This study presents position changes of a few radiotherapy‐relevant thoracic organs between upright and typical supine patient orientations. Using tools in a commercial treatment planning system (TPS), key anatomical distances were measured for four‐dimensional CT data sets and analyzed for the two patient orientations. The uncertainty was calculated as the 95% confidence interval (CI) on the relative difference for each of the four analyzed changes for upright relative to supine, as follows: the distance of the bottom of the heart to the top of the sternum, it changed +2.6% or +4 mm ; the distance of the center of the C3 vertebra to the backrest, it changed +29% ; the contoured left and right lungs increased their volumes respectively: +17%  for the left, and +9.9% ; and lastly, the distance from the top of the sternum to the top of the liver, but its uncertainty far exceeded the average change by a factor of two. This last result is therefore inconclusive, the others show that with 95% confidence that a change in internal positions is observed for lung volumes and heart position that could be important for upright treatments. The context for this paper is of increasing interest in upright/seated, patient positioning for radiation therapy. Upright treatments were more common in the distant pastThe patient position can affect the quality of treatments, because gravity may bring organs at risk (OAR) closer to the planning treatment volume (PTV) making radiotherapy more challenging, or vice versa. In the process of evaluating the impact of different positioning orientations on treatment efficacy, the first step is to establish what is changing, so that treatment planning can be optimal. The next step is to explore the effect on dose calculations. This paper works towards the first step: considering which key organ positions are changing, by how much, and whether this is significant. This paper adds to a growing body of recent research that observes changes in organ positions from recumbent to upright.Much of the efficacy gain in radiotherapy has occurred from technological advancements that separate the treatment dose being applied to the PTV from the OARs as much as is possible.Studied here are four key positional changes as follows: the distance between the bottom of the heart and the top of the sternum, for a measure of superior‐inferior heart location; the distance between the center of the C3 vertebra and the backrest for a measure of patient posture; the contoured left and right lung volumes, for a measure of lung volume; and lastly, the distance from the top of the sternum to the top of the liver, to measure lung movement excursions. The heart position matters for the risk of Radiation Induced Heart Disease (RIHD).2The datasets used for this study consist of 18 pairs of 4DCT scans for the contoured lung volume measurements. 15 pairs of 4DCT scans that had no CT artifacts around the heart or the C3 vertebra were used to establish the heart location, and for the patient posture measurements. 14 pairs of 4DCT scans had no CT artifacts around the liver, and these were used for the lung excursion measurements.  Each pair of images included a 4DCT in both the supine and the upright position.  All image pairs were obtained at the Northwestern Medicine Proton Center (NMPC) in Warrenville, Illinois, USA and all patients received radiotherapy at NMPC and provided permission to use anonymized images. Patients provided written consent through the Proton Collaborative Group (PCG) registry study, and all patient data were anonymized prior to evaluation.Supine 4DCT image pairs were acquired on a GE Light Speed large bore scanner, with a resolution on the order of 1 mm and geometric accuracy < / = 1 mm. A Phillips Brilliance large bore scanner configured by P‐Cure Ltd  was used to acquire upright 4DCT pairs. The resolution and geometric accuracy of the Phillips scanner are both on the order of 1 mm. In this upright scanner, the patient positioning device is reclined backwards at an angle of 20 degrees from the vertical position. This slightly reclined positioning provides the patient with additional comfort and stability relative to the fully vertical position.The scans were imported and analyzed using a commercial TPS: RayStation version 9A . Measurements were made to quantify the variations in the inferior depth of the heart, posture, lung volume, and diaphragm excursion. The posture change was measured to investigate any potential correlations to the other differences between supine and seated positioning.The 4DCT image sets were acquired and binned into 10 motion phases. Only the 0%, 30%, 60%, and 90% respiratory phases were used to measure the sternum‐to‐heart distances. These sternum‐to‐heart distances were then averaged to obtain a single value. Two orientations were used to measure the distances, sagittal, and coronal. The sagittal and the coronal values were also averaged to obtain a single distance value for each of upright and supine CT scan of each patient. The data between the upright and supine measurements for each patient was paired, and as above, the relative difference was measured, and its uncertainty calculated as described later in this section.2.1The distance measurements for superior/inferior heart location are made from the top of the sternum to the bottom of the heart Figure . The bot2.2The landmarks used for the patient positioning and posture measurements were the center of the C3 vertebra to the front surface of the backrest Figure . The dis2.3The average lung volume measurements were made with contours on the 4DCT average scans (composites of scans from each respiratory phase) for each of the supine and the seated image sets. The average scan was also deformed onto each of the ten phases, along with the lung contours. Maximum and minimum lung volumes for the 10 phases were gathered from each image set and a mid‐point volume was calculated.2.4The landmarks used for the diaphragm excursion distances are the top of the sternum Figure  to the t2.5N, is first calculated to give the standard error. This standard error is then multiplied by ± 1.96 to provide the uncertainty range for 95% confidence, given a normal distribution that is, indeed satisfied in all cases with a correlation coefficient to normal of greater than 90%.The average difference in these measurements from supine was calculated: /. For uncertainty analysis, the sample standard deviation of the relative differences from supine divided by the square root of the sample size, 3The data is highly paired with substantial variation from subject to subject. The uncertainty of the average relative difference is presented here as a CI. In all but the lung excursion measurements, average movements occurred that are on the order of, or exceed, the uncertainty range. The results are summarized in Table 3.1With the 15 subjects in this case, the average change observed was an increase of 2.6%, or 4 mm, upright relative to supine. The uncertainty with a 95% (CI) was found to be in the range  or ± 2.3%.3.2The horizontal distance between the middle of the C3 vertebra and the front face of the backrest (or couch top in supine positioning) was measured to quantify the variation in patient postures and to correlate with the heart location data (to consider whether neck/spine posture impacted heart location). The same 15 subjects in the heart location cohort are used here. The average change observed was an increase of 29%, upright relative to supine. The uncertainty with a 95% (CI) was found to be in the range , or +/‐ 6.6%.3.3The volumes of both the left and right lungs were measured to quantify the relative difference from the supine to the upright position Figure . The sam3.4The diaphragm movement amplitude was measured to assess the variation in lung excursion between the supine and upright positions. The relative difference in diaphragm excursion between the upright and supine positions for each patient is detailed in Figure 3.5The results in this paper indicate that organ position changes do occur in subjects’ anatomies when repositioning from supine to upright. The results presented in Table When patients lie down on the couch for treatment in supine cases clinically, the liver is observed to deform from the influence of gravity over a period of tens of minutes. The deformation is, on average, several millimeters at its maximum deformation point 12. This situation is similar to our study if one considers that the lung volume changes from gravity are dominated by increased superior‐inferior dimensions, especially near the lower parts of the lungs adjacent to the liver. In our study, the left lung increased its volume by 244 mmThe present study's trend towards larger lung volumes for upright patients is consistent with the findings of Yang et al.Meanwhile, the small but significant increase found in the distance between the top of the sternum and the bottom of the heart (for upright positioning relative to supine) is consistent with an inferior internal organ shift. This agrees with the findings of Reiff et al.,Future work should aim to test/validate the inferior cardiac shift reported here and to consider the position of cardiac substructures such as the left ventricle and the left descending arteryThis study was partially funded by Leo Cancer Care


Placenta interception is extremely rare, and herein, we report the case of a 33-year-old woman with placenta interception during cesarean section caused by carbetocin, which was intravenously injected immediately after delivery of the infant to prevent postpartum hemorrhage. There was no sign of placental separation in the third stage of labor. A protuberance with gross subserous blood vessels in the left fundus of the uterus was detected and was misdiagnosed as placental accreta. The patient was transferred to the district referral hospital to manage the protuberance after stitching up the incision. On opening the original incision in the tertiary hospital, the protuberance disappeared, and the placenta was found in the lower segment of the uterus cavity. The intercepted placenta showed a spontaneous resolution from the uterine wall and was removed intact. This case report details the typical presentation of placenta interception to make obstetricians aware of the possibility that carbetocin might lead to this adverse event. Carbetocin is an artificial synthetic long-acting oxytocin that can cause uterine rhythmic contraction, which enhances the frequency, intensity, and duration of the uterine contraction. Its effect is observed 2 min after intravenous injection and can last for 60 min . Like otHerein, we present a case report of placenta interception caused by carbetocin during a cesarean section. To our knowledge, this is the first reported case of an adverse event caused by carbetocin and the first described case of placenta interception during cesarean section.A 33-year-old woman, gravida 4 para 1, underwent a cesarean section under epidural anesthesia with ropivacaine for premature rupture of membranes and fetal breech presentation at 34 weeks gestation at a local hospital. After the cesarean delivery of the infant and before the expulsion of the placenta, 100 μg of carbetocin was intravenously injected over 1 min to prevent PPH. After a few minutes, there was no sign of placental separation, and a protuberance (∼10 × 10 × 8 cm) with gross subserous blood vessels was detected in the left fundus of the uterus , with a The WHO recommends active management of the third stage of labor to prevent PPH through the administration of a uterotonic immediately after the birth of an infant . HoweverPlacenta interception during a cesarean section due to EUC caused by carbetocin is extremely rare and has not been previously reported. There are no established guidelines for the prevention and management of placenta interception. In the present case, the reason for placenta interception is regarded as the result of EUC due to hypersensitivity to carbetocin. The duration between the two interventions was 109 min, which was longer than the action time of carbetocin, so the intercepted placenta showed a spontaneous resolution from the uterine wall once the carbetocin action time elapsed. According to the management of dealing with EUC, administering a tocolytic agent, such as Magnesium sulfate, or terbutaline, may assist in separating the intercepted placenta from the uterine wall before the carbetocin action time elapsed .Our case shows that carbetocin might lead to placenta interception and provides the typical presentation of placenta interception to familiarize obstetricians with this adverse event.


Transvenous lead extraction (TLE) is an indispensable procedure in the management of cardiac implantable electronic devices.A 72‐year‐old man had undergone implantation of a dual‐chamber pacemaker  for complete atrioventricular block 13 years previously. He noticed that the lower part of his pacemaker pocket in the left chest had been exposed for 1 month, and he was referred to our hospital to undergo TLE for treatment of pocket infection. After a discussion with the cardiac team, we decided to remove the leads because of device infection. We planned to perform the TLE procedure in a hybrid operating room using general anesthesia with the presence of on‐site cardiac surgery backup. Additionally, we planned to insert the NES from an 18‐Fr long sheath and use the NES to grasp the ventricular lead without a free end. After opening the left pacemaker pocket, we removed the generator and debrided the infected area in the pacemaker pocket. A locking stylet  was then inserted into the ventricular lead, and an attempt was made to grasp the lead in the right atrium using the NES. However, instead of hooking the lead with the cobra head, the lead got caught on the outside of the cobra (the indentation on the front side) Figure . In thisA tandem femoral‐superior approach is a useful and safe method for TLE.When the heart‐shaped sign was observed, we confirmed that the lead could not be grasped even with the advancement of the threader, which created no space for closure Video . HoweverIn conclusion, the occurrence of the heart‐shaped sign when performing the spaghetti twisting technique using the NES provides a clear and prompt explanation for the failure to grasp the lead, contributing to a reduction in the risk of complications related to the NES and a decrease in the fluoroscopic and procedure times.The authors declare no conflict of interests for this article.This study was conducted according to the principles of the Declaration of Helsinki. The study was approved by the Institutional Review Board.The patient provided written informed consent.N/A.Video S1.Click here for additional data file.Video S2.Click here for additional data file.Video S3.Click here for additional data file.


Chamaecyparis obtusa) by using point dendrometers and those of local xylem potential by using stem psychrometers located next to the dendrometers to determine how these variations were related to each other, to phloem turgor and carbohydrate transport. We also estimated the axial hydrostatic pressure gradient by measuring the osmolality of the sap extracted from the inner bark. The inner bark shrunk during the day and swelled during the night with an amplitude related to day‐to‐day and seasonal variations in climate. The relationship between changes in xylem water potential and inner bark thickness exhibited a hysteresis loop during the day with a median lag of 2 h. A phloem turgor‐related signal can be retrieved from the diurnal variations in the inner bark thickness, which was higher at the upper than at the lower position along the trunk. However, a downward hydrostatic pressure gradient was only observed at dawn, suggesting diurnal variations in the phloem sap flow velocity.The inner bark plays important roles in tree stems, including radial exchange of water with the xylem and translocation of carbohydrates. Both processes affect the water content and the thickness of the inner bark on a diurnal basis. For the first time, we simultaneously measured the diurnal variations in the inner bark thickness of hinoki cypress ( 2 of the bark, including the cambium, was removed. Both were attached to a frame fixed to an 18‐cm‐long screw inserted deeply into the trunk.Installation of a two‐point dendrometer at a height of 18.6 m at the base of the crown of a hinoki cypress to measure the diurnal variations in trunk and xylem radius. The inner bark thickness was calculated as the difference between the two radii. One sensor was set on the surface of the inner bark; the second sensor was placed on the xylem surface after 1 cm Sieve cells or elements are involved in carbohydrate translocation; fibres provide structural support; and parenchyma cells store water, carbohydrates, and several other compounds such as amino acids, storage proteins, or secondary metabolites Niklas, .The whole tree water stores contribute to 10–50% of the daily transpiration of trees during sunny day (probably more on cloudy days), with the water stored in the stem tissues, including the inner bark, which contains more elastic cells than those in the wood, contributing from 5% to 20%  or are transiently stored. A hydrostatic pressure gradient generated by the difference in osmolality of the phloem sap between the sources and sinks due to loading and unloading of carbohydrates is responsible for the bulk flow through the interconnected sieve cells  over several months, by subtracting the xylem radius from the entire trunk radius simultaneously measured using dual‐point dendrometers  was measured using a pyranometer ; air temperature and humidity were measured using a Vaisala sensor  at a height of 28.5 m. Rainfall was measured in a nearby open area using a tipping bucket rain gauge (Ikeda Keiki). All measurements were stored every 10 or 15 min on dataloggers . The vapour pressure deficit was calculated from air temperature and humidity by using R package “plantecophys” . Measurement interval was set to 10 min, and the data were stored on a high‐resolution (0.01 mV) datalogger  The resolution of the dendrometer was 2.2 µm/mV .Variations in trunk and xylem radius were measured using a two‐point dendrometer  attached to a frame fixed to an 18‐cm‐long screw inserted deeply into the trunk heartwood. The distance between the two dendrometers was 6 cm with the screw between them. One dendrometer was set on the surface of the inner bark after the dead outer bark was carefully incised because the hygroscopic properties of the dead outer bark would have contributed to variations in the stem radius  was measured at a short distance from point dendrometers by using a stem psychrometer . A 2 cm2 piece of bark (including cambium) was removed, and the sensor was set on the xylem tissue and firmly held with vinyl tape. The remaining part of the exposed xylem was covered with silicon grease. The sensors were insulated with cotton and wrapped with aluminum foil. An aluminum shelter was attached to the stem above the sensor to prevent the entry of rainwater. The data of each sensor were recorded every 10 min by using a microvolt meter .Xylem water potential (Ψ2.5Two replicates of two inner bark disks with 10 mm diameter were collected at dawn (from 5:00 to 6:30 depending of the time of sunrise) and early afternoon (around 15:00 in summer and around 13:30 in December) on three occasions in August, September, and December at a short distance from the sensors installed on the three trees. The disks were enclosed in plastic bags and immediately stored at −18°C in a portable freezer in the field before being transferred to −30°C in the laboratory. After the disks were thawed in plastic bags, the inner bark samples were weighed fresh. A disk of filter paper was sandwiched between the two discs of the inner bark with the conductive phloem facing the filter, and the samples were pressed to extract the cell sap  in the inner bark tissue, including the turgor pressure and effect of gravity, was estimated by adding the osmotic pressure calculated from the sap osmolality (mean of the two samples) to the xylem water potential that was recorded at the time of sampling:T is the temperature in Kelvin; R the universal gas constant (0.008314 l MPa mol−1 K−1); CS the osmotic concentration, expressed in mol/L, approximated by the osmolality of the sap.The hydrostatic pressure  for each tree was calculated from the model coefficients of the fitted relation between the amplitude and temperature. Cross‐correlations (“ccf” function in R) were used to estimate the lag between diurnal variations of xylem water potential and those of bark thickness.X) instead of the diurnal variation in xylem radius or xylem sap velocity as a proxy for the xylem water potential dThThe difference between the predicted and observed changes in the inner bark thickness reflects the change due to the variation in the osmotic content of the inner bark, a turgor‐related signal  to the end of October  with two periods of more than a week without rain in early August and mid‐September Figure . The min3.2The inner bark thickness exhibited diurnal variations, decreasing during the day and increasing during the night, with large day‐to‐day fluctuations Figure . Higher The amplitude depended on the climatic conditions, with larger variations on sunny than on cloudy days Figure . On a seThe maximum thicknesses were often recorded a few hours after sunrise, earlier at the upper position  than at the lower position  than at the lower position , especially for tree #1, which showed higher turgor signal amplitude at the upper position than that of the other trees Figure . No clea3.4Inner bark water content did not differ between the sampling time and sampling position, but was lower in December, especially at the upper position Table . In contPH) and xylem water potential (ΨX) measured at early afternoon  predicted the pressure to be 0 when the xylem water potential dropped below −1.0 MPa. A small hydrostatic pressure gradient between the upper and lower positions was only observed at dawn in summer (less than 0.2 MPa), whereas a higher gradient was observed both at dawn and early afternoon in December . The inner bark thickness responds in a few hours to the changes in transpiration but requires few days to respond to the changes in photosynthesis and phloem loading. In Scots pine, the turgor signal was related to canopy photosynthesis with a lag of 1 day at the top of the tree and 9 days at the bottom, but the highest correlation coefficients were found with a lag of 10 days at the top and 31 days at the bottom (Mencuccini et al., The low velocity of carbohydrate transport in gymnosperms (Dannoura et al., The highest osmolality values observed in December may be related to an increase in soluble sugar concentrations during autumn for cold acclimation to tolerate freezing temperature in winter (Lintunen et al., 5Diurnal variations in the inner bark thickness in hinoki cypress are mainly driven by the changes in xylem water potential. However, because the observed changes in the inner bark thickness could not be completely predicted by assuming a constant osmotic content in the inner bark, a turgor‐related signal was detected, which is in line with the Münch pressure‐flow hypothesis for long‐distance transport of carbohydrates. The weak axial osmotic gradient in the trunk confirms the role of gravity in phloem transport in hinoki cypress, and potentially the importance of a leakage‐retrieval mechanism. Considering that the hydrostatic pressure gradient decreases during the day, and that the turgor signal was the highest a few hours after sunset, the velocity of the phloem sap flow may exhibit diurnal variations in trees, which has to be addressed in future studies even if it remains a challenge for tall trees in the field.The authors declare no conflict of interest.Fig S1Click here for additional data file.Note S1Click here for additional data file.


In the original published version of this article, the authors did not include a sentence in their acknowledgements section that they wished to include. The author wants to add “We express our thanks to Dr. Márta Kiniczky for the development and formulation of Elice16Indures” in the acknowledgment part. The authors apologize for the errors. Both the HTML and PDF versions of the article have been updated to correct the errors.


These a*b* values were then used to define two methods of segmenting the exact areas in which there was a transfer of reddish pigment. The area studied in the painting was originally black, and the contamination with reddish pigment occupied 13.87% to 32% of the total area depending on the selected method. These different solutions can be explained because the lower limit is segmentation based on pure pigment and the upper limit considers red as an exclusion of non-black pigment. Over- and under-segmentation is a common problem described in the literature related to pigment selection. In this application case, as red pigment is not original and should be removed, curators will choose the method that selects the highest red area.Restorers and curators in museums sometimes find it difficult to accurately segment areas of paintings that have been contaminated with other pigments or areas that need to be restored, and work on the painting needs to be carried out with minimum possible damage. It is therefore necessary to develop measurement systems and methods that facilitate this task in the least invasive way possible. The aim of this study was to obtain high-dynamic-range (HDR) spectral reflectance and spatial resolution for Dalí’s painting entitled Two Figures (1926) in order to segment a small area of black and white pigment that was affected by the contact transfer of reddish pigment from another painting. Using Hypermatrixcam to measure the HDR spectral reflectance developed by this research team, an HDR multispectral cube of 12 images was obtained for the band 470–690 nm in steps of 20 nm. With the values obtained for the spectral reflectance of the HDR cube, the colour of the area of paint affected by the transfer was studied by calculating the  Restoration and curation techniques in the area of cultural heritage require the use of technologies that allow for the characterisation of the pigments that make up artworks in a precise and non-invasive manner ,2. To caThe proper characterisation and identification of pigments in artworks depend on the spatial and spectral resolution of the system . ImagingMSI and HSI can obtain diffuse spectral reflectance with a resolution that depends on the pixel size of the system sensors and the optical quality of the system, as they measure the spectral information of each pixel (px) of the image . CommercNumerous studies have been carried out with the aim of capturing HSI with a high spatial resolution. In their research, Yifan et al. developed an algorithm that could obtain images with the spatial resolution of MSI and the spectral resolution of HSI, using the 3D wavelet transform . In ordeIn the field of cultural heritage restoration and conservation, it is necessary to obtain HSI with high spatial resolution to perform the segmentation of large artworks. Super-resolution algorithms are widely used to perform pigment segmentation of artworks ,19. The When documenting and analysing artworks, the gigapixel technique is widely used with RGB cameras, as commercial RGB cameras enable images with a high spatial resolution to be obtained .Pigment segmentation is a technique that can be mathematically executed with the HSI technique and post-processing. Post-processing is used in segmentation because over- or under-segmentation can take place . Magro eHowever, the colorimetric properties of the pigments that make up the paints alter over time due to the action of temperature, humidity, and exposure to light, among other things . In addiA Spectral Angle Mapper (SAM) is a technique that is often used to identify similarities between the spectral profile of pigments in a painting and reference pigments that have been previously characterised and are available in a library ,25. In tIn this work, we present spectral reflectance measurements of Dalí’s painting using multispectral images with high-dynamic-range and 4K spatial resolution. Based on these measurements, two methods are developed for performing pigment segmentation and identification, taking into account variations due to pigment mixing.Salvador Dalí’s Two Figures (1926) was affected by the transfer of a reddish pigment when another painting came into contact with this work. The segmentation and localisation of the area of the artwork affected by the reddish pigment require previous colorimetric characterisation based on the spectral reflectance. In order to identify this pigment, this research team has developed a multispectral image capture system (Hypermatrixcam) that is capable of obtaining spectral images with a high spatial resolution .This image capture system consists of a matrix array of 12 RGB sensors with 4K spatial resolution a; patentIn its recommendation 15-2004, the International Commission on Illumination (CIE) established specific geometrical conditions for spectral reflectance measurements depending on the surface to be tested and the instrument used . FurtherDalí’s painting Two Figures (1926) measures 1.98 × 1.49 m, and the distance at which the camera should be placed with respect to the painting depends on the field of view of the measurement system. Each sensor has a field of view of 30° × 27.7° ; hence, considering the geometric displacement of the 12 sensors, the field of view of Hypermatrixcam is 23.4° × 20.5° . This gives a value of 4.8 m for the distance 2 of the artwork for each pixel of the HSI obtained . The expression obtained .Three Art Lux 500 Flex LED array panels with a total size of 410 × 1830 mm  were chosen as the light source for the reflectance measurements. The choice of LED panels was made due to the absence of UV and IR radiation in their emission to avoid damaging the artwork [Once the geometrical configuration for the spectral reflectance measurements had been established, the system was calibrated. For this purpose, an HSI image was initially captured without the painting; as a calibration standard, we used a foamed PVC sheet, a uniform material with good diffusive properties and a uniform reflectance value. The PVC sheet had to be of the same dimensions as the Dalí painting in order to calibrate the nonuniformity of the illumination system. The mean reflectance ectional . Measuren, m) is the size in pixels of the images taken. With the resolution of Hypermatrixcam, these values were m = 3322 pixels and n = 2510 pixels.An image of the PVC was then captured with Hypermatrixcam to give the spectral HDR of the reference target Without changing the positions of the camera or the lighting system, images of Dalí’s painting were then captured in the same place where the foamed PVC was previously located to give the spectral HDR of the painting To complete the measurement, multispectral images of the dark current were captured, with the sensors covered, to give the HDR of the dark current of the system Multispectral and hyperspectral cameras typically consist of sensors with a limited dynamic range, resulting in low-dynamic-range (LDR) images . These LIn order to obtain spectral reflectance measurements using HSI, all of the pixels must have a value for the grey level that is within the linearity zone of the sensor ; otherwiTo define the linearity limits in the response of the CMOS sensors, the curve of the sensors as a function of exposure time was obtained . For theDalí’s painting Two Figures (1926) has very light and dark areas on its surface. As shown in The system used in this work allowed HDR multispectral images to be obtained by capturing them over different exposure times. Based on LDR images, an HDR image is obtained from a combination of the grey levels in each pixel that are not saturated or underexposed.The MSI acquisition system consisted of RGB sensors and spectral filters. The sensitivity of the RGB sensors and the transmittance of the spectral filters varied spectrally for each wavelength, and images were therefore captured with different exposure times. These exposure times were selected by adjusting them to minimise the saturated pixel values in each of the intervals of the working spectrum.n, m) was calculated using Equation (1):The range of exposure times chosen for wavelengths in the range 470–630 nm was 0.5–12.5 s in steps of 3 s. For wavelengths in the range 650–690 nm, the range of exposure times was 8–20 s in steps of 4 s. After obtaining the HDR multispectral images of the calibration, paint, and dark current, the high-dynamic-range spectral reflectance a* and b*. These data are related to the pixel colour.A spectral reflectance cube can be used for pigment segmentation; in this case, two methods are described and applied to the painting. Both methods require processing a spectral reflectance cube with a standard illuminant to obtain CIELab data, a* and b* values, this division suffers the same problem, and establishing a separation boundary becomes quite arbitrary. To help in the segmentation process, we need some extra information. We propose two methods that basically focus on image areas with a predominance of a type of pigment (black or reddish in our application case).Due to the mixture between pigments and the alterations they suffer in terms of their colorimetric properties over time, the segmentation of two pigments whose reflectance spectra are close to each other is difficult . When prMethod 1: Inverse segmentation by characterising a black area without the transfer of reddish pigment.a* and b* data of the black pigment from an area that has no red pigment at all.In this method, additional data consist of obtaining representative If you segment black according to these data, then red will be the remaining pixels because there are only two colours in the selected area.U with all a*b* data in the image:In this method, we can define by a set K:a*b* data representation that permits a simple segmentation. This process can be described byAdditionally, we can define a subset Method 2: Segmentation based on an area with a high incidence of red pigment.a* and b* data from a selected area strongly related to the red pigment. Selection in other areas is made by obtaining data that have the a* and b* that are inside the boundary obtained by directly analysing the red pigment.This method takes In this case, any image subset that only has red pigment gives:a*b* data are surrounded by a boundary βred that will enclose all red pigment related to the selected boundary. So, it is possible to segment, in any image with any colour, with these set data to obtain red.In Equation (5), the Multispectral images (MSI) were acquired with different exposure times to give HDR images of Dalí’s painting Two Figures (1926). From these images, and using Equation (1), the HDR spectral reflectance was processed, as shown in The segmentation of the pigments in the painting was carried out using the multispectral images obtained as described above. Each multispectral image had a spatial resolution of To segment the pigment, it was first necessary to characterise it colorimetrically. For this purpose, a small area of the paint affected by the transfer of the reddish pigment (Reference Area 1) was selected, with a size of 6.8 × 4.9 cm. Using illuminant A as a reference and a standard CIE 1931 observer, the first step is to calculate the XYZ tristimulus values from the reflectance spectrum of each pixel of Reference Area 1, The CIELab a XYZn,m ,34.Method 1: Inverse segmentation by characterising a black area without the transfer of reddish pigmentIn this case, a black area was selected a, and itpainting b.Once the region with the values  pigment a. The ge pigment b.To validate this method, we selected an area  that was larger than the one selected as a reference for the analysis. Using the egmented .Method 2: Segmentation based on an area with a high incidence of red pigmentRather than performing segmentation of the reddish pigment based on the previous characterisation of a black area, it is also possible to perform segmentation based on the HDR spectral reflectance of an area with only a high incidence of red pigment, called Reference Area 2 .In the same way as described in the previous section, the coordinates k values .Since these two regions do not overlap, segmentation can be performed directly on the segmentation area based on the region with the values eddish_2 .The results obtained with both methods are shown in For each of the two proposed methods, the mean value of the spectral reflectance spectra of all pixels included in the segmentation was calculated. The spectral reflectance values for each method have been processed to obtain the corresponding RGB values for method 1 a and metThis study presents measurements of the HDR spectral reflectance for Dalí’s painting entitled Two Figures (1926) and a colorimetric analysis of the reddish pigment that affects the work due to the transfer between pigments.To enable non-contact measurements, the segmentation and quantification of the pigments that make up a painting are typically carried out through a colorimetric analysis using spectral reflectance measurements. Since pigments are distributed in very small quantities over the artwork, in order to carry out characterisation and segmentation, it is necessary to use methods that allow spectral information to be obtained with high spectral and spatial resolution. Commercial MSI and HSI capture systems do not have sufficient spatial resolution to segment pigments in large artworks. Hence, although a combination of HSI and MSI increases the spatial resolution of HSI, it is not sufficient to perform pigment segmentation accurately . AdequatSuper-resolution algorithms perform a posteriori processing of the spectral reflectance information obtained from HSI ,19, and 2 of Dalí’s painting in each pixel of the image obtained. The spectral and spatial resolution of these HDR spectral reflectance measurements allowed us to characterise the reddish pigment present in the painting.With the multispectral image capture system used in this research, it was possible to obtain spectral information of an area of 0.35 mmDue to the difficulty of defining the thresholds between a pure pigment, its mixtures, and the rest of the pigments, SAM and divergence techniques are interesting for use in pigment segmentation ,25,26. Wa* and b* coordinates, thus simplifying the process.In this study, the pigment present in the paint itself was used for characterisation, and a comparison with reference spectral libraries was avoided. Furthermore, prior to segmentation, the two methods proposed here were used to characterise the pigment in its pure and mixed states based on the In Method 1, a segmentation was performed that included areas in which the pigment had been mixed and which were imperceptible to the naked eye. Method 2 involved an analysis based on the most visible areas, since Reference Area 2 was an area of the artwork containing pure red pigment. The choice between the methods described above will depend on the needs of restoration and conservation experts in the field of cultural heritage, since the line that delimits a pigment is not clear; this is especially the case if red and black pigments are compared, as was the case here, as they are colorimetrically similar to each other. As pigment is on the painting surface, the reflectance is not always strictly related to the added pigment; this is because is the deposition layer is thin, and the reflectance is a mix between the original layer and the added pigment layer. In this way, pigment segmentation has a limitation in method 2 because this selection only obtains a big pigment layer. Method 1 can select the thinnest layer of red because it is obtained by the exclusion of black; this is only useful if there is only black and red. If there are additional colours, they will be segmented like red because they are not black.In the application case of this Dalí painting, the curator selection of interest is the highest area (Method 1); thus, all of it is intrusive pigment that must be eliminated because it is a transfer from another painting.This study has presented HDR spectral reflectance measurements of Dalí’s painting entitled Two Figures (1926), with 12 spectral bands and high spatial resolution. The data obtained represent objective information on the colours of the painting for future interventions and analyses of its state of conservation. Our approach allows for a resolution of 3322 × 2510 px. As part of our analysis of the spectral reflectance of the painting, the reddish pigment transfer affecting a piece of the artwork was characterised and segmented with two proposed methods. In the same area, Method 1 gives 32% of reddish pigment and method 2 gives 13.87% of reddish pigment. Method 2 obtains a pure red component and method 1 obtains more colour variations around the reddish pigment. The proposed methods can provide additional tools for the objective, non-contact analysis of the pigments used in artworks. In this application case, Method 1 will be selected by curators; thus, all of the red pigment is not from the original painting and needs to be eliminated.Patent ES2819052-B2. Cámara multi o hiperespectral para mantener el aumento lateral ajustando el enfoque. Fernández-Balbuena A. A., Bernárdez Vilaboa, R., Molini, D. V., Pinilla, S. M., & Gómez Manzanares, A.Patent ES2911099-B2. Instrumento y método para calibrar la uniformidad de la iluminación con aplicación en medida de reflectancia con imágenes multiespectrales o hiperespectrales. Fernández-Balbuena A. A., Gómez Manzanares, A., Molini, D. V., Pinilla, S. M., Martínez-Antón, J. C., & Bernárdez Vilaboa, R.


In underground mining, the dip angle is one of the widely recognized factors that cause the asymmetric deformation of the goaf/stope roof, but characterizing the degree of asymmetric roof deformation is still a challenge. The goal of this research is to try to solve this problem with a theoretical model and numerical method. In an inclined ore seam, the mining load produces both normal and tangential effects on the inclined roof. A theoretical model was developed employing thin plate theory for enabling describe the asymmetric deformation of the roof caused by inclination. The proposed model describes not only the bending deformation state of the roof but also the deformation characteristics. Subsequently, the law of asymmetric deformation of roofs with varying inclinations was presented by numerical method. Under the same conditions, the numerical results of the asymmetric deformation of the roof are consistent with the theoretical results. Finally, the degree of asymmetrical deformation was characterized and quantified by the distance between the maximum subsidence point and the center of the roof. There exist three modes of asymmetric deformation, which are controlled by both dip angle and in-situ stress ratio. The results show that the shear load caused by dip angle is the root cause of asymmetric deformation of the roof. This study provides a theoretical basis for the asymmetric deformation control of the inclined roof. Room and pillar mining is one of the essential methods for underground mining, which features a series of temporary or permanent pillars to support the overlying rock pressure and maintain the stability of the roof. In this mining method, workers conduct mining activities in a space (stope) supported by natural or artificial pillars. In the process, the space (stope) must be stable to ensure the safe mining of the ore body. After the ore body mining is completed, this space (goaf) also needs to be durable to control the surface collapse caused by the movement of the rock strata. Once the pillars in the goaf are destabilized, or the exposed area of the roof is too large, it may induce the deformation and instability of the roof and bring severe challenges to the safety of underground production. Therefore, studying the deformation characteristics of the stope/goaf roof is one of the significant ways to reveal its stability.1 investigated the destabilization mechanism and stability control in stope mining roadway below the remaining coal pillars based on theoretical analysis, numerical simulation, and industrial testing. They found the law of stress transfer and proposed the corresponding support technology. The paraffin was melted to simulate the mining process in an actual three-dimensional physical experiment; the results show that the floor and roof deformation is symmetric, and the maximum flexure point is in the center of the excavation area2. The field monitoring and numerical method were used to explore deformation and failure patterns of gob-side entry driving heading adjacent and concluded theoretical criteria. Based on these results, a series of preventive techniques were developed to control the roof3. Abousleiman et al.4 investigated deformation mechanics and parametric sensitivities through the discrete element method. The results of parametric sensitivities confirmed that the self-supporting capacity is greatly influenced by entry depth and fine-scale bedding and then is determined by the stiffness and strength of intact materials. Zhu et al.5 carried out two physical similarity experiments to find the failure propagation of pillars and roofs. They divided it into two stages: the first stage is steady movement, and the second stage is the instability propagation stage. Roof collapse due to inefficient support of rock bolts is studied by field observations, numerical simulation, and lab tests. According to the situation, the improved support systems were designed to prevent such accidents7. In room and pillar mining, the remaining pillars will aggravate the damage to the roof. Thus, it is worthwhile to explore how the pillars affect the roof 9. Wang et al.11 drew stress circles of the entry roof in each stage of the whole life cycle based on the Mohr-Coulomb theory to judge whether the roof is damaged according to the strength envelope curve. The large deformation of the surrounding rock is not only affected by the stress but also by the movement of the upper roof. Sinha et al.13 proposed that three separate reinforcement factors are used to evaluate roof support plans. Mondal et al.14 established a predicted model that described the correlation between the cut-out distance of the continuous miner and the roof convergence through numerical simulations. This model was verified by observed data to determine the optimal cut-out distance. Chai15 and Pan et al.16 reveal the mechanism of ground pressure behavior induced by roof strata deformation using field testing technology and theoretical method.In flat seam mining, physical experiments, numerical simulations, and field monitoring are performed to reveal the deformation and failure modes. Fu et al.17 evaluated the stability of roadways with a hard roof by beam theory and numerical method and compared it with field monitoring. Besides, the roof is modeled as an Euler-Bernoulli beam clamped by pillars and rocks to deduce the roof fracture process18. Zhang et al.19 explored failure and deformation characteristics in working face end by numerical simulation and thin plate theory. As the advance of the working face, the failure of the roof at the end of the goaf is periodic. According to the breaking characteristics, a thin plate model with three fixed sides and one free side is established. As the excavation of the ore body, the roof, regarded as a thin plate, is subjected to different boundary conditions. The stress distribution and fracture modes will change under different supports21. Ma et al.22 considered that pressure arch theory is used to derive the load borne by the goaf roof. Based on this load, the roof is modeled as a thin rectangular plate with four fixed support points to determine the optimum thickness. The thin plate theory is no longer applicable to this situation if the thickness is thick enough. These studies are aimed at the flat seam.In terms of theoretical research on roof deformation, Sun et al.23 and mining projects24. Affected by the inclination of the orebody, the surrounding rock behavior of inclined orebody mining is different from that of horizontal orebody26, such as stress state, deformation law, and failure mode. Das et al.27 studied the influence of dip angle on the mechanical behavior of pillar and roof, the results show shearing effect and stress concentration is comparatively more severe at the dip side working. Li et al.28 used physical simulation and theoretical analysis to research roof structure stability formed by a three-hinged arch. With the dip angle increasing, the possibility of the roof structure becoming unstable due to large deformation decreases significantly, while the probability of the roof structure’s sliding instability above the tailgate increases. And a detailed field survey was proposed to evaluate the stability of inclined bedded surrounding rock mass and identify the high risking regions29. The influence of inclination on the deformation and failure of the roof is negligible32. Though existing research have revealed that the roof forms symmetrically in the strike direction and asymmetrical bending in the dip direction, the degree of dip influence on the asymmetric deformation of roofs needs to be further studied.In general, the dip angle of geological strata will influence rock engineering characterizations, which is a recognized phenomenon in tunnelThe goal of this research is to solve the issue mentioned above by combining theoretical and numerical methods. The theoretical model of asymmetric deformation of an inclined roof is developed by thin plate theory. Then the characteristics of roof deformation with variable dip angle are studied by numerical method. The numerical results and theoretical model results are compared and analyzed to look forward to the inclination effect of the roof asymmetric deformation mechanism. In order to further explore the law of asymmetric deformation, the coupling effects of in-situ stress ratio and dip angle on the magnitude and degree of roof deformation are studied. Finally, three deformation modes are proposed.In underground mining, the roof of the goaf/stope could be regarded as a thin plate, and then the thin plate theory is employed to investigate the deformation law. Existing research has proved that the stope/goaf roof mainly undergoes the expected load and bends symmetrically in flat seam mining. When the room and pillar method is used to extract the inclined ore seam, the goaf/stope roof is subjected to the load of the overburden rock mass, the horizontal lateral pressure, and the support of pillars, as shown in Fig. To simplify the model and calculations, some assumptions need to be made.(1) The pillars will not yield under combined compression-shear loading and be regarded as an elastic foundation. (2) There is no large crack around the roof; the boundary condition is regarded as fixed support. (3) The tangential load only deforms the roof along the inclined direction and ignores the shear deformation.33, the stress distribution on the four sides of the roof need not precisely satisfy the stress boundary conditions as long as the resultant force meets. Then,σx represents the normal stress in the x direction, h is the thickness of the roof, and FTx represents the resultant force of normal stress on the surface in the x direction. Similarly, FTy is the resultant force of normal stress on the surface in the y direction, and FTxy are resultant force of shear stress around the boundary, as shown in Fig. qn is the support loads of the pillars, and its expression isn is the number of pillars; Ap is the top surface area of a pillar; Ar is the area of the roof; L is the height of the pillar; Ep is the elastic modulus of pillar material, and w represents the deflection of the roof.When the roof is subjected to normal load only, there is lateral ground pressure along the direction of roof thickness and the lower surface is subjected to the support force of the mine pillars. According to St. Venant’s theoryentclass1pt{minimaD is bending stiffness, and it is obtained asEr is the elastic modulus of the roof rock mass; μ is the Poisson’s ratio of the roof.According to the thin plate theory, the equilibrium equation of the roof is given in the differential form,From the assumption (2), the boundary condition is considered as fixed support, and the boundary condition is expressed in terms of deflection asC is constant, and wm is an arbitrary function to ensure that the deflection satisfies the displacement boundary condition.Let the roof deflection equation be expressed as follows,Vε is the deformation energy of the roof. Under the boundary condition of fixed support, the deformation energy could be given as,In addition, the Ritz method establishes the variational equation of the roof.a and b are half the length and width of the roof, respectively.Ulteriorly, the functional expression of the deflection isC is obtained by substituting Eqs. (The expression of parameter ing Eqs.  and 9)  C is obting Eqs. ,10\documThen, substituting Eqs.  and 11)11) into According to assumption (3), on the boundary opposite to the direction of tangential stress , the ground stress will prevent the roof from moving, on the other boundary, as the new displacement space caused by the roof deformation, the rear rock layer does not affect the longitude deformation under the ground stress. For the transverse flexural deformation of the roof, considering the clamping effect of the upper and lower strata, the roof rock has no deformational space, thus, is fixed around. The longitudinal deformation is the deformation of the roof strata itself, which needs further solving. Since the longitudinal deformation is minimal, the influence of the rock mass at the boundary of the strike is ignored. Therefore, the equilibrium equation of the roof is as follows,Fx obtained from the boundary condition isThe From physical and geometric equations in elasticity, the expressions are given as,By combining Eqs.  and 16)16), the x + x0) in the inclined direction. At this time, the deflection equation of the roof under combined compression-shear load is written asC is determined by Eq. .Equation  indicated by Eq. , and thed by Eq. . From Eqθ is the dip angle of the seam.Further, the expression of vertical displacement is obtained from Eq. ,19\documA gently inclined phosphate deposit is regarded as the research object to study the dip effect on the deformation behavior of the roof by numerical method. The phosphate ore layer is located at the Doushantuo Formation of the Upper Aurignacian. The orebody is stratified and produced in line with the occurrence of the strata, without horse-stone. The occurrence elevation of the ore layer is from 480 to 1130 m; the buried depth is about 250–600 m, and the dip of the seam varies from 0° to 25°. And the thickness of the seam is equal to from 0.55 to 9.13 m. The roof is dolomite containing phosphorus bands and phosphorus nodules, and the rock layer is medium-thick and stable in distribution. Some areas of the floor are mudstone and shale containing banded phosphorite or phosphorus masses, and the rest are phosphate-bearing powdery dolomite. According to the occurrence characteristics of the ore layer, the room and pillar method was selected. A rip pillar of 5 m in width is left between the ore blocks, the top and bottom pillars are arranged along the direction, the top pillar is equal to 5 m, and the bottom pillar is 5 m. The sectional transportation roadway is arranged in the top and bottom pillars. The room is arranged horizontally along the strike in the block, and regular point pillars are left in the goaf. The length and width of the point pillar are 5 m × 5 m, the interval along the strike is equal to 10 m, and the interval along the dip is 8 m, as shown in Fig. 35 is used to estimate the strength parameters of rock mass and is given as,The Hoek-Brown criterionσmc and tensile strength σmt of rock mass are obtained by making σ3 = 0 and σ1 = 0, respectively.In the above formula, the uniaxial compressive strength m, s, and RMR is given as,mi is a constant for intact rock, the strength of rock mass can be evaluated by Eqs. (And the relationship between the constant  by Eqs.  ~ (22).36.Em represents the elastic modulus of rock mass, Ei represents the elastic modulus of intact rock; and D is the blasting influence coefficient (0 ~ 1).In addition, the elastic modulus of rock mass is calculated by the empirical equation proposed by Hoek and DiederichsAccording to the mine geological report and laboratory test results, Eqs.  ~ (23) a3D software 37 is used to establish numerical deposit models with dip angles of 0°, 10°, 20°, 30°, and 40°, respectively. To the dip of the seam is the negative x-axis. The strike length of the stope is 85 m, and the width along the inclined direction is 47 m. There are 15 pillars left in the goaf, whose length and width are 5 m × 5 m, and the height of the pillar is 6 m. The deposit model is divided into 8 layers from bottom to top, and the model dimensions are 425 m × 282 m × 208 m, as shown in Fig. To explore the dip effect on the displacement of the goaf roof, the FLACThe average overlying strata thickness of the seam is 300 m. The overlying rock load is about 6.7 MPa, and the ratio of in-situ stress is equal to 1.2, then the horizontal ground stress applied is 8.2 MPa. The fixed support at the bottom and around the model prevents the model from moving. The model is assigned to the Mohr-Coulomb model.x-axis. The curves on the right side of the contour are vertical displacements on the two lines (V1 and V2) along the strike direction. The curves below the contour are vertical displacements on the four lines  along the inclination direction. When the dip angle is equal to 0°, the vertical displacement of the roof is more than 18 cm. The negative sign indicates the displacement direction. The vertical displacement in the center of the roof is the largest and reaches 21 cm. Taking the central axis of the roof as the center, the displacement in the strike direction and inclination direction are equal, respectively, and the distribution law is consistent, as shown in Fig. Figure θ is equal to 0°, the displacement mainly occurs in the vertical direction, and the total displacement is similar to the vertical displacement. As the increase of dip angle, the total displacement increases appreciably, while the vertical displacement changes little relatively. The deformation law is in accordance with that in the vertical direction, and the total displacement continues to reflect symmetry along the strike direction and asymmetry along the inclination direction.Figure x = 136 m, the displacement of the left side increases with the increase of the dip angle, while the displacement of the right decreases with the increase of the dip angle, as shown in Fig. Figures Figures According to the decomposition of force, the normal load acting on the roof is obtained,σv represents the vertical in-situ stress before mining; σh represents the horizontal in-situ stress before mining.In the same way, the tangential load acting on the roof is obtained:a = 23.5 m, b = 42.5 m, Eq. a = 23.5 rom Eqs.  and 25)a = 23.5 x-axis, namely the inclination upward direction, as shown in Fig. The contour map of the roof can be drawn from Eq. , as showxoff is the offset distance; Δxmax is the maximum longitudinal compression of the roof boundary, i.e., the boundary end with free deformation space; Δx0 is the distance between the geometrical center before and after deformation, i.e., the offset distance of the geometrical center. If the offset distance is larger, the asymmetrical deformation is more serious; on the contrary, the asymmetrical deformation is smaller.To analyze the asymmetry of the roof deformation, the distance between the maximum subsidence point of the roof and the center of the roof is used to characterize the degree of asymmetrical deformation. This distance is called “the offset distance,” as shown in Fig. θ = 45° as the turning point, when θ is smaller than 45°, the offset distance increases as the dip angle increases. Conversely, when θ is greater than 45°, the offset distance moves backward as the dip angle increases. It can be concluded from Eq.  is obtained,To conclude the variation law of vertical displacement with inclination angle, the ratio of in-situ stress is regarded as a constant, then the differential of (σv is constant and has no influence on the variation law of the derivative. LetThe in-situ stress θ ∈ , the slope at the two ends,Due to the inclination angle θ = 0°, the vertical displacement slope equals 0. And when θ = 90°, the slope is associated with the ratio of in-situ stress. This law is consistent with the variation as shown in Fig. Obviously, when Let the derivative in Eq.  be equalλ is equal to 1.5 at the left branch curve, and the maximum is equal to 0 at the right branch curve. The results show that Eq. (λ, the maximum vertical displacement increases or decreases with the addition of inclination angle. When the ratio of in-situ stress is between 0 and 1.5, the maximum vertical displacement of the roof decreases with the increase of inclination angle.The function curve of Eq.  was presthat Eq.  has two that Eq. . The casλ is equal to 1.0. when λ is greater than 1.0, the maximum vertical displacement shifts downward and vice versa. As far as the variation of the maximum vertical displacement is concerned (As shown in Fig. λ is equal to 1.5 is the demarcation point of the maximum vertical displacement. When λ is greater than 1.5, the maximum vertical displacement increases and decreases with the change in the inclination angle. When λ is less than 1.5, the maximum vertical displacement decreases with the increase of the inclination angle. Thus, to directly present the pattern of asymmetric deformation of the roof in the above law, when the ratio of in-situ stress λ is equal to 0.6, 1.4, and 2.0, respectively, the function graph was drawn, i.e., the vertical displacement along the centerline of the roof, as shown in Fig. x-axis, namely the roof tilt upward. When the ratio of in-situ stress is greater than 1.0, the maximum vertical displacement point moves in the negative direction of the x-axis, namely the tilt down, as shown in Fig. As the aforementioned show that the roof asymmetrical deformation mode will be determined by the ratio of in-situ stress and inclination angle, and the mode of asymmetric deformation of the roof will be presented. In terms of the maximum vertical displacement deviating from the central position of the roof (As shown in Fig. A theoretical model was developed to describe the asymmetric deformation of the roof caused by inclination. The proposed model incorporates the deformation effect of the roof under the combined action of normal compression load and tangential shear load. Normal compression load bends the roof, while the tangential shear load causes the roof deformation along the inclined direction and changes the symmetry of the roof deformation. These two kinds of deformation effects are superimposed together, resulting in asymmetric roof deformation.The numerical method was used to investigate the asymmetric deformation characteristics of the roof with varying dip angles. The vertical displacement changes less, and total displacement increases faster as the increase of dip angle. The influence of horizontal displacement is small in the goaf with a small inclination, but the closure of the goaf with a large inclination arises from it. In terms of displacement distributions, inclination leads to the displacement of the roof being symmetrical along the strike and asymmetrical along the inclined direction. The numerical results were compared with the theoretical model, which shows that the roof deformation laws obtained by the two methods are consistent.The distance between the maximum subsidence point and the center of the roof was defined to characterize the degree of asymmetric deformation, the larger the distance is, the greater the degree of asymmetric deformation is; on the contrary, the smaller the asymmetric deformation. When λ > 1.0, the maximum deformation position shifts downward along the roof inclination, and the greater the degree of asymmetric deformation is with the increase of the ratio of in-situ stress. Similarly, when λ < 1.0, the maximum deformation position shifts upward to the tilt, and the smaller the initial stress ratio, the greater the degree of asymmetric deformation. When λ is constant, the degree of asymmetric deformation increases at first and then decreases with the increase of inclination angle. The degree of asymmetric deformation is the most when the dip angle is equal to 45°.There exist three modes of asymmetric deformation, which are determined by both dip angle and in-situ stress ratio λ. When λ < 1.0, the maximum subsidence position shifts upward along the dip, and the maximum vertical displacement decreases with the increase of the dip angle. When 1.0 < λ < 1.5, the maximum subsidence position migrates downward along the dip, and the maximum vertical displacement decreases with the inclination increase. When λ > 1.5, the maximum subsidence position is shifted downward along the dip. With the rise of the dip angle, the maximum vertical displacement gradually increases and then decreases.In this research, the dip effect mechanism of asymmetric deformation of the goaf roof was investigated by theoretical and numerical methods. A theoretical model was proposed for describing the asymmetric deformation of the roof. Then the degree of asymmetric deformation was characterized, and several modes of asymmetric deformation were revealed. The main conclusions have been summarized as followings.


In this work, we report evolution of atomic clusters in a highly under-expanded supersonic jet of Argon. A high resolution and sensitive Rayleigh scattering based experimental set-up is designed to overcome the limitations encountered in conventional set-ups. Further, the measurement range could be extended from a few nozzle diameters to 50 nozzle diameters. Simultaneously, we had been able to generate 2D profiles of the distribution of clusters inside the jet. This paves the way to track the growth of clusters along the flow direction experimentally, which until now was limited to few nozzle diameters. The results show that spatial distribution of clusters inside the supersonic core deviates considerably from the prediction of the free expansion model. We exploit this to estimate cluster growth along the expansion direction. Further, it is observed that the growth of the clusters gets saturated after a certain distance from the nozzle. At the jet boundary, we see substantial cluster strengthening immediately upstream of barrel shock while the normal shock exhibits disintegration of clusters. These observations are noticed for the first time, which, we believe will further the understanding of cluster dynamics in a supersonic jet. Furthermore, the information regarding cluster formation is an important aspect in the study of photo induced chemical reactions5. Clusters are formed when free expanding jet undergoes isentropic cooling along the flow and the temperature of the gas reaches below the condensation point. During this, the gas molecules get coagulated due to weak nuclear force and form clusters. Relatively large . Despite a number of works on the clusters in the last two decades9, accurate prediction of their size still remains a grey area. Further, the cluster size reported from different experiments differs by at least an order of magnitude under similar experimental conditions9. The well-known Hagena parameter10 and its modified version11 are simple empirical relations used to predict the cluster size for a particular nozzle operating at particular reservoir density and temperature. However, its predictions often differ from the experimental measurements12 which indicates further scope of including more parameters which are responsible for cluster growth. It is well known that the size of the cluster  depends on the system’s sensitivity as well as on the size of the clusters. Thus, each has its own advantages and limitations. For instance, Mie scattering requires wavelength of incident light to be smaller than the size of the cluster8 and Raman scattering cannot be applied to monoatomic gas. Rayleigh scattering is hence ideal for low pressure cluster jets. The accuracy in measuring the cluster size using Rayleigh scattering depends on the calibration. In many reported works, calibration is carried out by assuming the cluster size at the onset of the signal to be 100 atoms12. This approach is not universal as the detector sensitivity and light collection geometry vary for different setups. This vague assumption during the calibration can result in inaccuracy in the estimation of the cluster size11. To circumvent this, Reyleigh scattering technique is often combined with interferometry12. However, as mentioned earlier interferometry can only be used for measurements close to the nozzle. This limits the effective measurement range of the combined setup to a few nozzle diameters. Hence, Rayleigh scattering approach used to map cluster density profile needs to be independent as well as sensitive enough to measure low-density at relatively longer distances from the nozzle. Interferometric Rayleigh scattering technique has also been successfully demonstrated for turbulence velocity measurements19.The adopted techniques to measure cluster size can be broadly categorized as scatteringAs the evolution and dynamics of cluster growth at longer distances is very important, we significantly improved the sensitivity of Rayleigh scattering system. We adopted a sonic nozzle and the total density is estimated using free expansion model which does not have the need of supplementary approach to measure total density, thus making Rayleigh measurements independent. In our experiments, we use a pulsed ns Nd-YAG laser with high gain ICCD camera to image the spatial distribution of the scattering signal from the cluster. We improved our density detection limit to In the subsequent sections the experimental setup is described in section “The experimental setup for jet imaging is shown in Fig. l/s) mounted at the bottom (DN 160 CF flange) of the vessel and a Pfieffer ACP-15 dual stage root pump (230 l/m) is used as backing pump to the TMP. Root pump is also used for initial rough vacuum generation  argon gas is supplied to the valve at pressure ranging from 1–6 bar through high pressure gas supply line. Pressure inside the gas supply line is regulated by a precision needle valve and is monitored using a diaphragm type pressure transducer (DMP 320) having 1% accuracy.A pulsed nanosecond Nd-YAG laser  having 10 ns pulse for 1064 nm at 30 Hz is used as the laser source. Pulsed laser is preferred over continuous laser due to certain advantages. First, the laser pulse duration is small, hence the integration time of imaging system can be kept as short as laser pulse width , diffusion of light from the glass window, as well as back reflection from the surfaces of the optics used to align and focus the laser beam. We tried to minimize the laser background with precise alignment, by using Brewster windows at the entrance and the exit of the laser to the vacuum vessel. Positioning these windows very far 1.5 m) from the region of interest and shielding the diffused light from the window with multiple orifices placed along the beam also helps remove scattered background light. With this, we are able to reduce the background sufficiently to record the scattering signal from neutral argon atoms for number density as low as  m from t22. Hence, measurements are recorded in steady flow condition by synchronizing the laser within 1–1.5 ms region of the input gas pulse.To decrease the background filling, the jet is operated in short bursts by opening the pulse valve for 1.5 ms at 10 Hz using IOTA-One pulse valve controller. The background pressure increases initially due to dynamic gas injection and stabilizes after a few seconds based on the average gas injection rate established by the nozzle pressure and pumping rate of TMP. The pulse length is adjusted from 1 to 5 ms depending on the nozzle pressure  of the scattered signal is averaged over 100 frames to minimize the effects of the fluctuation in laser energy. Measurements are done at different spatial locations along the jet axis by moving the UHV translation stage of the valve in steps of 1 mm , V is the scattering volume and 12.Rayleigh scattering intensity for an incident light of intensity mentclass2pt{minimr) of the cluster can be related to number of atoms per cluster  in all the experiments and also the laser beam size. Thus, for a single pulse, we can safely replace the intensity 11 which is the ratio of atoms forming clusters to the total number of atoms. Mathematically, g is given by Equation  assumes In the subsequent discussion regarding calibration curve we see that contribution from neutrals is not significant relative to the cluster. Hence, Rayleigh scattering for a cluster jet is given by Eq. .7\documek is determined from calibration and 23 as shown in the Eq. (b is the angular factor (3 for monoatomic gas) and 24. For pulse duration of 1–5 ms, 23) and the orifice diameter which results in experimental value of flow rate is 0.6 mm. The absolute density determined by free expansion model with this approach has been substantiated experimentally24.In this work,  the Eq. . where, g and Equation  thus givg and 12. However, this would be a vague assumption for low pressure room temperature jet in our case11. Considering these discrepancies, we believe the product It is rather difficult to predict the value of This section is divided into subsections based on the experiment steps. In the first step we estimate the geometric constant using the calibration. In the second, constants of power law are estimated by measuring the scattering intensity at different reservoir (nozzle) pressures at different axial distances from the nozzle. Finally, in the third and last step spatial distribution of sing Eq. . Additiok) for each radial position is calculated by fitting a linear-quadratic surface to the data points. This compensates the difference in the scattered intensity produced by the change in differential scattering cross-section due to the tilt in optical axis of the individual pixel relative to the optical axis of all pixels of the camera combined. To minimize round off error during curve fitting, slope is determined in terms of counts/mbar and then translated to counts/no.density by multiplying a conversion factor Calibration is done by measuring the scattered intensity at different background pressures in the vessel ranging from 1 to 100 mbar. Figure 15.The most appropriate way to ensure cluster formation is by measuring the scattered signal from the jet at different nozzle pressures. In the absence of cluster formation, increase in the nozzle pressure will linearly increase Rayleigh signal as absolute value of total number density at any location inside the jet is linearly dependent on the reservoir pressure. However, when clusters are formed, it has been reported that scattering signal follows power law Figure Figure 10 for nozzle pressures of 4 bar and 6 bar come out to be 4205 and 5047 respectively. Using Hagena parameter, one can estimate the theoretical value of liquid mass fraction for from Tao’s work11 which is approximately 0.15 for both the cases. It should be noted that g regardless of axial location. Our results, on the other hand, show that g can vary along the axis. Apparently, Hagena model corresponds to data from a single axial location near the nozzle exit. As a result, it only makes sense to compare our data to the predictions of Hagena model in the area near the nozzle exit. The values of atoms/cluster for 27 are 965 atoms/cluster and 1481 atoms/cluster for The Hagena parameters estimated by scaling law of Hagena28, and Young’s theoretical approach 29 for nozzle diameter of 0.6 mm estimated from the flow rate. It is interesting to see that the emission intensity is higher at barrel shocks, while it is completely absent at normal shocks. This indicates that clusters are present in significant number at barrel shocks. We believe this effect may be related to absolute temperature of the gas at shock regions. At normal shock, flow becomes subsonic which increases the static temperature of the gas. For argon jet, temperature at shock front , Mach number should be greater than 2.71  and the size of cluster  required to estimate cluster size are estimated using established free expansion model for the flow rate measured experimentally. Enhancement in cluster formation is reported in terms of the product of liquid mass fraction (