True Width Research Articles

Detection of moisture and size of winter melon seeds based on hyperspectral imaging and convex polygon size measurement

The level of moisture content and size of winter melon seeds affect their storage, germination and growth processes. Moderate moisture and size are essential for seed germination and growth. Therefore, detecting the moisture and size of winter melon seeds is beneficial to improve their germination rate. Traditional seed moisture testing methods are complex to operate and require destructive sample preparation or chemical treatment. Common dimensional measurement methods are also time-consuming and laborious. Hyperspectral imaging technology can acquire information about the surface and internal structure of the target separately, it can be used to quickly and non-destructively detect the moisture and size of winter melon seeds. In this study, partial least squares regression (PLSR) and partial least squares support vector machine (LSSVM) models were established to predict the moisture content of winter melon seeds by using reflection and transmittance spectral data. The models were optimized using five variable selection methods. The optimal performance of the LSSVM model based on the CARS algorithm was achieved in both single reflection and transmission spectra. The RP2 and RMSEP of the model based on the reflection spectra were 0.9667 % and 0.0215 %, respectively. The RP2 and RMSEP of the model based on the transmission spectra were 0.9644 % and 0.0223 %, respectively. In low-level data fusion, the LSSVM model based on the CARS algorithm also achieved optimal performance, but with only a little improvement compared to a single model (reflection spectra or transmission spectra), with RP2 and RMSEP of 0.9679 % and 0.0212 %, respectively. In the mid-level data fusion, the LSSVM model also based on the CARS algorithm achieved the optimal performance, and the performance of the model was further improved. The RP2 and RMSEP of the model were 0.9738 % and 0.0191 %, respectively. Finally, the image processing algorithm and the convex polygon size measurement method was proposed to measure the size of winter melon seeds. The absolute error between the calibrated winter melon seed length and width and the true length and width was less than 0.22 mm, and the relative error was less than 2 %. The results show that hyperspectral imaging technology can accurately detect the water content of winter melon seeds. Data fusion method and LSSVM model based on CARS algorithm can detect the water content of winter melon seeds more accurately. The image processing algorithm combined with the convex polygon size measurement method can be effectively used to detect the size of winter melon seeds with high precision.

The Use of Linear Formulas to Estimate Glenoid Bone Loss in the Lebanese Population: A 3-Dimensional Computed Tomography Study.

Glenoid bone loss (GBL) is common in patients with shoulder instability and plays a major role in surgical decision-making. While a plethora of GBL estimation methods exist, all of which present specific challenges, recent studies have developed simple linear formulas estimating GBL based on glenoid height. To assess the correlation between glenoid height and width, and to develop specific formulas based on age and sex to calculate the native glenoid width in the Lebanese population. Cross-sectional study; Level of evidence, 3. Computed tomography scans for 202 normal shoulders were extracted from our database. The glenoids were reconstructed in 3 dimensions and their width and height were measured. Glenoid width and height were compared between male and female groups. Correlation analysis was also performed on the width, height, age, and body mass index. Formulas estimating glenoid width were developed using regression analysis including all variables significantly influencing the model. Results were then compared with the values calculated using previously published formulas to determine the external validity when using linear formulas to estimate GBL. Significant differences were found between men and women. Regression analysis found that glenoid height and width strongly influenced the model, and that age showed a weak but significant correlation; therefore, the following 2 sex-specific formulas were developed: width (mm) = 6.1 + 0.51 ×height+ 0.03 ×age, and width (mm) = 4.55 + 0.51 ×height+ 0.03 ×age, in men and women, respectively. The values yielded from the formulas developed in this study and the true width significantly differed from those calculated from previous reports. A strong correlation was found between glenoid height and width in a the Lebanese population and demonstrated that glenoid width can be accurately calculated based on the glenoid height and patient's age and sex using the following simplified formulas: width (mm) = 6 + 0.5 ×height+ 0.03 ×age, and width (mm) = 4.5 + 0.5 ×height+ 0.03 ×age, in men and women, respectively.

Construction of the Ecological Security Pattern in Xishuangbanna Tropical Rainforest Based on Circuit Theory

Urban modernization and economic globalization have led to significant changes in traditional natural landscapes. The unregulated and large-scale expansion of rubber plantations in Xishuangbanna has resulted in water and scenic forests being replaced by rubber forests and the complex rainforest ecosystem being replaced by simple artificial forests. This has resulted in increasingly prominent ecological problems such as soil erosion, regional microclimate changes, and sharp declines in biodiversity. The ecological security pattern is an important way to protect regional ecological sustainability. Taking the tropical rainforest in Xishuangbanna as an example, this study identified ecological sources through the evaluation of the importance of ecosystem services, constructed resistance surfaces through ecological sensitivity evaluation, and used circuit theory to simulate ecological processes in heterogeneous landscapes by calculating “electricity” or “resistance”, thereby identifying ecological corridors and key ecological nodes. The results identified 31 ecological source areas, 65 key ecological corridors, 7 potential ecological corridors, 37 ecological pinch points, and 99 ecological barriers. The overall distribution of ecological sources was scattered, with higher density in the northwest and southeast regions. Ecological corridors were distributed along high mountains, and both ecological sources and corridors were mainly composed of forest land. Based on circuit theory, this study filled the gap in the MCR model’s inability to identify the true width of corridors due to ignoring the randomness of biological migration. It determined the spatial range of ecological corridors and the specific locations of ecological nodes and barriers, providing a reference for solving ecological problems in Xishuangbanna, such as “rainforest fragmentation”.

Determination of the width of the presacral space on magnetic resonance imaging among adults in south-western Nigeria.

The presacral space is a clinically relevant potential space and contents may give rise to a variety of benign and malignant conditions, hence the need for detailed knowledge of its dimensions. To determine the width of the presacral space and existing variations among adults in south-western Nigeria using a magnetic resonance imaging (MRI) technique. A total of 369 consenting adults were included in the study. Measurements of the presacral space were then made electronically by consensus of two radiologists. Values derived were recorded and subjected to analyses of variance. The mean normal widths of the presacral space in men and women were 11.7 mm and 11.1 mm at the S1 level, 11.7 mm and 10.35 mm at the S2 level, and 12.3 mm and 9.7 mm at the S3 level, respectively. Measurements of the presacral space width were significantly larger in the male population. Variations in the dimensions due to age greater than 40 years, male sex, and increasing body mass index (BMI) were also noted. This study provides baseline dimensions under more physiological conditions and gives more accurate information about the true width of the space in Nigerian adults. Variations due to age, sex, and BMI may also be considered while interpreting abnormal values.

Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *

The purpose of this study is to recover the diffuse interface width parameter for nonlinear Allen–Cahn equation by a continuous data assimilation algorithm proposed recently. We obtain the large-time error between the true solution of the Allen–Cahn equation and the data assimilated solution produced by implicit–explicit one-leg fully discrete finite element methods due to discrepancy between an approximate diffuse interface width and the physical interface width. The strongly A-stability of the one-leg methods plays key roles in proving the exponential decay of initial error. Based on the long-time error estimates, we develop several algorithms to recover both the true solution and the true diffuse interface width using only spatially discrete phase field function measurements. Numerical experiments confirm our theoretical results and verify the effectiveness of the proposed methods.

How does the chromatic number of a random graph vary?

AbstractThe chromatic number of a graph is a fundamental parameter, whose study was originally motivated by applications ( is the minimum number of internally compatible groups the vertices can be divided into, if the edges represent incompatibility). As with other graph parameters, it is also studied from a purely theoretical point of view, and here a key question is: what is its typical value? More precisely, how does , the chromatic number of a graph chosen uniformly at random from all graphs on vertices, behave? This quantity is a random variable, so one can ask (i) for upper and lower bounds on its typical values, and (ii) for bounds on how much it varies: what is the width (for example, standard deviation) of its distribution? On (i) there has been considerable progress over the last 45 years; on (ii), which is our focus here, remarkably little. One would like both upper and lower bounds on the width of the distribution, and ideally a description of the (appropriately scaled) limiting distribution. There is a well‐known upper bound of Shamir and Spencer of order , improved slightly by Alon to , but no non‐trivial lower bound was known until 2019, when the first author proved that the width is at least for infinitely many , answering a longstanding question of Bollobás. In this paper we have two main aims: first, we shall prove a much stronger lower bound on the width. We shall show unconditionally that, for some values of , the width is at least , matching the upper bounds up to the error term. Moreover, conditional on a recently announced sharper explicit estimate for the chromatic number, we improve the lower bound to order , within a logarithmic factor of the upper bound. Second, we will describe a number of conjectures as to what the true behaviour of the variation in is, and why. The first form of this conjecture arises from recent work of Bollobás, Heckel, Morris, Panagiotou, Riordan and Smith. We will also give much more detailed conjectures, suggesting that the true width, for the worst case , matches our lower bound up to a constant factor. These conjectures also predict a Gaussian limiting distribution.

Virtual outcrop-based analysis of channel and crevasse splay sandstone body architecture in the Middle Jurassic Ravenscar Group, Yorkshire, NE England

Well-exposed fluvio-deltaic deposits of the Middle Jurassic Ravenscar Group (Yorkshire coast) provide a direct analogue for North Sea reservoirs, but previous studies were restricted to a few accessible bays. This study used lidar and drone photogrammetry to create near-continuous virtual outcrops, 21 km long and 30–150 m thick, in an area which is largely inaccessible. Remote sensing data were supplemented by 45 outcrop logs and data from 27 pre-existing, behind-outcrop boreholes to improve understanding of the geometries, architectures and stacking patterns of 10 distinct sandbody types; the most important reservoir analogue units are channels and crevasse splay bodies. Channel bodies are 30–2038 m wide and 2–28 m thick with W / T ratio ranges of 5–105; the majority are multi-storey with an average thickness of 8 m and width of 182 m, while the single-storey channel bodies average 4 m thick and 50 m wide. Crevasse splays are 15–>1285 m wide and 0.3–6.5 m thick with W / T ratio ranges of 50–>541. There is a marked lateral and vertical change in channel body dimensions and facies proportion. The study suggests that the channel architecture and depositional nature of these successions are controlled by base-level fluctuation and floodplain topography. Supplementary material : Fieldwork-based sedimentary logs, borehole core-based sedimentary logs with facies proportions, workflow to prepare virtual outcrop, method to estimate true width of sandbody, correlation panel of crevasse splay bodies, interpreted virtual outcrops, and dimensional data of channel, crevasse splay and crevasse channel bodies are available at https://doi.org/10.6084/m9.figshare.c.5795793

Evaluation Analysis on Leakage Performance for Beam Seal With Two Sealing Areas

As a special type of aviation hydraulic pipe joint, a beam seal comprises two annular sealing areas. This paper presented a leakage model for an annular sealing area based on a developed three-dimensional percolation grid model and the porous medium theory. Both average contact pressure and true contact width of the beam seal were simulated using the finite element method. An experimental study of beam seal verified the accuracy of the numerical results. Considering that the two sealing areas and the groove in the beam seal form an isolated sealing system, a leakage model of the beam seal is proposed based on the leakage model for annular sealing area. We evaluated the effects of the roughness of the surface, preload and fluid pressure on the leak rate of the beam seal. Furthermore, the geometry of the beam seal was modified to improve its sealing performance. This study provides an evaluation method for optimizing the design and improving the sealing performance of the beam seal.

Objective Laryngoscopic Measures From Older Patients With Voice Complaints and Signs of Aging.

The purpose of this study was to use objective measures of glottal gap, bowing, and supraglottic compression from selected images of laryngoscopic examinations from adults over 60 years of age with voice complaints and signs of aging to test current hypotheses on whether degree of severity impacts treatment recommendations and potential follow-through with treatment. Records from 108 individuals 60 years or older with voice complaints and signs of aging were reviewed. Three objective measures (normalized glottal gap area [NGGA], total bowing index, and normalized true vocal fold width) were derived. Each measure was subsequently divided into three categories by severity: absence, small degree, or large degree. Nonparametric statistics tested associations between severity and treatment recommendations as well as potential follow-through. Noninvasive treatments (observation/voice therapy) were marginally associated with no glottal gap (p = .09). More invasive treatments (injection/bilateral thyroplasty) were associated with glottal gaps being present (p = .026), but bilateral thyroplasty recommendations were not significantly associated with the largest gaps. Treatment modalities were not characterized by specific severity categories for any of the objective measures. No significant differences were found for any of the three objective measures between those who followed through with recommended treatment and those who did not. Results demonstrated some support for current hypotheses on how degrees of severity of objective measures relate to treatment recommendations. Of the three measures, NGGA appears to be more informative regarding treatment recommendations and follow-through, but due to low power, larger sample sizes are needed to confirm clinical relevance.

A precise method to determine the energy scale and resolution using gamma calibration sources in a liquid scintillator detector

Gamma sources are routinely used to calibrate the energy scale and resolution of liquid scintillator detectors. However, non-scintillating material surrounding the source introduces energy losses, which may bias the determination of the centroid and width of the full absorption peak.In this paper, we present a general method to determine the true gamma centroid and width to a relative precision of 0.03% and 0.50%, respectively, using energy losses predicted by the Monte Carlo simulation. In particular, the accuracy of the assumed source geometry is readily obtained from the fit. The method performs well with experimental data in the Daya Bay detector.

Assessing the Projection Correction of Coronal Mass Ejection Speeds on Time‐of‐Arrival Prediction Performance Using the Effective Acceleration Model

AbstractWhite light images of coronal mass ejections (CMEs) are projections on the plane‐of‐sky (POS). As a result, CME kinematics are subject to projection effects. The error in the true (deprojected) speed of CMEs is one of the main causes of uncertainty to Space Weather forecasts, since all estimates of the CME time‐of‐arrival (ToA) at a certain location within the heliosphere require, as input, the CME speed. We use single viewpoint observations for 1,037 flare‐CME events between 1996 and 2017 and propose a new approach for the correction of the CME speed assuming radial propagation from the flare site. Our method is uniquely capable to produce physically reasonable deprojected speeds across the full range of source longitudes. We bound the uncertainty in the deprojected speed estimates via limits in the true angular width of a CME based on multiview‐point observations. Our corrections range up to 1.37–2.86 for CMEs originating from the center of the disk. On average, the deprojected speeds are 12.8% greater than their POS speeds. For slow CMEs (VPOS < 400 km/s) the full ice‐cream cone model performs better while for fast and very fast CMEs (VPOS > 700 km/s) the shallow ice‐cream model gives much better results. CMEs with 691–878 km/s POS speeds have a minimum ToA mean absolute error (MAE) of 11.6 h. This method, is robust, easy to use, and has immediate applicability to Space Weather forecasting applications. Moreover, regarding the speed of CMEs, our work suggests that single viewpoint observations are generally reliable.

Comparative Accuracy of 1.5T MRI, 3T MRI, and Static Ultrasound in Diagnosis of Small Gaps in Repaired Flexor Tendons: A Cadaveric Study

We hypothesized that magnetic resonance imaging (MRI) would more accurately diagnose small gaps (<6 mm) after flexor tendon repair than static ultrasound (US) and that suture artifact would negatively impair accuracy. A laceration of the flexor digitorum profundus was created in 160 fresh-frozen cadaveric digits and randomized to either an intact repair (0-mm gap) or repairs using a locked 4-strand suture repair with either 4-0 Prolene, Ethibond, or and gaps of 2, 4,or 6 mm; or no suture in which 2-, 4-, or 6-mm gaps were created without a suture crossing the repair site. We performed 1.5T and 3T MRI and static US studies; gap widths were estimated by radiologists blinded to suture presence and true gap widths. The 1.5 and 3.0T MRI had a lower mean error than US for gap sizes 0 and 2 mm. All 3 modalities performed similarly for 4- and 6-mm gaps. Documentation of imaging artifact worsened error, and odds of seeing artifacts were 1.72 higher with MRI than with US. Suture did not worsen artifact nor impair accuracy for any of the 3 modalities. When no suture was used, all 3 modalities significantly overestimated the true gap. MRI is most accurate for small gaps less than 4 mm. Although all modalities overestimated gap sizes in specimens with a 0-mm gap (intact tendon repair), mean overestimation (<2 mm) was not clinically relevant. Ultrasound overestimated 2-mm gaps (clinically intact repairs), whereas MRIs did not. We recommend MRI for evaluation of gaps after flexor tendon repair. The 1.5T has slightly better sensitivity and specificity for distinguishing clinically intact (gap < 3 mm) from clinically impaired (gap > 3 mm) repairs than the 3T. Accurate diagnosis of intact repairs or small gaps (<3 mm) might prevent unnecessary exploration or allow modification of rehabilitation protocols. Diagnosis of clinically relevant gaps (3-6 mm) may allow for earlier revision surgery before significant tendon retraction and adhesions develop, possibly necessitating a staged reconstruction.

DSC-based Generation of Sinusoidal PWM Signals with the Least Number of Variables for Single-, Two- and Three-phase inverters(Dept.E)

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A 4-year Retrospective Review of the Presence and Pattern of Ventricular Hyperadduction Following Unilateral Vocal Fold Paralysis, Paresis, and Unilateral Cordectomy

The aim of our study was to determine the presence and pattern of ventricular hyperadduction (VH) following unilateral vocal fold (VF) paralysis/paresis and that following unilateral cordectomy (UC). The authors independently reviewed charts and flexible videostroboscopic recordings of 214 patients diagnosed with unilateral VF paralysis/paresis and those who had undergone UC from 2015 to 2018. The presence and pattern of VH was noted. VH was considered to be present when the false vocal fold (FVF) obliterated 50% or more of the true vocal fold width during phonation, with or without FVF vibration. The true vocal fold width was considered to be that which was visible on abduction of the VFs. Categorical variables were presented in numbers and percentages and qualitative variables were correlated using Chi-Square test. Odds ratio with 95% Confidence Interval was calculated. In 154 patients diagnosed as unilateral VF paralysis/paresis 85 patients had a VH pattern (55.19%) with contralateral VH observed in 74 (87.05%), ipsilateral VH observed in 6 (7.05%) and bilateral VH observed in five patients (5.88 %). The total number of patients of UC was 60 with 36 of these patients developing a VH (60%). Ipsilateral VH was observed in 28 of these 36 patients (77.77%), three patients developed contralateral VH (8.33%) and five patients developed bilateral VH (13.88%). Ipsilateral ventricular hyper-adduction following unilateral cordectomy in the group of patients that develop hyperadduction is a significant finding in our study suggesting possibility of unilateral central phonatory control of the FVF. Contralateral ventricular hyper-adduction following unilateral paralysis and paresis, in the group of patients that develop hyperadduction is a significant finding in our study and this finding resonates with previously published papers. A finding of unilateral VH may serve as a possible indicator of the occasionally challenging diagnosis of vocal fold paresis. Retrospective, Observational.

Connecting 3D Evolution of Coronal Mass Ejections to Their Source Regions

Abstract Since coronal mass ejections (CMEs) are the major drivers of space weather, it is crucial to study their evolution starting from the inner corona. In this work we use graduated cylindrical shell model to study the 3D evolution of 59 CMEs in the inner (&lt;3 R ⊙) and outer (&gt;3 R ⊙) corona using observations from COR-1 and COR-2 on board the Solar TErrestrial RElations Observatory (STEREO) spacecraft. We identify the source regions of these CMEs and classify them as CMEs associated with active regions (ARs), active prominences (APs), and prominence eruptions. We find 27% of CMEs show true expansion and 31% show true deflections as they propagate outwards. Using 3D kinematic profiles of CMEs, we connect the evolution of true acceleration with the evolution of true width in the inner and outer corona, thereby providing observational evidence for the influence of the Lorentz force on the kinematics to lie in the height range 2.5–3 R ⊙. We find a broad range in the distribution of peak 3D speeds and accelerations, ranging from 396 to 2465 km s−1 and 176 to 10,922 m s−2 respectively, with a long tail toward high values coming mainly from CMEs originating from ARs or APs. Further, we find that the magnitude of true acceleration is inversely correlated with its duration with a power-law index of −1.19. We believe that these results will provide important inputs for the planning of upcoming space missions that will observe the inner corona and for models that study CME initiation and propagation.

Automatic Crack Detection and Measurement of Concrete Structure Using Convolutional Encoder-Decoder Network

The detection and measurement of crack at pixel level is a challenge to existing methods. To overcome this challenge, this paper proposes a convolutional encoder-decoder network (CedNet) to detect crack from image, and the maximum widths and orientations of cracks are measured using image post-processing techniques. To realize this, a database including 1800 crack images (with 761×569 pixel resolution) taken from concrete structures is built. Then the CedNet is designed, trained and validated using the built database. The validating results show 98.90% accuracy, 93.58% precision, 94.73% recall, 93.18% F-measure, 87.23% intersection over union (IoU) of crack and 98.82% IoU of background. Subsequently, the robustness and adaptability of the trained model is tested. To measure true maximum widths and orientations of cracks, a laboratory experiment is carried out to calibrate a relation between ratio (pixel distance / real distance) and field of view (camera's view range on concrete surface included in image) and distance from the smartphone to concrete surface. In the post-processing techniques, the perspective transformation is employed to correct distorted images caused by the existence of the oblique angles between the smartphone and concrete surfaces. Then the maximum widths and orientations of cracks in predicted results are measured respectively using the Euclidean distance transformation and least squares principle. As comparison, two existing deep learning-based crack detection and measurement method are used to examine the performance of the proposed approach. The comparison results show that the proposed method substantiates quite good performance to detect cracks and measure maximum widths and orientations of cracks in our database.

Preoperative assessment of medial acetabular wall bone stock in dysplastic deformation

Acetabular reconstruction remains to be one of the crucial aspects of total hip replacament in developmental dysplasia of the hip (DDH) that provides endoprosthesis’ long-term stability and general success of the operation. Among the parameters that influence surgical technique of acetabular reconstruction, medial wall bone stock of the endoprosthesis’ bed zone should be taken into consideration. Purpose of the work to assess medial wall bone stock in the site of acetabular component’s bony bed in normal and dysplastic deformed hips and to define correlation with indices of sphericity and sectoral deficiency of the acetabulum based on MSCT-morphomerty. Materials and methods. A complex comparative MSCT-mophometric investigation of 32 normal hips and 65 hips with DDH (Crowe I – 26 hips (40.0 %), Crowe II – 23 hips (35.4 %), Crowe III – 16 hips (24.6 %)) was performed. There were assessed width of the medial wall bone stock in the projection of the crucial ligament’s and acetabular component’s bony beds according to the proposed method; their correlation with indices of femoral head’s cranial migration and acetabular horizontal sphericity angle. Results. It has been revealed that measurements in he site of the crucial ligament’s bony bed based on pelvic images obtained by a conventional biplanar X-ray remains to be biased and doesn’t correspond to true width of medial acetabular wall bone stock. Absolute width of the medial acetabular wall in sites of the crucial ligament’s / acetabular component’s bony beds carried out through the special MSCT-recontruction methodic was defined as: 4.3 mm [3.3; 4.8]/7,2 mm [6.2; 7.8] for normal hips, 9.95 mm [7.5; 11.6]/11.85 mm [9.8; 13.5] for Crowe I hips,15 mm [11.7; 17.3]/15,7 mm [13,5; 17,3] for Crowe II hips and 15.45 mm [13.7; 19.8]/16.05 mm [12.8; 20.2] for Crowe III hips, respectively. Correlations between medial acetabular wall bone stock in site of acetabular component’s bony bed and indices of femoral head’s cranial migration and acetabular horizontal sphericity angle were defined as: r = 0.36 (P = 0.006); r = 0.36 (P = 0.007), respectively. Conclusions. Weak correlation of medial acetabular wall bone stock with indices of acetabular sphericity and sectoral deficiency requires the necessity of independent evaluation of this index during preoperative planning. Due to the impossibility of the index assessment based on the conventional pelvic X-ray, application of elaborated MSCT-morphometric methodic seems to be clinically valuable and should be applied during preoperative examination of patients with DDH.

Remplissage Procedure: When and How?

Hill-Sachs lesions were first described in 1940 as grooved defect in the posterior aspect of the humeral head associated with traumatic anterior glenohumeral dislocation. The reported incidence of ...

Shock‐thermal history of the Agoudal (IIAB) iron meteorite from microstructural studies

AbstractThe Agoudal IIAB iron meteorite exhibits only kamacite grains (~6 mm across) without any taenite. The kamacite is homogeneously enriched with numerous rhabdite inclusions of different size, shape, and composition. In some kamacite domains, this appears frosty due to micron‐scale rhabdite inclusions (~5 to 100 μm) of moderate to high Ni content (~26 to 40 wt%). In addition, all the kamacite grains in matrix are marked with a prominent linear crack formed during an atmospheric break‐up event and subsequently oxidized. This feature, also defined by trails of lowest Ni‐bearing (mean Ni: 23 wt%) mm‐scale rhabdite plates (fractured and oxidized) could be a trace of a pre‐existing γ–α interface. Agoudal experienced a very slow rate of primary cooling ~4 °C Ma−1 estimated from the binary plots of true rhabdite width against corresponding Ni wt% and the computed cooling rate curves after Randich and Goldstein (1978). Chemically, Agoudal iron (Ga: 54 ppm; Ge: 140 ppm; Ir: 0.03 ppm) resembles the Ainsworth iron, the coarsest octahedrite of the IIAB group. Agoudal contains multiple sets of Neumann bands that are formed in space and time at different scales and densities due to multiple impacts with shock magnitude up to 130 kb. Signatures of recrystallization due to postshock low temperature mild reheating at about 400 °C are also locally present.

New results on orbital resonances.

Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently reexamined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called "low-eccentricity resonant bridges" connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some - though not necessarily entire - resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances.