2) to test the unidimensionality, local independence, and psychometric properties of the 9 Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) internet gaming disorder (IGD) criteria adapted to screen use in a community sample. We hypothesized that the 9 DSM-5 IGD criteria adapted to ScUD would show unidimensionality, local independence, and good discrimination, with criteria distributed on the severity continuum.MethodsThis cross-sectional survey in a French suburban city targeted adults and adolescents. A self-administered questionnaire covered the main types of screens used and their use for various activities in the past month. Presence of ScUD diagnostic criteria in past 12 months was also self-evaluated in the questionnaire. Factor and 2-parameter Item Response Theory analysis were used to investigate the dimensionality, local independence, and psychometric properties of the ScUD criteria.ResultsAmong the 300 participants, 171 (57.0%) were female (mean age 27 years), 297 (99.0%) used screens, 134 (44.7%) reported at least one criterion (potential problem users), and 5 (1.7%) reported 5 or more criteria and endorsed an ScUD. The most endorsed criteria were loss of control (60/300, 20.0%) and preoccupation (52/300, 17.3%). Screen types used and screen activities differed between participants with no ScUD criteria and those with at least one ScUD criterion. The latter were more likely to have a computer as the most used screen type, and more video gaming, communication/social network, and watching news and research of information as activities. Unidimensionality was confirmed by all fit indices. Local independence was confirmed by the absence of residual correlation between the items. Criteria had relatively high factor loading, with loss of interest in other recreational activities having the highest. However, criteria with the lowest factor loading all remained above the cut-offs, sanctioning unidimensionality. Most discriminating criteria were loss of interests, preoccupation, deceive/cover up, and risk/lose relationship/opportunities, which also provided the most information on the measurement of the latent trait.ConclusionsWe described screen uses in a French community sample and have shown that the adaptation of the DSM-5 IGD to “ScUD” has good psychometric validity and is discriminating, confirming our hypothesis. We suggest to use those criteria to assess potential “ScUD.” Further studies should determine if all criteria are needed and whether others should be added.

Implementation and Analyses of an Eco-Driving Algorithm for Different Battery Electric Powertrain Topologies Based on a Split Loss Integration Approach

Eco-driving algorithms optimize the speed profile to reduce the energy consumption of a vehicle. This paper presents an eco-driving algorithm for battery electric powertrains that applies a split loss integration approach to incorporate the component losses. The algorithm consistently uses loss models to overcome the drawbacks of efficiency maps, which cannot represent no-load losses at zero torque. The use of loss models is crucial since the optimal solution includes gliding, during which there are no-load losses. An analysis shows, that state-of-the-art nonlinear programming algorithms cannot represent these no-load losses at zero torque with a small modeling error. To effectively compute the powertrain losses with only a small error in comparison to the measurement data, we introduce a tailored combination of nonlinear inequality constraints that interleave two polynomial fits. This approach can properly represent reality. We parameterize the algorithm and validate the vehicle model used with real-world measurement data. Furthermore, we investigate the influence of the proposed interleaved fits by comparing them to a single continuous high-order polynomial fit and to the state of the art. The algorithm is published open source.

(n-Bu)4NBr-Promoted N2 Splitting to Molybdenum Nitride.

Splitting of N2 via six-electron reduction and further functionalization to value-added products is one of the most important and challenging chemical transformations in N2 fixation. However, most N2 splitting approaches rely on strong chemical or electrochemical reduction to generate highly reactive metal species to bind and activate N2, which is often incompatible with functionalizing agents. Catalytic and sustainable N2 splitting to produce metal nitrides under mild conditions may create efficient and straightforward methods for N-containing organic compounds. Herein, we present that a readily available and nonredox (n-Bu)4NBr can promote N2-splitting with a Mo(III) platform. Both experimental and theoretical mechanistic studies suggest that simple X- (X = Br, Cl, etc.) anions could induce the disproportionation of MoIII[N(TMS)Ar]3 at the early stage of the catalysis to generate a catalytically active {MoII[N(TMS)Ar]3}- species. The quintet MoII species prove to be more favorable for N2 fixation kinetically and thermodynamically, compared with the quartet MoIII counterpart. Especially, computational studies reveal a distinct heterovalent {MoII-N2-MoIII} dimeric intermediate for the N≡N triple bond cleavage.

Numerical approximation of singular forward-backward SDEs

In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are used, for example, in the modelling of carbon market [1] and are linked to scalar conservation law perturbed by a diffusion. Classical FBSDEs methods fail to capture the correct entropy solution to the associated quasi-linear PDE. We introduce a splitting approach that circumvent this difficulty by treating differently the numerical approximation of the diffusion part and the non-linear transport part. Under the structural condition guaranteeing the well-posedness of the singular FBSDEs [2], we show that the splitting method is convergent with a rate 1/2. We implement the splitting scheme combining non-linear regression based on deep neural networks and conservative finite difference schemes. The numerical tests show very good results in possibly high dimensional framework.

Is There a Nerve-free Zone in Which a Subscapularis Split Can Safely be Performed? An Anatomical Study Using Embalmed Specimens.

The subscapularis muscle, which is part of the rotator cuff, is located anterior to the shoulder. In anterior approaches to the shoulder, its supplying nerves are at risk of iatrogenic injury, which may cause postoperative complications. It is unclear whether there is any nerve-free zone in which a subscapularis split can be performed without risking nerve damage. In an anatomical study, we asked: (1) With the arm abducted 60° and externally rotated, what are the median and shortest distances between the entrance point of the subscapular nerves into subscapularis muscle and the myotendinous junction of this muscle? (2) What are those distances in other positions of the shoulder? (3) Did those measurements differ between specimen sexes or sides? In 84 shoulders of 66 embalmed anatomic specimens, the distance from the myotendinous junction of the subscapularis muscle to the entrance points of the subscapular nerves into the subscapularis muscle was measured using an inelastic thread and a millimeter gauge with the arm abducted 60° and rotated externally. In 16 of 84 shoulders, which were selected randomly, after taking the measurements with the arm abducted 60° and rotated externally, arm positions were changed and further measurements were taken with the arm abducted 60° and rotated neutrally, abducted 60° and rotated internally, and abducted 90° and rotated externally. The positions of the entrance points were described with statistical parameters and compared between different sides, sexes, and joint positions. Measurements were verified using eight fresh-frozen shoulders, showing no difference in distances compared with embalmed specimens and confirming reproducibility of measurements. Absolute distances were used to minimize possible distortion when using correlations and for straightforwardness and clinical applicability. The median (range) distance was 43 mm (24 to 64) for the upper subscapular nerve and 38 mm (23 to 59) for the lower subscapular nerve with the arm rotated externally and abducted 60°. In the 16 subsamples, internal rotation decreased the distance to 34 mm (24 to 49) and 31 mm (15 to 43), respectively, and maximal external rotation and 90° of abduction increased it up to 49 mm (30 to 64) and 41 mm (27 to 56). Comparison of left and right sides yielded no difference. Comparison of sexes showed distances for the lower subscapular nerve of 36 mm (23 to 54) in females versus 39 mm (24 to 60) in males. In no specimen did the nerve come closer than 23 mm medial to the myotendinous junction with the arm rotated externally and abducted. Therefore, not exceeding a distance of 20 mm medial to the myotendinous junction with the arm rotated externally seems to provide sufficient protection from nerve injury during surgery. Based on the described zone of 20 mm medial to the myotendinous junction, the risk of nerve injury in a subscapularis split approach can be minimized.