Orbital Shape Research Articles

Orbital Eccentricity Study of Planets: A Comparative Analysis of Manual Simulation and Digital Visualization

Understanding planetary orbits is a fundamental concept in astronomy. Many secondary school students encounter difficulties comprehending the shape and characteristics of orbits, which are not perfect circles but ellipses with varying degrees of eccentricity. These challenges are particularly evident when students are tasked with sketching or calculating the eccentricity of a planet's orbit, a measure of how elongated the orbit is. This study aims to explore and compare the efficacy of two pedagogical approaches manual simulation and digital simulation—in enhancing students' understanding of planetary orbit shapes and the concept of eccentricity. A descriptive-comparative research design is employed to depict and contrast the effectiveness of these two teaching methods. The experiment, crafted based on expert design, involves four qualified astronomy educators to apply both approaches. The manual simulation requires students to draw orbits and compute eccentricity manually, whereas the digital simulation leverages software to visualize the motion of planetary orbits. Evaluation is conducted through Focus Group Discussions (FGD) with four subject matter experts to provide feedback on the effectiveness of the two methods, the challenges faced by students, and the level of comprehension achieved. The results from the manual experiment indicate that the orbital eccentricity ranges between 0.2 and 0.4, suggesting that the planets' orbits are elliptical. These findings align with Kepler’s laws, which state that planetary orbits are elliptical, with the Sun at one of the foci. Results from the NASA Eyes application further corroborate this, showing that the orbits of planets in the solar system are indeed elliptical, both at perihelion (the point closest to the Sun) and aphelion (the end farthest from the Sun). In conclusion, this research substantiates that the orbits of planets in the solar system are elliptical, consistent with Kepler's laws.

Surgical Correction of Unicoronal Synostosis: Fronto-orbital Distraction versus Calvarial Switch.

There is a need for a new, less invasive surgical option for unicoronal synostosis (UCS). The aim of this study was to compare the resulting morphology and symmetry in patients with UCS following fronto-orbital distraction (FOD) or calvarial switch (CS). 79 patients with isolated UCS operated between 2005 and 2021 were analyzed. Follow-up was until 3 years of age. Angles describing orbital dystopia (ODA) and the anterior cranial fossa deviation and cant (ACFD and ACFC, respectively) were measured. Key linear dimensions, cranial cavities, and indices were calculated. 66 patients were included (14 in the FOD group and 52 in the CS group). The 3-year follow-up revealed significant improvement in all angles in both groups, with significant superiority in ODA correction following FOD (median improvement of 5.7 degrees as compared with 3.3 degrees after CS). Additionally, nasal and orbital volumes tended to be smaller, especially following CS; however, FOD resulted in a smaller absolute difference in orbital volume. Asymmetry in the orbital, nasal, and sphenoid regions also improved at the 3-year follow-up in both groups, although FOD resulted in complete normalization of the affected orbital shape and significantly improved overall asymmetry relative to that observed in the CS group. This study found that FOD achieves superior overall symmetry, as well as better shape correction of the cranium, as compared with CS, while also being less invasive. These findings suggest FOD as a safe and effective alternative to correct UCS and possibly the preferred surgical method.

Variations in orbital morphology, globe:orbit volume relation, and ophthalmological outcome in unicoronal synostosis.

Nonsyndromic unicoronal synostosis is associated with variability of severity in orbital morphology and ophthalmological manifestations. The relation between the two is not fully understood, nor how surgical treatment with fronto-orbital advancement and remodelling (FOAR) changes the relation. The aim of this study was to elucidate associations between ophthalmological manifestations and variations in orbital morphology and globe:orbit volume ratios preoperatively and at long-term follow-up after surgery. Twelve children referred to Uppsala Craniofacial Center who underwent computed tomography and standardized ophthalmological examinations regarding strabismus, spherical equivalent, astigmatism, anisometropia, and subnormal vision preoperatively and at 3 years of age were included. Orbits and globes were segmented. Principal component analysis elucidated morphological variation, and symmetry between orbital pairs was measured as the Dice similarity coefficient and globe:orbit volume ratios were calculated. The defined orbital shape variations were correlated with strabismus, refractive error, and subnormal vision. Different shape variations were associated with strabismus pre- and postoperatively and ipsi- and contralateral astigmatism. Greater improvement in orbital symmetry after surgery was associated with improvement in astigmatic anisometropia and new onset strabismus at follow-up. A small globe:orbit volume ratio was associated with preoperative strabismus, while the opposite was seen at follow-up. Different mechanisms seem to cause strabismus pre- and postoperatively, and FOAR might not sufficiently correct orbital morphology.

Efficient and Accurate Force Replay in Cosmological-baryonic Simulations

We construct time-evolving gravitational potential models for a Milky Way–mass galaxy from the FIRE-2 suite of cosmological-baryonic simulations using basis function expansions. These models capture the angular variation with spherical harmonics for the halo and azimuthal harmonics for the disk, and the radial or meridional plane variation with splines. We fit low-order expansions (four angular/harmonic terms) to the galaxy’s potential for each snapshot, spaced roughly 25 Myr apart, over the last 4 Gyr of its evolution, then extract the forces at discrete times and interpolate them between adjacent snapshots for forward orbit integration. Our method reconstructs the forces felt by simulation particles with high fidelity, with 95% of both stars and dark matter, outside of self-gravitating subhalos, exhibiting errors ≤4% in both the disk and the halo. Imposing symmetry on the model systematically increases these errors, particularly for disk particles, which show greater sensitivity to imposed symmetries. The majority of orbits recovered using the models exhibit positional errors ≤10% for 2–3 orbital periods, with higher errors for orbits that spend more time near the galactic center. Approximate integrals of motion are retrieved with high accuracy even with a larger potential sampling interval of 200 Myr. After 4 Gyr of integration, 43% and 70% of orbits have total energy and angular momentum errors within 10%, respectively. Consequently, there is higher reliability in orbital shape parameters such as pericenters and apocenters, with errors ∼10% even after multiple orbital periods. These techniques have diverse applications, including studying satellite disruption in cosmological contexts.

Online Task Switching and Scheduling Method for Attitude–Orbit–Shape-Distributed Control of Large Space Ring Structures

The attitude, orbit, and shape control actuators of large space structures on orbits are functional overlapping and task coupled, resulting in actuator redundancy and high-energy consumption. This paper explores the integrated attitude–orbit–shape control problem of large space ring structures and proposes an online task switching and scheduling method for multiple actuators of space structures (OTSS-MASS). An adaptive allocation framework is proposed for the task switching of distributed actuators. The objectives of attitude–orbit–shape control are decomposed into attitude adjustment, orbit change, and shape maintenance tasks through a task decomposition algorithm. Task value estimation models are designed to guide a greedy task allocation of actuators. The adaptive allocation framework achieves online task reconfiguration for multiple distributed actuators, thereby enhancing the maneuverability of large space structures, improving actuator work efficiency, and reducing energy consumption in orbit. Simulation results demonstrate that OTSS-MASS outperforms the conventional actuator distribution methods. The overall effectiveness is improved by over 24% in terms of the comprehensive index, time index, trajectory index, and shape index.

Orbital Debris Shape Effect Investigations for Mitigating Risk

Orbital Debris Shape Effect Investigations for Mitigating Risk

Evaluation of Shape and Volume Restoration of Orbit after Reduction of Orbitozygomatic Fractures

Abstract Background The appearance of the Orbitozygomatic complex (OZC) fracture terminology is contributed to the fact that a fracture in the lateral side of the midface is not strict to anatomical boundaries, however, it involves the zygoma, maxilla and orbital structures. Orbitozygomatic complex fractures are one of the most commonly encountered injuries of the craniofacial skeleton. The solid zygomatic bone acts as a part of the vertical and horizontal facial buttress, along with the malar eminence, which plays a key role in the determination of facial morphology. It forms a significant portion of the floor and lateral wall of the orbit thus it acts as one of the most common contributors to the orbital integrity, restoration of orbital volume is essential to prevent enophthalmos. Objective Evaluate restoration of orbital shape, volume and globe position in the anterior-posterior plane after reduction of zygomatico-orbital fractures. Methods This Prospective observational study was done from March 2023 to August 2023 at plastic, burn and maxillofacial department in El Demerdash Hospital, Ain Shams University. Eighteen (18) adult patients, complaining of post traumatic orbito-zygomatic fractures requiring operative intervention, were included in this study. Evaluations of orbital shape and differences between orbital volume measurements (damaged orbits compared to intact orbits before and after surgery), orbital volume calculated from area marked by delineating bony landmarks of the orbit interconnected by freehand cursor manually on a series of CT slices in the axial plane, the CT images were exported to the CMF orbital analysis software (adw4.7), where the volume was calculated automatically, Depth: measured from orbital rim to the orbital apex, from outer optic foramen to the middle point of a line passing through lateral and medial orbital rims; width: Maximal horizontal distance from lateral to medial rim and height: measured from superior to inferior margin at their maximum distance perpendicular to orbital width. Results The mean volume of the affected orbit throughout our study showed significant decrease from 24.81 ± 2.04 cm3 before the operation to 23.38 ± 2.22 cm3 after the surgical intervention (P < 0.001), indicating a highly significant difference, where volume has significantly increased on fractured side preoperative in comparison to the sound side (P = 0.016) indicating significant effect of trauma on increasing orbital volume from normal, while no statistical difference was noted (P = 0.75) between orbital volume of fractured side postoperatively 23.38 ± 2.22 cm3 and the sound side 23.24 ± 1.64 cm3, indicating proper reduction and restoration of orbital volume to near normal postoperatively, increased depth (45.46 ± 3.26), width (38 ± 2.94) and height (35.7 ± 2.98) of fractured side preoperatively; this increase was statistically significant, While Depth and width showed more increase than height; values were more statistically significant and return to near normal postoperatively (42.96 ± 2.68), (36 ± 2.88) and (34.23 ± 3.45) respectively; this decrease was still significant statistically except for height where it was non-significant, indicating better restoration of height than depth and width attributed to its lesser increase from the first place, as values of sound side weree (41.64 ± 2.25), (34.56 ± 3.25) and (34.51± 3.52) respectively. Conclusion Our study suggests that the surgical reduction of orbitozygomatic fractures has a significant role in restoration of the orbital shape, volume, and globe positioning in the anterior-posterior plane. And that enophthalmos occurrence is greatly influenced by increase of the bony orbital volume, also it’s affected by other factors for further research. Orbital dimensions were affected by trauma and restored to near normal after reduction but showed no major shape changes of the conical orbit.

Quantifying gender differences in orbital morphology with large MRI datasets

PurposeTo investigate gender differences in orbital morphology using large MRI datasets. MethodsUsing a deep learning-based approach, the orbit and eyeball were automatically segmented from high resolution 3D MRI images of the IXI and OASIS3 datasets. Orbital and eyeball morphological parameters, including orbital volume, eyeball volume, effective orbital volume (EOV, defined as the orbital cavity volume excluding the eyeball), and coronal orbital dimensions and shape, were quantitatively assessed. The volume index was defined as the ratio of orbital volume to eyeball volume. ResultsThis study included 1926 subjects with a mean age of 63.9 ​± ​15.3 years. The mean volumes of the eyeball and orbit were 7.1 ​± ​1.0 ​ml and 25.9 ​± ​3.5 ​ml, respectively. Significant gender differences (all P ​< ​0.001) were observed in the following parameters (males versus females): orbital volume (28.3 ​± ​3.0 ​ml versus 24.0 ​± ​2.7 ​ml), EOV (25.1 ​± ​3.0 ​ml versus 21.1 ​± ​2.6 ​ml), eyeball volume (7.3 ​± ​1.0 ​ml versus 6.9 ​± ​1.0 ​ml), volume index (3.9 ​± ​0.6 versus 3.5 ​± ​0.5), orbital depth (40.0 ​± ​3.1 ​mm versus 37.4 ​± ​2.9 ​mm), coronal orbital height (40.8 ​± ​3.0 ​mm versus 38.4 ​± ​2.4 ​mm), coronal orbital width (38.0 ​± ​1.9 ​mm versus 36.6 ​± ​1.7 ​mm) and coronal orbital area (1292.5 ​± ​97.1 ​mm2 versus 1177.9 ​± ​89.7 ​mm2). ConclusionsThis study employed deep learning to analyze a large dataset of 3D head MRI scans, achieving accurate and objective measurements of orbital morphology. We identified significant gender differences in orbital parameters, with males generally having larger structures. Additionally, we established a normative database for orbital dimensions, providing a valuable resource for future research on orbital disorders and potentially improving clinical diagnosis and treatment.

Effect of the solar radiation pressure on the motion of satellites in almost circular Earth orbits

This paper considers the effect of the solar radiation pressure on the motion of a satellite in an almostcircular low-Earth orbit. The formulation of the problem is due to the need to determine the effect of solar radiation pressure forces on the motion of light commercial Earth remote sensing (ERS) satellites with large surface areas (solar batteries and antennas). The goal is to determine the main regularities of this effect, construct reasonably simple and accurate estimates of changes in orbital parameters for the orbits under consideration, and clarify their physics (cause-and-effect relations) The novelty of this study also lies in the use of variables specially introduced to describe a motion in almost circular orbits. The study assumes that the solar radiation pressure force is constant throughout the entire orbit, and it is concerned with dawn-dusk orbits, which are often used for ERS satellites with radar observation systems. The paper presents simple analytical expressions that describe the main regularities of short-term (several days) changes in orbital parameters. It is shown that the change in the orientation of the orbital plane is determined by the action of the gyroscopic moment. This moment balances the effect of the moment of external forces aimed at changing the orientation and the change in the orientation perpendicular to the direction of the applied moment of the external forces. The main effect of the solar radiation pressure is the excitation of forced oscillations of the orbital radius, whose amplitude linearly increases with time. The maximums of these oscillations (apogee) are at the point where the light pressure forces maximally slow down the motion of the satellite (directed oppositely to the velocity), and the minimums (perigee) are at the point of the maximum motion acceleration. It is shown that the annual movement of the Sun can qualitatively change the picture of the evolution of orbital parameters. For sun-synchronous dawn-dusk orbits, compact analytical solutions for changes in orbital parameters are constructed, and it is shown that the annual movement of the Sun’s declination reverses the direction of evolution of the orbital shape. The calculations showed a reasonably high accuracy of the analytical solutions at the initial stage. The obtained numerical estimates make it possible to evaluate the effect of the solar pressure on changes in orbital parameters.

Symmetries and wave functions of photons confined in three-dimensional photonic band gap superlattices

We perform a computational study of confined photonic states that appear in a three-dimensional (3D) superlattice of coupled cavities, resulting from a superstructure of intentional defects. The states are isolated from the vacuum by a 3D photonic band gap, using a diamondlike inverse woodpile crystal structure, and they exhibit “Cartesian” hopping of photons in high-symmetry directions. We investigate the confinement dimensionality to verify which states are fully 3D-confined, using a recently developed scaling theory to analyze the influence of the structural parameters of the 3D crystal. We create confinement maps that trace the frequencies of 3D-confined bands for select combinations of key structural parameters, namely the pore radii of the underlying regular crystal and of the defect pores. We find that a certain minimum difference between the regular and defect pore radii is necessary for 3D-confined bands to appear, and that an increasing difference between the defect pore radii from the regular radii supports more 3D-confined bands. In our analysis, we find that their symmetries and spatial distributions are more varied than electronic orbitals known from solid-state physics. We surmise that this difference occurs since the confined photonic orbitals derive from global Bloch states governed by the underlying superlattice structure, whereas single-atom orbitals are localized. Based on this realization, we suggest that the extent symmetries of “photonic orbitals” could possibly translate to novel macroscopic behaviors of “photonic solid-state matter,” never before seen in the standard electronic solid-state systems. We also discover pairs of degenerate 3D-confined bands with p-like orbital shapes and mirror symmetries matching the symmetry of the superlattice. Finally, we investigate the enhancement of the local density of optical states for cavity quantum electrodynamics applications. We find that donorlike superlattices, i.e., where the defect pores are smaller than the regular pores, provide greater enhancement in the air region than acceptorlike structures with larger defect pores, and thus offer better prospects for doping with quantum dots and ultimately for 3D networks of single photons steered across strongly coupled cavities. Published by the American Physical Society 2024

The impact of orbital floor defect ratio on changes in the inferior rectus muscle and prediction of posttraumatic enophthalmos – A cadaver study

BackgroundOrbital floor fractures result in critical changes in the shape and inferior rectus muscle (IRM) position. Radiological imaging of IRM changes can be used for surgical decision making or prediction of ocular symptoms. Studies with a systematic consideration of the orbital floor defect ratio in this context are missing in the literature. Accordingly, this study on human cadavers aimed to systematically investigate the impact of the orbital floor defect ratio on changes in the IRM and the prediction of posttraumatic enophthalmos. MethodsSeventy-two orbital floor defects were placed in cadaver specimens using piezosurgical removal. The orbital defect area (ODA), orbital floor area (OFA), position and IRM shape, and enophthalmos were measured using computed tomography (CT) scans. ResultsThe ODA/OFA ratio correlated significantly (p < 0.001) with the shape (Spearman’s rho: 0.558) and position (Spearman’s rho: 0.511) of the IRM, and with enophthalmos (Spearman’s rho: 0.673). Increases in the ODA/OFA ratio significantly rounded the shape of the IRM (ß: 0.667; p < 0.001) and made a lower position of the IRM more likely (OR: 1.093; p = 0.003). In addition, increases in the ODA/OFA ratio were significantly associated with the development of relevant enophthalmos (OR: 1.159; p = 0.008), adjusted for the defect localization and shape of the IRM. According to receiver operating characteristics analysis (AUC: 0.876; p < 0.001), a threshold of ODA/OFA ratio ≥ 32.691 for prediction of the risk of development of enophthalmos yielded a sensitivity of 0.809 and a specificity of 0.842. ConclusionThe ODA/OFA ratio is a relevant parameter in the radiological evaluation of orbital floor fractures, as it increases the risk of relevant enophthalmos, regardless of fracture localization and shape of the IRM. Therefore, changes in the shape and position of the IRM should be considered in surgical treatment planning. A better understanding of the correlates of isolated orbital floor fractures may help to develop diagnostic scores and standardize therapeutic algorithms in the future.

New diagnostic criteria for metopic ridges and trigonocephaly: a 3D geometric approach

BackgroundTrigonocephaly occurs due to the premature fusion of the metopic suture, leading to a triangular forehead and hypotelorism. This condition often requires surgical correction for morphological and functional indications. Metopic ridges also originate from premature metopic closure but are only associated with mid-frontal bulging; their surgical correction is rarely required. Differential diagnosis between these two conditions can be challenging, especially in minor trigonocephaly.MethodsTwo hundred seven scans of patients with trigonocephaly (90), metopic rigdes (27), and controls (90) were collected. Geometric morphometrics were used to quantify skull and orbital morphology as well as the interfrontal angle and the cephalic index. An innovative method was developed to automatically compute the frontal curvature along the metopic suture. Different machine-learning algorithms were tested to assess the predictive power of morphological data in terms of classification.ResultsWe showed that control patients, trigonocephaly and metopic rigdes have distinctive skull and orbital shapes. The 3D frontal curvature enabled a clear discrimination between groups (sensitivity and specificity > 92%). Furthermore, we reached an accuracy of 100% in group discrimination when combining 6 univariate measures.ConclusionTwo diagnostic tools were proposed and demonstrated to be successful in assisting differential diagnosis for patients with trigonocephaly or metopic ridges. Further clinical assessments are required to validate the practical clinical relevance of these tools.

Orbital shape in goat and sheep: Symmetric analysis.

The aim of this study is to evaluate orbital symmetry in goat and sheep skulls. For this purpose, a total of 83 skulls, including 50 sheep and 33 goat skulls, were used in the study. Geometric morphometry method was applied. For symmetric analysis, one side of each orbit was photographed twice and mirror images were created. There were 36 landmards marked to determine the outer limit of the orbita. As a result of the study, asymmetric components (fluctuating asymmetry and directional asymmetry) for shape were statistically significant in both goats and sheep (p < 0.0001). The first three principal components explained 52.558% of the total shape variation in goats and 61.245% in sheep. This value for symmetric components was 59.095% and 67.742% for goats and sheep, respectively, and 66.791% and 71.154% for asymmetric components. As a result of discriminant function analysis, right and left orbital shapes showed grouping characteristics with similar success rates according to species. Although limited, the right orbit in goats (100%) and the left orbit in sheep (96.5%) were grouped more accurately.

Semiautomated MRI-Based Method for Orbital Volume and Contour Analysis.

The architecture of the orbital cavity is intricate, and precise measurement of its growth is essential for managing ocular and orbital pathologies. Most methods for those measurements are by CT imaging, although MRI for soft tissue assessment is indicated in many cases, specifically pediatric patients. This study introduces a novel semiautomated MRI-based approach for depicting orbital shape and dimensions. A retrospective cohort study. Patients with at least 1 normal orbit who underwent both CT and MRI imaging at a single center from 2015 to 2023. Orbital dimensions included volume, horizontal and vertical lengths, and depth. These were determined by manual segmentation followed by 3-dimensional image processing software. Differences in orbital measurements between MRI and CT scans. Thirty-one patients (mean age 47.7 ± 23.8 years, 21 [67.7%]) females, were included. The mean differences in delta values between orbital measurements on CT versus MRI were: volume 0.03 ± 2.01 ml, horizontal length 0.53 ± 2.12 mm, vertical length, 0.36 ± 2.53 mm, and depth 0.97 ± 3.90 mm. The CT and. MRI orbital measurements were strongly correlated: volume (r = 0.92, p < 0.001), horizontal length (r = 0.65, p < 0.001), vertical length (r = 0.57, p = 0.001), and depth (r = 0.46, p = 0.009). The mean values of all measurements were similar on the paired-samples t test: p = 0.9 for volume (30.86 ± 5.04 ml on CT and 30.88 ± 4.92 ml on MRI), p = 0.2 for horizontal length, p = 0.4 for vertical length, and p = 0.2 for depth. We present an innovative semiautomated method capable of calculating orbital volume and demonstrating orbital contour by MRI validated against the gold standard CT-based measurements. This method can serve as a valuable tool for evaluating diverse orbital processes.

The quantum states for Hydrogen atom: spherical harmonics and the orbitals geometrical representation

Our work utilizes the quantum model of the hydrogen atom which is based on the Schrödinger equation with Coulomb potential. Specifically, we concentrate on the angular components of the wave eigenfunctions derived from this model. We consider the quantum states with n ≤ 4. In order to visualize the orbital shapes of these states, we built in the spherical coordinates system their 3D geometric representations. Furthermore, we use the corresponding spherical harmonics, to calculate the θ nodal values that describe the configurations of these orbital states.

Deceptive orbital confinement at edges and pores of carbon-based 1D and 2D nanoarchitectures.

The electronic structure defines the properties of graphene-based nanomaterials. Scanning tunneling microscopy/spectroscopy (STM/STS) experiments on graphene nanoribbons (GNRs), nanographenes, and nanoporous graphene (NPG) often determine an apparent electronic orbital confinement into the edges and nanopores, leading to dubious interpretations such as image potential states or super-atom molecular orbitals. We show that these measurements are subject to a wave function decay into the vacuum that masks the undisturbed electronic orbital shape. We use Au(111)-supported semiconducting gulf-type GNRs and NPGs as model systems fostering frontier orbitals that appear confined along the edges and nanopores in STS measurements. DFT calculations confirm that these states originate from valence and conduction bands. The deceptive electronic orbital confinement observed is caused by a loss of Fourier components, corresponding to states of high momentum. This effect can be generalized to other 1D and 2D carbon-based nanoarchitectures and is important for their use in catalysis and sensing applications.

Comparative Analysis of Nickel-Phosphine Complexes with Cumulated Double Bond Ligands: Structural Insights and Electronic Interactions via ETS-NOCV and QTAIM Approaches.

This study presents a comprehensive analysis of nickel-phosphine complexes, specifically Ni(PH3)2(OCCH2), Ni(PH3)2(H2CCO), Ni(PH3)2(H2CCCH2), Ni(PH3)2(NNCH2), and Ni(PH3)2(η1-H2CNN). Utilizing ETS-NOCV analysis, we explored orbital energy decomposition and the Hirshfeld charges of the ligands, providing insights into the electronic structures and donor-acceptor interactions within these complexes. The interactions in the ketene and allene complexes exhibit similar deformation densities and NOCV orbital shapes to those calculated for Ni(PH3)2(NNCH2), indicating consistent interaction characteristics across these complexes. The total interaction energy for all η2 complexes is observed to be over 60 kcal/mol, slightly exceeding that of the analogous carbon dioxide complex reported earlier. Furthermore, the study highlights the stronger back-donation as compared to donor interactions across all η2 complexes. This is further corroborated by Hirshfeld analysis, revealing the charge distribution dynamics within the ligand fragments. The research offers new perspectives on the electron distribution and interaction energies in nickel-phosphine complexes, contributing to a deeper understanding of their catalytic and reactive behaviors.

Breed-Specific Skull Morphology Reveals Insights into Canine Optic Chiasm Positioning and Orbital Structure through 3D CT Scan Analysis.

This study's CT scan-based morphometric analysis of 50 adult dogs explored the relationship between skull shape variations (determined by the skull index, SI), optic chiasm, optic canals, and orbital shape. Dogs were classified as brachycephalic (SI ≥ 59), mesocephalic (SI ≥ 51 but <59), and dolichocephalic (SI < 51). No significant age or weight differences were observed. Skull lengths (brachycephalic: 11.39 ± 1.76 cm, mesocephalic: 15.00 ± 2.96 cm, dolichocephalic: 17.96 ± 3.44 cm) and facial lengths (brachycephalic: 3.63 ± 1.00 cm, mesocephalic: 6.46 ± 1.55 cm, dolichocephalic: 8.23 ± 1.03 cm) varied significantly, with shorter orbital depths (brachycephalic: 2.58 ± 0.42 cm, mesocephalic: 3.19 ± 0.65 cm, dolichocephalic: 3.61 ± 0.77 cm) in brachycephalic dogs. The optic chiasm-to-inion horizontal length ratio to cranial horizontal length positively correlated with the SI (r = 0.883, p < 0.001), while the ratio to neurocranial length showed no SI correlation (range: 55.5-75.0). Brachycephalic breeds had a significantly wider optic canal angle (93.74 ± 16.00°), along with broader lacrimal-zygomatic and zygomatic frontal process angles. These findings highlight the zygomatic bone's role in influencing breed-specific orbital variations by connecting the face to the neurocranium, projecting the orbital rim outward and forward with facial shortening.

A theoretical study on application of BN/CC isosterism to modify topology of coronene aromaticity and HOMO–LUMO energy gaps

A gradual replacement of peripheral CC bonds of coronene with BN ones can isolate aromatic carbocyclic subunits that dominate frontier orbital shapes and energies, thus enabling their modulation.

Real-space tight-binding model for twisted bilayer graphene based on mapped Wannier functions

Twisted multi-layer heterostructures have been considered a platform for studying highly correlated many-particle systems, hosting the emerging phenomena of correlation physics. Electronic structure calculations of such materials which mainly focused on Twisted Bilayer Graphene (TBG) in the framework of the independent-electron approximation, despite the complexity, accurately match the experimental results around the Fermi level. Here, we present a convenient real space π-bands tight-binding model to calculate the band structure of TBG based on the Wannier interlayer hopping parameters obtained from non-twisted bilayer graphene. Our approach is based on mapping hopping parameters onto the real space TBG interlayer couplings, using Radial Basis Function (RBF) interpolation method. This accurate mapping, naturally, transfers all the symmetries and orbital shape features of the bilayer graphene lattice to the TBG lattice and preserves coupling orientation dependencies in addition to distance dependencies. The importance of this fact is explained by showing the effect of the threefold rotation symmetry of AB′ interlayer coupling on the flat band of the TBG band structure. In addition, due to real space study, the model gives us a comprehensive and intuitive view of the role of each interlayer orbital coupling in the TBG band structure and the structural variation relative to twisting.