Early mother–child skin-to-skin contact (SSC) in the first 2 h postpartum is highly beneficial for both mother and child. However, cases have been reported of newborns who have experienced apparently life-threatening events (ALTEs) or sudden death during this procedure. The causes of these events are unknown. Newborn’s prone position could influence the onset of these events but there is very little evidence to support any recommendation. We hypothesize that newborns’ breathing obstruction episodes increase as mothers lie more horizontally.The main objective of this study is to compare the occurrence of desaturation and bradycardia episodes as a function of mother’s bed incline.The study is designed as a randomized, controlled, assessor blind, multicenter, superiority trial with two parallel groups and 1:1 allocation ratio.The study participants will be full-term healthy mother–newborn dyads from ten hospitals in Spain. Participants will be randomly assigned to one of two study arms defined by mother’s bed inclination (45° or 15°). The planned sample size is 5866. Centralized permuted blocks randomization and assessor blinding will be implemented.2 and heart rate (HR) limit alarms, as well as an action protocol in the event of alarm activation.The newborns will be monitored remotely with pulse oximetry, from 10 min to 2 h after delivery. We established SO2 ≤ 90%. Secondary outcomes are the mean SO2 level, the number of newborns who experience episodes of SO2 ≤ 85%, the time to SSC discontinuation due to abnormal SO2 or HR, and episodes of HR < 111 beats per minute (bpm) or > 180 bpm. Subgroups and pooled analysis will be performed to identify if breast-feeding and mother and child positions favor the occurrence of desaturation or bradycardia episodes.The primary outcome is the number of healthy newborns who undergo episodes of SOA simple intervention such as modifying mother’s bed angle of inclination while in SSC with her child during the first 2 h postpartum could favor newborn’s hemodynamic and respiratory stabilization and thus contribute to reducing the onset of ALTEs.NCT02585492. Registered on 22nd October 2015.ClinicalTrials.gov, 2 (30th June 2015).The online version of this article (10.1186/s13063-019-3256-0) contains supplementary material, which is available to authorized users. Placing newborns in skin-to-skin contact (SSC) with their mother’s abdomen immediately after birth is currently recommended. This intervention has been recommended by the Baby Friendly Hospital Initiative  and the SSC promotes the establishment of an affective link between parents and child, a crucial part of the child’s survival and emotional development , 8. SSC Coinciding with the widespread use of this intervention, however, cases have been reported of newborns who have experienced apparent life-threatening events (ALTEs) or sudden death in the first 2 h postpartum. These newborns had a gestational age ≥ 37 weeks, were born vaginally, and were apparently healthy –16. ThesThe cause of these episodes is unknown , 22, 24,2 and HR. Instability in either of these two parameters could precede these devastating events.Due to the low incidence of ALTEs or sudden deaths in the first 2 h of life in SSC, it is very difficult to conduct prospective studies that enable the assessment of the efficacy of an intervention to prevent the ALTEs and sudden deaths. However, the fact that these events occur during the 2 h after delivery, a period in which most newborns are in a healthcare center, makes it feasible to design studies that evaluate the effect of various interventions on certain biological parameters that can be continuously monitored, such as SO2 and HR outcomes. Only a case study by Rodríguez-Alarcón et al. [We found no information in the reviewed literature on the influence of the angle at which the mother’s bed is inclined while in SSC on SOn et al.  recommen2 ≤ 90% during the first 2 h after birth while in SSC with their mother while she is sitting up at a 45° or 15° angle above the horizontal plane of the bed.We therefore decided to conduct a randomized, multicenter clinical trial to compare the number of healthy newborns who experience episodes of SO2 ≤ 90% between the two groups.The main objective is to compare the proportion of healthy newborns who undergo at least one episode of SO2 levelthe mean SO2 ≤ 85%the proportion of newborns who experience at least one episode of SO2 or HRthe rate at which SSC is interrupted due to abnormal SOepisodes of HR < 111 beats per minute (bpm) or > 180 bpmAs secondary objectives, we will compare.An additional secondary objective will be to identify positions for the mother and newborn that favor desaturation or bradycardia episodes.The study is designed as a randomized, controlled, assessor blind, multicenter, superiority trial with two parallel groups and 1:1 allocation ratio.The study has been approved by the Clinical Research Ethics Committee of the coordinating center  and of each participating center. Additional file This study emerged from the research group setting of the Spanish Collaborative Research Network for Maternal and Child Health  and is financed by the Carlos III Health Institute of Spain. Ten Spanish hospitals from various regions and healthcare levels are participating in the study, which together cover approximately 27,000 births a year. The coordinating center is Hospital 12 de Octubre of Madrid. The research groups involved in the study have experience in participating and coordinating relevant European and international projects.2 and HR monitoring system (Masimo Patient SafetyNet®) for the newborns and have computer systems that provide 24-h access to the study’s computer platform to conduct the randomization and data entry into the electronic notebook. The mean number of researchers per center is 10, with a range of 2–20.These hospitals have beds with adjustable tilt for the women. Each of the centers is equipped with a remote SOAll women who, at the start of labor, meet the inclusion criteria and none of the exclusion criteria (prerandomization criteria) and who have signed the consent form . Considering the LNCS® sensor directions for use, the precision of the sensors is ± 3% for SO2 with or without movement and for the HR ± 3 bpm without movement and ± 5 bpm with movement. The saturation accuracy of the neonate was validated on adult volunteers and 1% was added to account for the properties of fetal hemoglobin. During these first 10 min after birth, the mother’s bed position is changed according to the corresponding randomization group . To standardize the intervention, two cardboard models (15° and 45°) have been manufactured that exactly reproduce the angle  on the right hand or wrist  next to the newborn and mother for the 2 h of the study. The system transmits the data to the central station in real-time every second, displaying them on a monitor. The pulse oximeter’s alarms can be silenced and the screen light turned off so as to disturb the mother and newborn as little as possible. The alarms can be silenced in both the monitor and pulse oximeter. The pulse oximeter’s lighting can be reduced to a minimum to disturb the mother and newborn as little as possible. A practitioner is continuously monitoring the display and can respond to an alarm. As a safety mechanism, four locator-searchers  provide alerts on the various alarms generated during the recording.At 10 min after birth, the sensor cable is attached to the pulse oximeter. After the connection, the pulse oximeter begins continuously recording the HR and SODuring the intervention period, the newborns remain at all times in SSC with their mother and will not undergo any procedure. If the newborn is separated from their mother for a reason other than those contemplated in the study , the recording will be stopped and the newborn will be removed from the study.The mother may place a pillow behind her head but not behind her back and may choose her position in the bed, provided the assigned inclination angle is not changed Fig. .In those hospital centers in which the delivery and immediate postpartum do not take place in the same room, the transfer will be performed with the newborn in skin-to-skin contact, and the time of the transfer will be recorded. The monitor alarm, which will occur when disconnecting the pulse oximeter, will thereby be accounted for.The protocol to be followed when an alarm sounds or when a practitioner is requested to come assess the newborn is shown in Fig. Table The practitioner will classify the alarm as clinical or nonclinical depending on whether the events that justify these alarms are clinical (CEs) or nonclinical events (NCEs), respectively. The CEs can, in turn, be clinically relevant (CREs) or nonclinically relevant events (NCREs).NCEs do not entail that the intervention is terminated and can occur due to excessive ambient light, problems with the pulse oximeter’s connection cable or sensor, low battery levels, interference, and lack of system connectivity or availability.2 < 91%, a HR > 180 bpm or < 111 bpm, and a newborn with symptoms. The protocol to be followed when clinical alarm sounds is shown in Figs. 2 < 91% clinical alarm goes off; Fig. The CEs include an SOIf the CE cannot be explained by any of the above causes, the CE will be considered a CRE depending on whether it occurs for the first or second time, the magnitude of the desaturation, additional heart rate impairment, or if the newborn is symptomatic. A CRE entails the termination of the intervention.Investigators at the coordinating center will review the compliance with the intervention protocols. If noncompliance is detected, the head of each participating center will be contacted, and the deviations from the protocol will be discussed.2 ≤ 90%.The main outcome collected in both intervention groups will be the proportion of healthy newborns who undergo at least 1 episode of SO2 level and HR in the first hour, in the second hour, and for both hours combined.The mean SO2 ≤ 85%.The proportion of newborns who undergo at least one episode of SOThe proportion of SSC interruption due to a medical indication.The number of HR episodes < 111 bpm and > 180 bpm.2 ≤ 90% or HR < 111 bpm.The mother’s posture  and that of her child  at the time of the episode of SOThe following secondary outcomes will also be recorded:The participant timeline is shown in Fig. 2 ≤ 90%.We conducted an observational pilot study in the coordinating center. In this study, the mothers performed SSC with their child in the first 2 h postpartum, and there was no intervention on the maternal position adopted. The mothers could choose their position, partially sitting up with an angle between 15° and 50°. We observed that approximately one of every ten healthy newborns had an episode of SO2 ≤ 90% (with a 95% confidence level and a power of 80%), we calculated that we would need to include 1275 newborns in each group, which represented a total of 2550 newborns. In the pilot study, we observed that approximately 50% of the initially included cases had to be excluded due to established postrandomization criteria  will be extracted and analyzed in the coordinating center by researchers who will be blinded to the mother’s sitting angle in bed.The randomization was conducted using permuted blocks. To this end, we employed a shared computer platform. Each center was assigned a block, and the patients were randomized one after another according to the random numbers contained in the corresponding block. Each center’s block size was created after an initial calculation of the number of mother/newborn dyads the center could recruit over the course of a month (the block sizes ranged from 193 to 1076 cases). The patients will be randomized at the start of labor. Once the informed consent form is signed, the researcher who obtained the consent will access the shared computer platform with the center’s specific login. The platform will then take the researcher directly to their block of random numbers and show them the mother’s degree of inclination. Beforehand, the researcher must answer a series of questions to confirm that the dyad meets all study inclusion criteria and none of the exclusion criteria. The center’s researcher is not allowed to know the block of numbers they are given nor the sequence of numbers. The recorded pulse oximetry data . The strategies for missing-data imputation and the subgroup analysis will be documented a priori.The distribution of the baseline prognostic variables will be analyzed with the mean and standard deviation for the continuous variables  and with numerators/denominators and percentages for the categorical variables. The statistical analysis will be conducted using the software environment R .An independent committee, which will include an independent biostatistician, will review the results of the interim analysis.p value below 0.001 to protect the overall type I error of the trial. The study will also be interrupted on safety grounds due to any other results that show a negative effect on the child or mother considered relevant by the committee.The study will be halted if differences in the main outcome show a Problems were detected after an initial pilot trial. A meeting was held with all centers from which emerged proposals for changing the initial trial protocol. These changes were presented to the coordinating center’s Clinical Research Ethics Committee (EC), who approved the changes (2015-06-30), which were then sent to the ethics committees of the participating hospitals, who in turn approved the changes.One of the required inclusion criteria is that the mother must have a companion during the first 2 h postpartum, given that the episodes have been more frequently reported when the mothers were not accompanied during this period. There is currently no recommendation on the ideal position for the mother and child immediately after delivery. Therefore, neither of the two positions in the study differ from any standard nor change the established risk. In current standard practice, newborns in SSC are not monitored.The principles of the Declaration of Helsinki will be respected during the project’s implementation. All documentation generated by the study shall be treated, communicated, and transferred in accordance with the requirements laid out in the Spanish Organic Law 15/1999 of December 13 on the Protection of Personal Data. Documentation confidentiality will be ensured. The study protocol was submitted for approval to the Clinical Research Ethics Committee of Hospital 12 de Octubre and those of the other participating centers. A single informed consent  are susceptible to hypoxic episodes, either from a central origin or by obstructive problems , 25–27. This study, which uses the methodology of a clinical trial, will be the first to assess whether the mother’s bed incline in the immediate postpartum could influence the onset of desaturation episodes and/or changes in the HR in the newborn. In the SSC position, the newborn is usually in decubitus prone on their mother. It is easy to assume that the more reclined the mother, the greater the possibility of compromising the newborn’s breathing, even more so during the first 2 h of life, a critical period for adapting to extrauterine life. This study will also assess the role of breastfeeding during SSC in the onset of these events.2 levels and HR during the first 2 h postpartum in full-term newborns with no complications and delivered vaginally who are in SSC with their mother.This clinical trial is the first to continuously monitor SO2 in newborns in SSC is scarce. A number of studies have examined the SO2 range of full-term healthy newborns, but only during the first minutes of life. It has been observed that newborns have low SO2 levels that increase slowly, without generally reaching the 90% level after 5 min [2 of preductal oxygen (higher) and postductal oxygen during the first 15 min after delivery [2 of 90% between newborns born by caesarean section and those born vaginally [2 in full-term newborns in SSC, our understanding is much lower. Dawson [2 > 90%. Takahashi [2 and HR for 30 min in two groups of newborns. In the first group, SSC was started during the first 5 min after delivery. In the other group, SSC was started after 5 min or more. The group that started SSC earlier achieved HR stability sooner (between 120 and 160 bpm), but there were no differences in terms of SO2 stability (readings between 92% and 96%).Our understanding of the progression of SOer 5 min –33. Othedelivery , 33. Theaginally , 33–35. . Dawson  reportedakahashi  studied Other factors that contribute to the relevance of this study are that it focuses on a clinical problem of considerable significance for the health of the newborn who experiences this condition, one that has been reported in practically all developed countries. In addition, currently available information on this problem is very scarce , 24–26. Based on the study results, a preventive strategy for these episodes of sudden death and ALTEs could be designed. If keeping the mothers in a more upright position is associated with a lower rate of desaturation in the newborn, the change in maternal position could act as a protective factor for ALTEs and sudden deaths in the first 2 h.The study is multicenter, which could entail certain variability in a number of the study procedures despite previous agreements, which could represent a limitation. Thus, in the hospitals in which the delivery and postpartum take place in different rooms, the pulse oximeter will be disconnected while the mother and child are transferred, and there will be a loss of data during this time interval. The SSC procedure itself or the method for achieving proper bed inclination might not be uniform. Lastly, the clinical practice of the various centers regarding the clamping of the umbilical cord  varies. Another limitation consists of the fact that the study will not have the services of a contract research organization (CRO). The coordinating center’s researchers will be responsible for monitoring the proper application of the study protocol.The study results may not be applicable to newborn groups with different characteristics but who are still candidates for SSC .One of the study risks is that it can lead to the monitoring of all newborns during their time in SSC and potentially to separating many newborns from their mothers. This is not the study’s objective, which seeks only to observe the effect of the bed position.The study is focused on analyzing what occurs during the first 2 h after delivery. It would be interesting to extend the analysis time to the first 24 h of life while the mother and child are in SSC. It would also be important to determine whether the degree of inclination could influence the mother’s recovery and state of health during the immediate postpartum.Even if the results of this study can shed some light on our understanding of these events, they will not preclude medical personnel from continuing to give mothers and their companions the recommendations that various experts have indicated in terms of safely implementing SSC , 38, 39.The trial has completed the planning and pilot phases and is currently enrolling participants. The first patient was recruited in November 2015.Additional file 1:Corresponds to List of SPIRIT confirmation. (DOCX 20 kb)Additional file 2:Corresponds to Informed Consent. (DOCX 51 kb)


Stochastic schemes, designed to represent unresolved subgrid‐scale variability, are frequently used in short and medium‐range weather forecasts, where they are found to improve several aspects of the model. In recent years, the impact of stochastic physics has also been found to be beneficial for the model's long‐term climate. In this paper, we demonstrate for the first time that the inclusion of a stochastic physics scheme can notably affect a model's projection of global warming, as well as its historical climatological global temperature. Specifically, we find that when including the “stochastically perturbed parametrization tendencies” (SPPT) scheme in the fully coupled climate model EC‐Earth v3.1, the predicted level of global warming between 1850 and 2100 is reduced by 10% under an RCP8.5 forcing scenario. We link this reduction in climate sensitivity to a change in the cloud feedbacks with SPPT. In particular, the scheme appears to reduce the positive low cloud cover feedback and increase the negative cloud optical feedback. A key role is played by a robust, rapid increase in cloud liquid water with SPPT, which we speculate is due to the scheme's nonlinear interaction with condensation. The inclusion of a stochastic scheme reduces climate sensitivity in a general circulation modelThis reduction, of around 10%, is linked to changes in cloud cover and cloud optical depth feedbacksWell‐calibrated stochastic schemes may give more accurate global warming projections However, despite significant efforts in model development, estimates from state of the art climate models have remained relatively unchanged since the original Intergovernmental Panel on Climate Change report  from the ith physics parametrization scheme and r a random variable. Note that only tendencies for prognostic model variables  are perturbed. Diagnostic variables (such as cloud water) are computed as normal using the prognostic variables. The perturbation r is a random scaling factor that is constant in the vertical, with the scaling tapered by μ∈, which is smoothly reduced to 0 in the boundary layer and stratosphere, and 1 otherwise. Roughly speaking, μ=1 between pressure levels 900 and 100 hPa , which ensures that the perturbation is not too large: In particular, Pperturbed always has the same sign as the “deterministic tendency” P=∑Pi.The SPPT scheme has been used in ECMWF's operational ensemble forecasts since 1998 and is designed to represent forecast uncertainty that arises from the unpredictable subgrid‐scale variability. This is done by perturbing the total net tendency from the physics parametrizations using multiplicative noise:r et al. . The totNote that even though the perturbations are mean zero, because of the nonlinearity of the underlying equations, the introduction of such perturbations may have systematic effects on the model state, such as changing the amount of energy in the system. Since the scheme is actively trying to represent unresolved subgrid‐scale variability and this variability has a nonzero amount of energy associated to it, such an injection of energy is plausibly beneficial to the model. In fact, the excessive dissipation of small‐scale energy in climate models has been used as motivation for the development of so‐called “backscatter schemes,” which explicitly reinsert estimates of this dissipated energy back into the large scale  are defined using the standard error. The standard error is computed as the standard deviation across the sample divided by the square root of the number of samples . When considering differences, we always pair up the corresponding deterministic/stochastic simulations that started from the same initial condition.For the FastSPHINX experiments, statistical significance is calculated using a two‐tailed 3For a given SPHINX simulation, we measure the extent of (transient) global warming by taking the difference between the global mean surface temperature averaged over the first 30 years of the simulation 1850–1880) and the last 30 years (2070–2100). We will refer to this as the model's greenhouse gas sensitivity, or GHG sensitivity for short: It should not be confused with either the equilibrium climate sensitivity or transient climate response. Figure 850–1880 Figure Figure Figure Through the rest of the paper we will aim to understand the drivers behind the evolution seen in Figure 4In this section we will aim to understand why the stochastic model has a cooler climate during the historical period.Changes in global mean surface temperature (T2M) are associated with imbalances in the energy budget, since surface temperatures will change in order to bring the system to equilibrium. Therefore, we will take as our starting point the model's surface energy budget and use this to determine the dominant drivers of change when turning on SPPT.decrease in evaporation (an upward flux), and vice versa. The upshot of this convention is that the net surface energy can be conveniently obtained by adding up the other fluxes, and so the dominant source of change can be identified at any point in time. As before, we have smoothed the time series by a 10‐year running mean, in order to retain only the fluctuations taking place on climate timescales.Figure 2, which grows to around twice that by the end of the 21st century, consistent with both the cooler mean climate and the reduced GHG sensitivity. Anthropogenic forcings lead to a net positive surface energy imbalance for both configurations, which both sets the historical mean temperature, and, as this imbalance increases throughout the RCP8.5 scenario, the extent of global warming. The reduction of this excess amount of energy due to SPPT in the historical period leads to a cooler historical climate, and the growth of this reduction implies a weaker GHG sensitivity.During the twentieth century the mean difference in the net flux is around −0.1 W/mWe will begin by trying to understand the initial lower average net surface energy flux and then follow up by trying to understand the decreased GHG sensitivity.4.1response to the cooling induced by reduced solar radiation, so we do not discuss the role of water vapor further.Figure Changes in net solar radiation will be determined by changes to the albedo of the surface, the cloud coverage, and the albedo of the clouds. This latter property, a function of the optical thickness of the cloud, depends to a large extent on the CLWC of the clouds, that is, the total amount of liquid water per unit volume of air in a cloud parcel; this is sometimes also referred to as the “liquid water path”  corresponding to an increase in evaporation. Surface temperatures rapidly cool as a result of this drop in surface energy, before temporarily warming again as the system begins to respond (not shown). As we know from the SPHINX simulations, eventually a new, cooler equilibrium is reached.As explained in section Let us first discuss solar radiation changes. Figure Next, we consider the other major contributor to the reduced surface flux, namely, the increased evaporation with SPPT. In the IFS, the amount of evaporation at a grid point depends primarily on the surface wind speeds and the extent to which the specific humidity at the surface grid point differs from the saturation humidity (a function of surface temperature). There is also a contribution from turbulent processes, which depend on surface roughness  the cloud optical feedback in the model is.One simple way of measuring the potential strength of this feedback due to the first mechanism above was outlined in Somerville  see als, which wλ across the full deterministic ensemble at 700 hPa is 3.62·10−6 kg·m−2·K−1, with a standard error of 0.117·10−6 kg·m−2·K−1. The stochastic mean is 3.81·10−6 kg·m−2·K−1, with a standard error of 0.046·10−6 kg·m−2·K−1. The difference is statistically significant and represents an increase of around 5% with SPPT. An almost identical, statistically significant increase is found at the 500‐hPa level. However, at 850 hPa, there is no statistically significant change in the gradient across the two ensembles. This may again be due to the tapering of the stochastic perturbations near the surface, which imply a weakening of the scheme's impact at lower pressure levels.We estimated this metric for clouds in the FastSPHINX experiments for pressure levels 850, 700, and 500 hPa, which span the approximate range for which we find clouds in the right temperature range. The mean value of As noted previously, the difference between the stochastic and deterministic ensemble mean CLWC stays roughly constant in time, despite the stochastic simulations warming less, consistent with the above calculations. While changes in CLWC cannot be easily untangled from changes in cloud cover, already seen to be different for the two sets of simulations, this suggests that SPPT has increased the negative cloud optical feedback.λ could not be carried out for these. We cannot therefore rule out that this change in λ may be a feature of the spin‐up phase only.Note that because CLWC was not available on levels in the SPHINX simulations, the computation of 5.3There is some evidence that there is a dependence of the amount of global warming (due to some fixed forcing) on the initial global mean temperature  can significantly impact both a GCMs reproduction of historical data, as well as its projections of future climate change. However, some important outstanding questions remain. Most importantly, is the impact on the cloud cover feedback an effect of the changed mean state alone, or is there a more dynamic interaction of SPPT with the cloud thinning processes? In other words, would the models' mean state climate sensitivities be more similar if the stochastic model were tuned in a similar way to the deterministic model? If so, it is possible that the same changes  could have been achieved through parameter perturbations in the model: This would require further investigation to answer. Another outstanding question is the importance of conservation in stochastic schemes. The implementation of SPPT used in our experiments included a global “humidity fix” due to the scheme's nonconservation of water, and while changes to the mean state were shown to be independent of this, it is unclear if the fix is influencing changes to GHG sensitivity. It should be noted that alternative stochastic schemes have been constructed that are more conservative by construction; one example of such a scheme was introduced in Sanchez et al. . SchemesIn light of our results, it would be of great interest to assess further the impact of SPPT on the key, small‐scale processes driving cloud feedbacks. This could potentially inform the development of new stochastic schemes. Given the ability of such schemes to improve other key aspects of models, this may, ultimately, lead to more accurate projections of global warming.


An alternating current potential drop technique is presented that exploits anisotropic magnetostriction to monitor changes in applied stress in steel. The background to the technique is provided together with an ad hoc approximation that describes the sensitivity of the sensor to the underlying properties. A uniaxial loading experiment has been conducted on duplex and mild steel specimens showing that changes in stress are measureable. Saturation and hysteresis afflict the measurement, which, in addition to sensitivity to temperature and magnetisation, may undermine inversion. With the capabilities and limitations of the proposed technique introduced, guidance on possible suitable applications are given, concluding that use for monitoring the number and relative size of fatigue stress cycles may be a suitable and attractive opportunity. Monitoring stress is potentially of great value to structural integrity engineers. Static stresses may drive plastic deformation, creep damage  or creepThe strain dependence of magnetic permeability has been exploited for stress measurements in the past; in this study it will be assumed that stress may be inferred from elastic strain according to Hooke’s Law. Brennan & Dover et al. developed an alternating current field measurement (ACFM) technique based on this principle , 14, 31.Potential drop measurements are a standard means of monitoring the geometric changes associated with the progress of damage in metallic engineering components, particularly crack growth  but alsoAlternating current (AC) measurements are subject to the skin effect. The current is electromagnetically constricted to the surface of the component, resulting in an exponentially decreasing current density with depth. In the simple homogeneous isotropic case, the skin-depth, Unfortunately, the magnetic permeability in ferromagnetic materials is also known to be sensitive to many other variables, most notably temperature and magnetisation, as well as microstructural material parameters. Specificity is therefore potentially an issue that will need to be addressed in assessing the viability of magnetic based stress measurements.In this paper the background to multi-frequency four-point potential drop measurements will be given to introduce the proposed technique; this will be followed by an ad hoc approximation that will be rigorously validated by computational simulation relating anisotropic permeability and conductivity to potential drop impedance measurements. A uniaxial loading experiment will be presented showing the stress sensitivity of the technique, followed by a demonstration of the sensitivity to temperature and magnetisation in an attempt to establish whether the technique is likely to have sufficient selectivity for practical applications.Potential drop measurements require four electrodes that are galvanically connected to the surface of the test component. A known electrical current, mentclass2pt{minimmentclass2pt{minimThe frequency dependence of potential drop measurements in electromagnetically isotropic materials has been previously reported , 11, whiFigure It is believed that the key to monitoring stress-dependent magnetic permeability changes is the anisotropy, i.e. stress-induced directional changes in magnetic permeability. The directional changes in magnetic permeability require a more sophisticated description of the skin depth than the isotropic description provided in Eq. ; the dirTo illustrate the influence of anisotropic permeability changes on the current distribution of an AC potential drop measurement a finite element study was completed. Two point current source electrodes were modelled on a block of material, as illustrated in Fig. distribution is unaffected by changes in magnetic permeability in the direction of electrode alignment; the ‘effective’ skin depth 17) by ex of Eqs.  and 8b)18\documeThis analysis illustrates that the potential drop measurements are primarily sensitive to permeability changes normal to the direction of current injection; the magnetic field is generated in the plane normal to the current flux and so will be sensitive to the current field in that direction.Although less relevant to the present study, it is worth pointing out that following the same logic as Eqs. , 23b, 24Again, these results have been validated using a finite element model of a square electrode configuration on a thick magnetically anisotropic cuboid of thickness 50 mm and electrode separation 10 mm, the results are shown in Fig. The excellent fit between the simulated data and analytical approximations on these figures proves the high accuracy of the ± 1/4 power regression lines previously indicated on Figs. In this section an experimental demonstration will be conducted to show that AC resistance measurements may be used as an indicative metric of applied stress. From the previous work of Dover et al. , 30, 31 The subsequent influence of permeability on AC potential drop measurements can then be inferred from Eqs. (23) and (24). An exact inversion between AC potential drop measurements and stress, via magnetic permeability would therefore at least require the parameters To illustrate the stress dependence of AC potential drop measurements through magnetic permeability two experiments were conducted; a ferritic S275 structural steel and a less permeable F51 duplex steel. Bars of material 20 mm × 50 mm × 750 mm were prepared with a square configuration of electrodes with 5 mm electrode separation; the electrodes were formed by 1.5 mm diameter stainless steel studs spot welded onto the component, as shown in Fig. Impedance measurements were taken using a lock-in amplifier based system. A typical set of impedance-frequency measurements are shown in Fig. A Fischer FMP30 Feritscope  probe waThe same data, plus additionally the quasi-DC resistance measurements, are displayed as measurement against applied stress in Fig. It is important to note that the observed changes in resistance are not a consequence of the geometric influence of electrode separation  or piezoThe ferritic steel was then tested in the same way. The Feritscope and AC resistance measurements are shown in Fig. Figure The potential drop technique is evidently sensitive to applied stress and the changes are clearly measureable. The primary issue in whether magnetic permeability can be exploited for practical engineering applications is selectivity: whether additional variables also influence readings, undermining a possible stress inversion.The proposed potential drop technique relies on the dependence of the skin effect on stress-dependent permeability. From Eq.  it is evAs noted in the introduction, numerous intrinsic parameters influence the magnetic permeability: alloy content, microstructural state and cold work form part of a non-exhaustive list that may cause long term ‘drift’ in permeability. Two parameters that are known to influence magnetic permeability are temperature and external magnetising field . In ordeThe same duplex material bar used in the stress experiments was demagnetised and placed in an environmental chamber, together with the Feritscope probe and the potential drop electrodes, all other measurement equipment remained outside of the chamber. The temperature was cycled between 10 and 50 °C 3 times with a period of 40 h.Figure The magnitude of the changes in AC resistance due to the 40 °C change is similar to that resulting from a 100 MPa imposed stress. Whether the temperature sensitivity will be problematic will depend on the anticipated range of applied stress and the temperature for that particular situation, but clearly the influence of temperature must be carefully considered. It is likely that the temperature dependence may be compensated by a variety of strategies; the simplest is using a direct temperature measurement, or indeed the resistivity dependent DC resistance measurement, and using simple regression. As the temperature dependence of magnetic permeability is apparently anisotropic, each direction will need to be compensated for individually and the compensation parameters may need to be regularly revised. Likewise, if the loading was known a priori to be uniaxial, then it may be possible to separate the influence of isotropic changes from the strongly anisotropic influence of stress, though again the effectiveness will be limited by the apparently anisotropic temperature dependence.The general arrangement of the magnetisation experiment is shown in Fig. Figure As an aside, it is interesting to observe the magnetisation dependence of the quasi-DC measurements. The behaviour is quite different from all the other measurements: there is negligible change in the direction normal to the magnetisation and an approximately linear relationship in the parallel direction. This relatively weak (≪ 1%), although clearly measurable effect, is anisotropic magnetoresistance , 25.The ability of the proposed potential drop technique to monitor stress-dependent, anisotropic, changes in magnetic permeability has been demonstrated; large, directional changes in impedance result from the imposition of stress. The two orthogonal impedance measurements are sensitive to the two components of the magnetic permeability tensor tangential to the surface. These two magnetic permeability components are determined by the three orthogonal elastic strain components, and therefore inversion to find strain is possible only if Poisson’s ratio is a priori known. For elastic solids Poisson’s ratio is one of the more stable material properties that can be usually estimated within ± 0.02 or better than ± 10%. Compared to intrinsic uncertainties of the magnetic properties, that is effectively a known constant. As an example, in the present paper a uniaxial stress is imposed, and so the three strains are related by Poisson’s ratio only  and where stresses are large then the influence of temperature will be acceptably small, but otherwise some attempt should be made to compensate. Importantly, the influence of uniaxial stress is directional, while temperature is much more (though not perfectly) isotropic. This difference enables a possibility in separating the two effects, though the slight anisotropy in the temperature dependence provides a challenge in reliable temperature compensation. The influence of temperature on the stress sensitivity has not been explored in this study. As an extreme example, approaching the Curie temperature the ordering effect of elastic strain would have to compete against the disordering effect of temperature, which is likely to lower the strain sensitivity. Whether this is significant over a modest temperature range should be investigated in future research.Magnetisation may also pose a problem, particularly in long slender components that may be susceptible to spontaneous macroscopic magnetisation. It is important to emphasise the magnetic field used in this study is many orders of magnitude larger than would be encountered in a typical engineering situation; provided there is nothing of note to drive the magnetisation, it is unlikely to be significantly problematic. The effect of magnetisation on the stress sensitivity should be explored in future.Various ‘intrinsic’ material parameters will also influence the magnetic permeability. It is possible that microstructural evolution will additionally influence the magnetic permeability, again adding complexity to a possible inversion. Such changes are likely to be long-term, monotonic, and approximately isotropic and may therefore be separable from the influence of at least dynamic loading. It has been suggested in previous literature that it may be possible to use magnetic properties to monitor the microstructural state of engineering components –20. ThisIt is important to remember that the information on the permeability-dependent skin effect may be obtained as a by-product of an existing potential drop measurement. Potential drop measurements are usually deployed for monitoring geometry changes associated with a particular damage mode such as crack size or strain. In ferromagnetic materials DC or quasi-DC is used to suppress the influence of the skin effect, it is proposed that the same hardware may be used to additionally take an AC measurement which may reveal additional useful information on stress state. It is also possible to extract the same information from the quasi-DC reactance without taking any additional measurements, albeit the quasi-DC reactance will be small and difficult to measure reliably because of inevitable inductive cross-talk between the injecting and sensing pair of cables. A suitable use might therefore be the monitoring of the number and relative size of fatigue stress cycles where the potential drop sensor may also be used to monitor crack size.A potential drop technique has been presented that is capable of measuring the anisotropic changes in permeability resulting from the inverse magnetostrictive effect. An ad hoc approximation has been developed which captures the main features of the sensitivity of the technique to anisotopic changes in resistivity and magnetic permeability.The sensitivity to applied stress has been demonstrated experimentally in uniaxial loading. The behaviour is broadly consistent with what is anticipated from the ad hoc description, yet there are complicating features of magnetism that are not included in the simplified analysis, which limit the ability to accurately invert measurements; saturation and hysteresis are evident in measurements which will need to be accounted for.Selectivity is frequently an issue in magnetic measurements, it has been shown that aside from the influence of elastic strain, temperature and magnetisation also influence permeability and therefore may undermine a stress inversion. Additionally, long-term material evolution may also influence measurements.The monitored component is ferromagneticThe temperature is relatively stable or compensated against, and there are no exceptionally strong static magnetic fields presentThe stresses of interest are non-stationary, so that they may be separated from spurious long-term ‘drift’ in permeabilityThe multiaxiality of the stress state is known or is at least repeatableThe situation is not suitable for conventional strain gaugesWith the above in mind, applications where stress monitoring using the proposed potential drop technique is appropriate must be carefully selected. Particularly suitable applications are those where:It is proposed that a broad opportunity where potential drop stress measurements may be suitable is monitoring the number and relative size of fatigue cycles. This may be particularly attractive as the stress information may be obtained as a by-product of an existing potential drop measurement for crack sizing.


The downtail location of the neutral line is not self‐consistent or in agreement with previous (independent) studies unless dissipation terms are included planetward of the reconnection site; potential physical explanations are discussed. In the future the model could be adapted to other environments, for example, the dayside magnetopause or other planetary magnetotails.A simple Monte Carlo model is presented that considers the effects of spacecraft orbital sampling on the inferred distribution of magnetic flux ropes, generated through magnetic reconnection in the magnetotail current sheet. When generalized, the model allows the determination of the number of orbits required to constrain the underlying population of structures: It is able to quantify this as a function of the physical parameters of the structures . The model is shown adapted to the Hermean magnetotail, where the outputs are compared to the results of a recent survey. This comparison suggests that the center of Mercury's neutral line is located dawnward of midnight by  Monte Carlo model allows the estimation of X‐line location and reconnection frequency given sampling with a single spacecraft0.37‐1.02+1.21RM) dawnward of midnightMercury's magnetotail reconnection site is consistent with a center offset (Mercury's downtail X‐line location is only self‐consistent if dissipation terms are included planetward of the X‐line Though the phenomenon occurs on very small spatial scales  down the magnetotail. Later, during two flybys of the National Aeronautics and Space Administration (NASA)'s MESSENGER  spacecraft (M2 and M3), the neutral line was inferred to be 2.8 and 1.8RM from the planet, respectively  was located between 3 and 6RM down the tail  reconnection interval could be observed . The model forms a two‐dimensional plane , approximating the plasma sheet on the nightside of the planet. The model is set up to simulate a given number of orbits, which are approximated as vertical passages through the plasma sheet to approximate the trajectory of MESSENGER. Therefore, for each orbit the spacecraft location (XMSM and YMSM) and plasma sheet dwell time are generated. The location is initially drawn from a uniform distribution, while the dwell time is drawn from a database of current sheet crossings identified in the MESSENGER data  and azimuthal width (WNL). It should be noted that while the neutral line in the model is implicitly assumed to be stationary during each plasma sheet crossing, neutral lines have commonly been observed to retreat tailward at Earth  coordinate system is used in this study. In this system, the This setup is illustrated in Figure YMSM axis) then the neutral line is considered to be “detected.” Selection effects, that is, those that would cause the flux rope to not be identified even when encountering the spacecraft, are considered in a companion paper  are detected and where they are missed, purely as a result of the spacecraft coverage. Figure It should be noted that no boundary effects are considered . Instead, the boundaries are implicitly provided by the limits of the spacecraft orbit and neutral line centers simulated. This does mean that some portion of the neutral line width may be outside of the region within which the spacecraft could observe it. Therefore, if the center of the neutral line is placed at the edge of the spacecraft's orbital region then the effective length of the neutral line could be up to a factor of two shorter than that explicitly generated.3To begin, the distributions that are recovered by (or inferred from) the virtual spacecraft will be compared to those that would be obtained with complete magnetotail coverage . This provides a measure of the effectiveness of the spacecraft sampling and can be evaluated as a function of the number of orbits, orbital selection, or properties of the dynamic structures of interest .3.1XMSMSC, YMSMSC), neutral line center , and neutral line width (WNL) from uniform distributions, the details of which are provided in Table In this section, the model results will be discussed while drawing the spacecraft position  do not change significantly: the underlying distribution is fairly settled. However, after 100 orbits have been completed the randomly located spacecraft has not adequately sampled the tail, and so the χ2 (between the true and inferred distributions) varies as a function of the number of orbital passes. Overall, the χ2 can be seen to drop rapidly with the addition of more orbits. Eventually, this effect is saturated and the χ2 plateaus after ∼300–350 uniformly distributed orbits. There are some exceptions to this behavior, with small jumps observed, perhaps when a region is temporarily over sampled and the stochastic nature of the modeled reconnection boosts the rate in a region to an unrepresentative value.Figure χ2 as a function of orbits . It can be seen that the value of the median χ2 drops steadily until around ∼250–300 orbits at which point diminishing returns begin to apply and the addition of more orbits does not significantly reduce the χ2. Therefore, it could be said that, for the parameters selected, at least 200–300 uniformly distributed orbits should be considered before commenting conclusively on the measured cross‐tail distribution. It should be noted that the assumption of uniformly distributed orbits represents the simplest possible case, while in practice spacecraft trajectories often provide unevenly spread coverage. Figure Figure 3.2RM . It should be noted that the χ2 metric cannot be evaluated if the true value for a bin is zero; therefore, the averages in Figures RM, in red) the χ2 is both higher and drops slower than for the wider neutral lines. This is likely a result of the fact that smaller reconnection products will be observed less often by the spacecraft, and thus, the observed distribution is always less representative of the full distribution. This can be seen in Figure N ∼ 500 × 0.5 × 0.1 = 25). It should be noted that the effective sampling can be improved by increasing the width of the bins considered . For a low probability  the measured χ2 is relatively high, once more linked to the low number of flux rope encounters . Additionally, orbits during which no dynamic product or evidence of reconnection is observed need to be accounted for when the spatial distributions are considered.More generally, this technique allows the quantification of the common sense results: if the dynamic structures of interest are more azimuthally confined or less likely to be produced, then more orbits are required to constrain their distribution. Another interesting result that may be inferred from Figure 3.3Sections Y0 and σY0. The reconnection probability is set to 0.5, while the neutral line width remains between 2 and 2.5RM (as above). Figure χ2 metric (as above); this has been repeated 10,000 times for randomly selected combinations of Y0 and σY0. The results of the 10,000 iterations have then been averaged, and the mean per bin is presented in Figures The effects of uneven spacecraft coverage will depend on the relative locations of both the spacecraft and the structures of interest. Therefore, for this investigation the uniform flux rope distributions are exchanged for normal distributions with a center and width defined by χ2 obtained for both narrow (low σY0) and wide distributions (high σY0) when the centers are located anywhere across the center of the magnetotail (−1RM≤Y0≤1RM). In contrast, the orbits used by Smith et al. . For this study the results of Smith et al.  will be First, the dawn‐dusk distribution of flux ropes will be considered. This will allow some of the physical parameters of the Mercury system to be estimated, for example, probability of reconnection and neutral line width. Once these parameters have been estimated, the model may be setup to provide an overall rate of flux rope detections that is consistent with observations. This will then allow the location of the NMNL to be explored by further investigation of the relative rates of planetward and tailward moving structures.4.1Y0) and a distribution width (σY0), as in section P) and the width of the neutral lines (WNL). The model can then be run, for the MESSENGER orbits, for millions of iterations with random combinations of the four parameters . Each iteration (consisting of the 319 orbits performed by MESSENGER) can be compared to the observed cross‐tail distribution from the survey  ensemble sampler , though the midnight meridian is within 1σ. The results are also most consistent with a relatively broad neutral line distribution .First, the distribution in Figure n Figure c, indican Figure c has bee2.16−0.98+0.96RM, just over half the width of the model magnetotail  is required to be offset further toward dawn. This is shown by the diagonal slope formed by the probability contours, from upper left to middle bottom. This is necessary to explain the relative lack of observations duskward of ∼1RM  versus probability (P) space  and a width .The previous section allowed the basic parameters of the model to be estimated, that is, those which provide a rate of flux rope observations that best match the survey results. The downtail location of the neutral line can now be investigated by using the derived parameters and comparing the relative rates of the tailward and planetward moving distributions. For this, the neutral line location is parameterized in terms of a distribution center . As with section Over a million simulations were performed with random selected combinations of h et al. , and twoX0=−2.92−1.28+1.04 and favor a relatively broad distribution (in σX0). This result is consistent with a previous statistical study: Poh et al. (RM (using an independent method).The results for the tailward distribution Figure a give a h et al.  inferred−1.70−0.85+0.49 appearing most consistent. The X‐line location inferred from the tailward moving population (X0∼−3RM) would result in too high a rate of planetward moving flux ropes, much greater than is observed. Therefore, the X‐line is inferred to be closer to the planet. It is also clear that simply increasing the variability in the location of the X‐line . The lack of self‐consistency in the neutral line location suggests that there is some physics of the underlying system not captured by the simple parameterization.However, the results for the comparison of the planetward moving distribution Figure b are notA. Physically, this could correspond to the flux rope becoming distorted, such that it is not well approximated by the force free model, or perhaps forming a dipolarization front . Physically, this could represent the distance at which the flux rope halts its planetward motion, re‐reconnecting with the planetary field  and shaded region (σXMin) in Figure A), the spacecraft must be located tailward of the distance of closest approach in order to observe a flux rope.To investigate this, additional parameters are added to the model. The first consideration is that there is perhaps some maximum distance that the flux rope can travel from the X‐line, at which point it becomes unrecognizable as a flux rope, parameterized as a distance X0 such that it is now fully consistent with both the tailward distributions in Figure X0=−2.93−1.32+1.15). This suggests that some form of dissipation planetward of the neutral line is fundamentally important at Mercury within the region surveyed by MESSENGER.Figure XMin, σXMin, or A. However, the addition of these dissipation mechanisms does allow the X‐line location to be self‐consistent. Additionally, a faint relationship is observed between XMin and A  increases the maximum travel distance (A) that is consistent with the observations. Physically this would correspond to a larger “quasi‐dipolar region” negating the requirement for a maximum travel distance, and vice versa.Once more, the median values quoted above the diagonal panels in Figure A Figure m: increa5+ and Na+, with the Na+ density determined to peak premidnight  has been suggested to increase the growth rate of the tearing mode instability  were found to be more consistent with the results, rather than narrower structures. The statistical downtail location of the neutral line was then probed. The distribution of tailward moving flux ropes allowed the recovery of a statistical location consistent with previous studies . It also allows the inference of the global properties of the system that are most consistent with a set of observations. This type of analysis, with specific adaptation, could be useful for both future statistical studies at Mercury and at other planets as well as for mission/trajectory design.


VOC) of 90 V and a closed‐circuit current (ICC) of 11 µA with a frequency of 200 Hz. As a stand‐alone device, this generator can power portable sensors and smartphones through hand rotation.With the rise of portable and wearable electronics, a fast‐charging, long‐lasting power solution is needed; thus, there are attempts to harvest energy from the ambient environment. Mechanical energy harvesting through piezoelectric and triboelectric nanogenerators (PENG and TENG) is a promising approach due to their light weight, low cost, and high‐power density in comparison to other technologies. Both types of generators are capable of charging portable and smart devices on their own by converting mechanical energy into electricity. However, most previous methods have excessive input conditions, such as high rpm and input frequency, that can be only applied with other actuators. Here, a hand‐held gyroscopic generator is presented that uses the gyroscopic principle to reach a rotation rate above 8000 rpm with only hand input. The generator comprises a rotating flywheel inside a casing. Both the flywheel and casing have a TENG, and with a hybrid generator, electrical power is produced from rotation, vibration, and centrifugal force during operation. The device shows a consistent open‐circuit voltage ( Although there have been various studies on batteries and charging methods, solutions for frequent recharging and powering of portable and wearable electronics are still required. To satisfy this need, there have been attempts to develop stand‐alone power generators that can produce electricity from ambient energy sources such as solar,VOC) of 90 V and a closed‐circuit current (ICC) of 11 µA with a frequency of 200 Hz. To demonstrate the feasibility of the proposed generator as a stand‐alone device, it was used to power a portable clock and smartphone through hand rotation.In this paper, we introduce a hand‐driven gyroscopic generator that can harvest rotating, vibrating mechanical energy into electricity. This generator has the shape of a gyroscopic wrist exerciser; it consists of a rotating flywheel held inside an external casing. Due to the gyroscopic motion, the flywheel can reach above 8000 rpm with only hand motion which can significantly increase the output frequency and power. We fabricated a TENG on the flywheel surface and a triboelectric–piezoelectric hybrid generator on the casing substrate; thus, the gyroscopic generator can generate electrical power from all mechanical energy during operation. In addition, the flywheel TENG has an alternating pattern of triboelectric materials with different electron affinities, which can increase the electrical power output of the freestanding‐type TENG by 19%. On the outer surface of the casing, a poled poly(vinylidene fluoride‐co‐trifluoroethylene) (P(VDF‐TrFE))‐based TENG and PENG hybrid nanogenerator is fabricated to harvest energy from hand gripping, centrifugal force, and vibration. The gyroscopic generator has shown a consistent open‐circuit voltage  film. 1 cm wide copper sheets are adhered to the inner surface of the upper and lower casing substrate as electrodes to harvest the rotating energy of the patterned flywheel. The whole gyroscopic generator is approximately the size of a tennis ball, so the operator can grasp and rotate it easily. As shown as Figure The gyroscopic generator has a flywheel rotating in the casing substrate as shown in f1. The flywheel rotates with two degrees of freedom, one rotating in the x‐axis with angular velocity of ωf1, and the other in the y‐axis with angular velocity of ωf2 . On the inner side of the casing substrate, there is a groove where the rotating axis of the flywheel (x‐axis) can be positioned and can rotate in direction of ωf2. The groove size is slightly bigger than the flywheel axis, so the flywheel can be slightly tilted . The casing of the gyroscopic generator is tilted during rotation by hand. Thus, one end of the flywheel axis is in contact with the upper surface of the groove, and the other end is in contact with the bottom surface when the flywheel is spinning. This makes the rotating flywheel receive torque to rotate in the direction of ωf1 when rotation is conducted by hand.The rotation and acceleration of the flywheel can be explained by gyroscopic precession. As shown in Figure v1, Figure S1c, Supporting Information), and friction force makes ωf1 faster. When the speed of hand rotation is constant, the precession velocity decreases as the flywheel rotation in the y‐axis (ωf2) and the x‐axis (ωf1) increases. At this stage, the flywheel reaches dynamic equilibrium, where the axis of the flywheel rotates in the ωf2 direction without slipping.f1), the operator must increase the speed of rotation by hand.VOC) of the flywheel TENG is shown in Figure VOC is measured as 90 V, and the frequency of the waveform is 200 Hz. The voltage has high frequency (Hz) due to the high‐speed rotation of the flywheel, which is over 8000 rpm. The rotation rate of flywheel during operation is measured by rpm meter connected to the gyroscopic device in Figure S2 of the Supporting Information.When the gyroscopic generator is rotated by hand, the flywheel axis is pressed against the groove surface due to gyroscopic precession, and this provides torque to the rotating flywheel. As the speed of hand rotation increases, the flywheel tends to tilt more due to the increased precession velocity, and the force between the groove and the flywheel axis increases as well. This increases the torque, and the flywheel axis starts to move along the groove , and the electrical potential of electrode B becomes the initial state (V0).−Vα– V0). When the negatively charged material moves from electrode A to electrode B  was tapped against the electrode and bent with the electrode. This result shows that P(VDF‐TrFE) can be used as both a triboelectric and piezoelectric material.As shown in Figure VOC output of the long casing generator covering the casing cylinder. The first high voltage peak is generated when the operator grasps the gyroscopic generator for the first time. Then when the casing generator starts to rotate, high‐frequency voltage output is generated from the vibration of the flywheel during rotation. The ICC output of the casing generator and magnified graphs of VOC and ICC are shown in Figure S6 of the Supporting Information. The output frequency of the casing generator during operation is about 240 Hz, which is similar to the output frequency of the flywheel TENG. This indicates that the output of the casing generator is from the vibration of flywheel rotation.Figure FigureThe peak electrical power produced by the gyroscopic generator is shown in To demonstrate the possibility of gyroscopic generator as auxiliary power source, the flywheel TENG and casing generator were connected to a rectifier circuit separately and shown to light up 30 white LEDs instantaneously with hand input  between two electrodes to generate output from the surface charge and piezoelectric property. Due to its design, the casing generator can produce output through the triboelectric and piezoelectric effects. Through both generator units, this generator can produce electrical power from all motions of the device caused by rotation, vibration, and centrifugal force. Through flywheel rotation speed over 8000 rpm, the gyroscopic generator can produce a The authors declare no conflict of interest.SupplementaryClick here for additional data file.SupplementaryClick here for additional data file.SupplementaryClick here for additional data file.


If the surrounding of a visual target unexpectedly starts to move during a fast goal-directed hand movement, the hand reflexively moves along with it. This is known as the ‘manual following response’. One explanation for this response is that it is a compensation for inferred self-motion in space. Previous studies have shown that background motion gives rise to both postural responses and deviations in goal-directed hand movements. To evaluate whether compensation for inferred self-motion is responsible for the manual responses we examined whether galvanic stimulation of the vestibular system would give rise to similar deviations in hand movements. Standing participants tried to quickly tap on targets that were presented on a horizontal screen. Participants could infer self-motion on some of the trials, either from galvanic vestibular stimulation or from background motion. Both perturbations took place during the hand movement. It took both the head and hand about 45 ms longer to respond to background motion than to respond to galvanic stimulation. The head responded in a similar manner to both types of perturbations. The hand responded about as expected to galvanic stimulation, but much more vigorously to background motion. Thus, the manual response to background motion is probably not a direct consequence of trying to compensate for inferred self-motion. Perhaps the manual following response is a consequence of an error in binding motion information to objects. The manual following response is a reflexive response of the hand to sudden motion in the background when making a goal-directed movement. The hand is diverted in the direction of the background motion within about 150 ms after the background starts to move  to suggest self-motion without moving the background or actually moving the participant.The effects of GVS on apparent self-motion have been well documented  participated in this study. Three of them self-reported being left-handed. All participants had normal or corrected-to-normal vision, and had no disease that is known to affect motor or sensory function. This study was approved by the research ethics committee at the Faculty of Behavioural and Movement Sciences, Vrije Universiteit Amsterdam. Written informed consent was obtained from each participant.The setup is very similar to that used in previous research in our lab  sampling at 200 Hz was used to measure movements of the finger and head. The camera was located to the right of the participant  via gel-coated carbon rubber electrodes (3.9 × 3.3 cm) in a binaural bipolar configuration.A photodiode was attached to the far-right corner of the screen to help synchronize events on the screen with the recorded movements (to within 5 ms). The timing of the GVS was synchronized by measuring the signals driving the GVS with the analog input channel of the Optotrak system (ODAU).The participant started each trial by placing the right index finger at a starting point. A target appeared at a random time between 0.6 and 1.2 s later. The participant was instructed to tap on the target as fast as possible with the tip of the right index finger. As soon as the participant moved 5 mm from the starting point a perturbation was triggered. To check for overall changes in responses as a result of the different self-motion perturbations, we also included perturbations of the target itself . GVS occurred about 10 ms after the perturbation was triggered. It took about 50 ms longer for the visual perturbations (target jump or background motion) to take place due to the delay in rendering images on the screen. If the target was hit , a sound indicated success. Otherwise, the target drifted away from where the finger touched the screen.The experiment consisted of two blocks with background motion  and two blocks with galvanic stimulation . The vestibular block had 100 trials of GVS . Both visual and vestibular blocks had 40 trials with target jumps . The target jump trials served as a reference without illusory self-motion but with adjustments to the hand movement. The 140 trials of each block were presented in random order.The 3D kinematic data derived from the markers were filtered using a second-order low-pass Butterworth filter with a cutoff frequency of 30 Hz. We determined this cutoff frequency by determining the frequency at which the variance in the distances between the three markers on a cluster was minimal , and negative if it was to the other side. The main variable of interest is the response: how the lateral velocity profile was influenced by the perturbation. This variable is also defined as being positive when it is in the direction that we would expect for the perturbation. For this, lateral velocity profiles were determined for each direction of the perturbation, given the sign corresponding to that of the perturbation, and then averaged across the two directions. The response corresponds to half the difference between the two curves in the lower panels of Fig. t test. In this test, p values smaller than 0.05 were considered to be significant.The latency of the average response to each kind of perturbation was determined with the extrapolation method . Neither were there systematic differences between the two repetitions of the same type of block (within participants). All the data for each kind of trial in each kind of block were therefore combined.The average hand trajectories are affected differently by the two types of stimulation that were intended to cause equivalent apparent self-motion Fig. a. The haIn accordance with the hand’s trajectory only clearly being affected by the visually induced self-motion Fig. a, partic2; vestibular: 113 ± 7 ms, 6.5 ± 1.8 m/s2; t19 = 0.77, p = 0.45, t19 = 1.32, p = 0.20).The difference between the hands’ responses to background motion and to GVS can be observed in more detail when expressed as a function of time Fig. a. The haThe head responded 119 ms after the onset of background motion, at about the same time as the hand did so 124 ms). The head’s response to the GVS started 81 ms after the onset of stimulation, again at about the same time as the hand did so (77 ms). Thus, it took both the head and the hand about 45 ms longer to respond to background motion than to respond to GVS, regardless of when the perturbation happened. The similar difference in delay for the head and the hand is in line with an explanation based on inferred self-motion. However, the much weaker response of the hand to GVS than to background motion cannot simply be due to the vestibular stimulation giving rise to less inferred self-motion, because the GVS induced a larger head response than did background motion , we did not delay the GVS stimulation to correct for the slow response of the display, so stimulation was earlier for GVS than for background motion. The latency of online adjustment is independent of the moment of perturbation, but the intensity of the response increases as the remaining time until the end of the movement decreases  logical because vestibular neuronal delays are shorter than visual delays, partly due to the temporal response properties of the retina .Raw data used in this study are available on Open Science Framework at


In the present work, we propose an FFT-based method for solving blood flow equations in an arterial network with variable properties and geometrical changes. An essential advantage of this approach is in correctly accounting for the vessel skin friction through the use of Womersley solution. To incorporate nonlinear effects, a novel approximation method is proposed to enable calculation of nonlinear corrections. Unlike similar methods available in the literature, the set of algebraic equations required for every harmonic is constructed automatically. The result is a generalized, robust and fast method to accurately capture the increasing pulse wave velocity downstream as well as steepening of the pulse front. The proposed method is shown to be appropriate for incorporating correct convection and diffusion coefficients. We show that the proposed method is fast and accurate and it can be an effective tool for 1D modelling of blood flow in human arterial networks. Mathematical and numerical modelling of blood flow in a human arterial network allows researchers to understand various flow related phenomena and disorders. It can help us to understand the genesis and progression of various diseases in the cardiovascular system, and it also provides us with a platform for developing methods for detecting such diseases. The arterial haemodynamics is influenced essentially by pulse wave propagation phenomena. At present time, one of the most effective and fruitful ways to understand wave phenomena in an arterial network is through one-dimensional (1D) flow modelling. Recent works on 1D blood circulation modelling have demonstrated its accuracy in predicting various flow quantities  derived, for example, in Formaggia et al. , SherwinMajority of the existing models, however, assume the convection velocity to be average over the cross section of an artery. Although this approximation is generally accepted, such approximations appear to give incorrect results, even for a steady-state flow. This error is pronounced in highly time-dependent flows, such as the pulsating flow experienced by an arterial network. In addition, space–time methods do not account correctly for the vessel skin friction of an arbitrary pulsating wave in an artery. The viscous effects should be based on the use of the Womersley solution  downstream as well as steepening of the pulse front. In addition, in the implementation of the proposed method, the system of algebraic equations for every harmonic component is built automatically for any arbitrary arterial network. Finally, the nonlinear equations we employ contain the correct convection and diffusion coefficients.This paper is organized into the following sections. In Sect. p is the pressure; q is the flow rate; A is the lumen cross-sectional area; subscripts t and x denote partial derivatives with respect to time t and axial coordinate x, respectively; The following system of partial differential equations (PDEs) for an arterial network can be derived from the incompressible Navier–Stokes equations  form form3) fu is the flow velocity profile; the integral is taken over the lumen cross section S. The The entclass1pt{minimaa et al.  and is aa et al. . Its vala et al. . This isn et al. , only foentclass1pt{minimad Taylor . In a puh et al.  and it ih et al. .a can be calculated via the equationr denotes the partial derivative with respect to r, which is the polar coordinate in the lumen cross section S  is a linear function, the first term is nonlinear with respect to p. Derivative p(A) is proposed in Formaggia et al.  is obviously nonlinear, i.e.,p(A) are considered below, and they are also nonlinear. Nevertheless, all of them can be expanded around the equilibrium state: p and subscript 0 means that the value is calculated at the equilibrium state. In order to further analyse pressure–area relationship, lets introduce the pulse wave velocity (PWV) of a small perturbation to the equilibrium state Resolving relation  with resConstant wall stiffness model Differentiating function  dependance becomes linear up to the third-order terms with respect to p(A) dependence is described in terms of elementary functions.In the power law relationship, if Armentano et al’s model One of the earliest models is proposed in Armentano et al.  is not well established and needs further investigations. Computational results of different studies can agree with each other only if nonlinear effects are small. A small nonlinear term in the A(p) dependence can be accounted through a correction to the linear problem. Thus, instead of the detailed study on dependance A(p) or p(A), one should focus only on nonlinear coefficients It appears that not all studies use identical pressure-area relationships, and the nonlinear parameter Note that integrating expansion , we obtas. Equation . They can be calculated using the integral over the cardiac period T, which is the direct Fourier transform of a periodic function, i.e.,nth harmonic component of the state vector N is the number of harmonic components required. We do not need to solve these equations for negative n as a real The real heartbeat waveform is quasi-periodic, but the numerical simulations assume periodicity for convenience. Often simulations are repeated over several cardiac cycles before the results are used to avoid the effect of any initial conditions  do  do 41) dSolution as a sum of travelling waves If A, c and Effect of blood viscosity on wave propagation In the presence of viscosity, the wavenumber is complex L. Its imaginary part, a and the wave frequency Dependence of entclass1pt{minima via Eq.  , Q(0), are given asP(0) and Q(0). Note that in Flores et al. (P(0) and P(L) are selected to determine the total field in the vessel. Below we show that the choice of P(0) and Q(0) has some advantages for numerical implementation.s et al. , two numA(x) and c(x). After analysing different possible approaches, we have selected the following two approaches.ODEs  and 41)41) do noNumerical integration of initial value problems ODEs (ems ODEs  and 41)Numericalate ODEs  and (41)Piecewise conic approximation Eliminating Q from ODEs Piecewisek, approximated by their average value over every element. Let A tapering vessel can be approximated by a sequence of truncated conic elements with values ith element can be used to calculate the corresponding mean values:i indicates that the value is calculated at point Accuracy of the piecewise conic approximation To study the accuracy of the piecewise conic approximation, we compute the reflection To accelerate the computation, the inlet and outlet values of every i. Using  we can wthiarasu  having sd by Eq.  proposedd by Eq. .x. Therefore the element lengths are adjusted to values Three basic element lengths are selected The reflection x is referenced from its inlet. The flow parameters sth segment can be calculated by the methods described above if the inlet flow parameters Consider a network containing Introduce the notations In Flores et al.  the follInlet boundary condition Let the periodic pressure waveform is set at the inlet of the network ransform .If thiarasu  as an inthiarasu  in the fAnalogously, if the periodic flow rate waveform ransform .Matching conditions at junctions Consider the sth segment of length sth segment for the nth harmonic component. Now, the outlet flow parameters can be written in the linear approximation through the transmission matrix sth segment ass as Matching conditions at junctions with merging arteries In some junctions two parent arteries can merge to form a single daughter artery. For example, the left and right vertebral arteries merge to form the basilar artery which is a common daughter segment for the vertebral arteries. There are few similar backward bifurcations in the cerebral arterial system. Similar situation can occur in an arterial system with a bypass. In a general case, for the node with If elations )62\documBoundary condition at the outlets of terminating segments In general, the Windkessel model is employed at the outlet of a terminating vessel Solution nditions  and 72)Solution quations  and 73)Solution quations ] form a n we have the same solutions but complex conjugate. Then for monitored site s, the waveform can be computed through the transmission matrix At this point, we have ansform, ,75\documNonlinear correction to solutions Let inlet parameters sth vessel segment are found for all n (subscript s is omitted in this section). The next stage is to substitute them into relation \documentransform  to relatous ODEs  and (41)n is omitted here for brevity. To calculate entries of the jth element are given asNonlinear corrections to the junction matching conditions With the account for nonlinear corrections, the outlet flow parameters take the following formsth segment, and ODEs  and 81)81) can b formula . In the  to ODEs  and (81)ous ODEs –(81) witSolving the nonlinear problem The second iteration of the network problem equations is different from the first iteration as inhomogeneous equations  hel hel97) hx in Eq.  is unitytive law  can giveHere, we consider the simplest network which comprises a 1-m-long pipe with uniform cross section, connected to a tapering segment and the outlet of the tapering part is connected to another 1-m-long pipe. Such long inlet pipe is chosen to have forward and reflected pulses clearly separated in time see Fig. . The dimo et al. . The nono et al.  is set a1—the inlet, 2—midpoint and 3—outlet of the first pipe and 4—the outlet of the tapering segment. The waveforms computed by the numerical scheme described in Carson and Van Loon (The pressure and flow rate waveforms are computed at four sites: Van Loon  are show3 (inlet of the tapering segment), in the vicinity of the main peak are shown in Fig. We now discuss how the waveforms depend on the inlet peak flow amplitude, p and q at a realistic amplitude In Fig. equation , the norequation , we carrNote that the nonlinear distortion of the pulse is high in this network due to a long  is linearly interpolated along the vessel length (Mynard and Nithiarasu A(x) and apply one of the known approximations for c(a)  are plotted in Fig. In most arterial network models, the exact variation of the blood vessel parameters is not specified as subject-specific information is very difficult to obtain  are better approximations. Nevertheless, for a typical artery, the difference between inlet and outlet radii is much smaller and discrepancies between the interpolations are hardly important.Different types of lumen radius variation, adapted by different authors, are depicted in Fig. For assessing the accuracy of the proposed method, we compare our results against the numerical modelling results of the human arterial network using a well established method, described in Mynard and Nithiarasu . Here weo et al. ; Boileauo et al.  with thethiarasu . The conThe comparison of results between the present and numerical computations is shown in Fig. Many of the currently used numerical models for arterial flow do not account correctly for the viscous friction, especially for a pulsating flow. It is obvious that several different values of viscosity coefficient A novel method, based on the perturbation technique and fast Fourier transform (FFT) in solving the 1D blood flow equations, has been proposed in the present work. The proposed method makes the FFT competitive against traditional space–time numerical schemes in terms of both robustness and speed. In contrast to the FFT approach described in Flores et al. , the proAlthough the proposed method is a substantial improvement to the existing methods, it requires further development in the following area. Further attention is required to deal with viscoelastic effects, blood mass loss due to smaller branches, porous nature of arteries and application to clinical environment.


In this paper we discuss three results. The first two concern general sets of positive reach: we first characterize the reach of a closed set by means of a bound on the metric distortion between the distance measured in the ambient Euclidean space and the shortest path distance measured in the set. Secondly, we prove that the intersection of a ball with radius less than the reach with the set is geodesically convex, meaning that the shortest path between any two points in the intersection lies itself in the intersection. For our third result we focus on manifolds with positive reach and give a bound on the angle between tangent spaces at two different points in terms of the reach and the distance between the two points. Let r centred at p in the normal space (Federer’s tubular neighbourhoods) Consider a manifold The fact that such a tubular neighbourhood exists is non-trivial, even if we take entclass1pt{minimaB that is tangent to p and whose radius r satisfies Let q. Then there exists an p such that q lies inside this ball. This again gives a contradiction. Let Here we prove the main result for i et al. , and thei et al.  with somWe start with the following simple observation:t.Let Because entclass1pt{minimaNote that We now have the following, which is a straightforward extension of an observation in Attali et al.  to generLet Because We can now turn our attention to the variation of tangent spaces. Here we mainly follow Niyogi et al. , but useu, v are vector fields. In particular The second fundamental form do Carmo  for a pru, v lying on the unit sphere We can now restrict our attention to mentclass2pt{minimu, v both lying in the direction of the unit eigenvector w of u, v of length one.We can now identify entclass1pt{minimaHaving discussed the second fundamental form, we can give the following lemma:Let p and q, parametrized by arc length. We consider an arbitrary unit vector u and parallel transport this unit vector along u(t) in the tangent spaces u(0) and u bounds the angle between u(t) is parallel and thus by definition u(t) can be seen as a curve on the sphere and thus Let This bound is tight as it is attained for a sphere.Combining Theorem Lemma mentclass2pt{minimWith the bound on the angles between the tangent spaces it is not difficult to prove that the projection map onto the tangent space is locally a diffeomorphism, as has been done in Niyogi et al. . AlthougWe shall now give a full proof of a variant of a statement by Boissonnat and Cazals  is tangent to Consider the distance function from g is Lipschitz. In the proof presented by Milnor, g is the gradient of a (Morse) function (in this case the distance function). This implies that it suffices that the gradient of the distance function is Lipschitz, or equivalently that the function itself is The key change compared to original statement by Milnor, which is in the f Milnor  mentionsy is a global isolated minimum of Let y as its tip. Because y does not lie on its boundary we have the following: Firstly, y. We can now use the following definition and result from topology  A complex K is called a combinatorial n-manifold if the link (the boundary of the star) of each vertex is an  point of c. We denote by c with radius c restricted to c is tangent to Let see Fig. . By Coroentclass1pt{minimaB is strictly less than the reach now gives that y lies inside this ball, meaning no such point z can exist. Let us now assume that there exists a point entclass1pt{minimaWe shall now give a bound on the angle between sufficiently close tangent spaces based on elementary arguments. Here we use elementary methods in the sense that we do not rely on differential geometry, although we will use the topological ball result. The bound we find here also encompasses the We start with the following lemma, which is due to Federer. It bounds the distance of a point  of Federer ) Let \doH in which v, q and p lie. Let in addition H that are tangent to p and thus to q cannot lie inside the interior of vq] and call the first intersection of this line with Write entclass1pt{minimaNext lemma establishes the converse statement of the distance bounds in Lemma Let In the following lemma we prove for all points v, if it exists. Then(Distance to Manifold) Suppose that It follows immediately that p and q, there is a significant part of This section revolves around the following observation: If We start with the following simple observation:ab] be a line segment with length ab] and Let  by pq] by z. We now consider the two dimensional curve pq] as the ‘z-axis’. We then project on the radial z’-direction. We also refer to the unit vector in the radial direction as We shall denote the orthogonal projection onto [t}ρ Fig. .Fig. 13AObserve that s. Using  we now sz-direction. There exists such an p and q we can assume that Let We now have the following estimates due to . It is cWe can now do the same analysis for any We also need the following lemma:Let p and q lie on the same connected component of p and q lie on different connected components then p lies on q on xy] is normal to both xy] is equidistant to both We first note that if ned Fig. . The linp. We now see thatyp] is normal to y and thus for all  is a chord. This chord divides the circle in two parts. pq]. Alternatively pq] is a cord on the boundary sphere of the ball  be a ball of radius p and q now be any points in B. Eventually we shall again impose that p and q lie on B. Consider any affine plane P spanned by containing [pq]. We look at the two circles of radius pq] is a chord. Because these circles of radius Let We are now ready to prove the following theorem in the mentclass2pt{minimB a ball of radius Let p and q. As we have seen above For any two points Our characterization of the reach in terms of metric distortion does hold for arbitrary subsets of Euclidean space and is not restricted to the