Orbital Vector Research Articles

Research on relative reachable domain in target orbit for maneuvering spacecraft

PurposeLots of successful space missions require that the maneuvering spacecraft can reach the target spacecraft. Therefore, research on relative reachable domain (RRD) in target orbit for maneuvering spacecraft is particularly important and is currently a hot-debated topic in the field of aerospace. This paper aims at analyzing and simulating the RRD in target orbit for maneuvering spacecrafts with a single fixed-magnitude impulse and continuous thrust, respectively, to provide a basis for analyzing the feasibility of spacecraft maneuvering missions and improving the design efficiency of spacecraft maneuvering missions.Design/methodology/approachBased on the kinematics model of relative motion, RRD in target orbit for maneuvering spacecraft with a single fixed-magnitude impulse can be calculated via analyzing the relationship between orbital elements, position vector and velocity vector of spacecrafts, and relevant studies are introduced to compare simulation results for the same case and validate the method proposed in the paper. With analysis of the dynamic model of relative motion, the calculation of RRD in target orbit for maneuvering spacecraft with continuous thrust can be transformed as the solution of the optimal control problem, and example emulations are carried out to validate the method.FindingsFor the case with a single fixed-magnitude impulse, simulation results show preliminarily that the method is in agreement with the method in Ref. (Wen et al., 2016), which treats the same case and thus is plausibly correct and feasible. For the case with continuous thrust, analysis and simulation results confirm the validity of the proposed method. The methods based on relative motion in this paper can efficiently determining the RRD in target orbit for maneuvering spacecraft.Originality/valueBoth theoretical analyses and simulation results indicate that the method proposed in this paper is comparatively simple but efficient for determine the RRD in target orbit for maneuvering spacecraft swiftly and precisely.

Statistical equivalence of metrics for meteor dynamical association

Meteor showers, originating as a result of the activity of comets or the disruption of large objects, provide a unique window into the composition and dynamics of our Solar System. While modern meteor detection networks have amassed extensive data, distinguishing sporadic meteors from those belonging to specific meteor showers remains challenging. In this study, we statistically evaluate and compare four orbital similarity criteria within five-dimensional parameter space (DSH,DD,DH, and ϱ2) to study dynamical associations using the already classified meteors (manually by a human) in CAMS database as a benchmark. In addition, we assess various distance metrics typically used in Machine Learning with two different vectors: ORBIT, grounded in heliocentric orbital elements, and GEO, predicated on geocentric observational parameters. To estimate their degree of correlation and efficacy, the Kendall rank correlation coefficient and the Top-k accuracy are employed. The statistical equivalence of the Top-1 results is examined using the Kolmogorov–Smirnov test and the percentage of Top-1 agreement is calculated on an event-by-event basis. Additionally, we compute the optimal cut-offs for all methods for distinguishing sporadic background events. Our findings demonstrate the superior performance of the sEuclidean metric in conjunction with the GEO vector. Within the scope of D-criteria, DSH emerged as the preeminent metric, closely followed by ϱ2. The Bray-Curtis metric displayed an advantage compared to the other distance metrics when paired with the ORBIT vector for Top-k accuracy, however, the Cityblock metric is more effective when considering the sporadic background. ϱ2 stands out as the most equivalence to the distance metrics when utilizing the GEO vector and the most compatible with GEO and ORBIT simultaneously, whereas DD aligns more closely when using the ORBIT vector. The stark contrast in DD’s behavior compared to other D-criteria highlights potential inequivalence. Our results suggest that geocentric features provide a more robust basis than orbital elements for meteor dynamical association. Most distance metrics associated with the GEO vector surpass the D-criteria when differentiating the meteoroid background. Accuracy displayed a dependence on solar longitude with a pronounced decrease around 180° matching an apparent increase in the meteoroid background activity, tentatively associated with the transition from the Perseids to the Orionids. Considering lately identified meteor showers, ∼27% of meteors in CAMS would have different associations. This work unveils that Machine Learning distance metrics can rival or even exceed the performance of tailored orbital similarity criteria for meteor dynamical association.

Lower Eyelid Dark Circles (Tear Trough and Lid-Cheek Junction): A Stepwise Assessment Framework.

Despite increasing popularity, the use of hyaluronic acid (HA) fillers for the correction of dark under-eye shadows remains challenging. Specific guidance on patient assessment is limited. The aim of this study was to develop a stepwise assessment framework for lower eyelid dark shadows to help practitioners classify patients based on their underlying problems and facilitate a more strategic approach to treatment. Literature review and peer collaboration informed the current availability of educational material for use by experienced injectors when assessing patients presenting with dark circles. A practitioner survey provided insight into current practices. A focus group convened to review the survey results and discuss best practice approaches to patient assessment. Surveyed practitioners (n = 39) reported patient concern about under-eye hollows (91%), dark eye circles (80%), and looking tired (60%). All (100%) agreed that midcheek volume was critical when treating tear-trough depression, and only 26% reported use of a tear-trough classification system. The focus group developed a framework for assessing tear-trough depression and the lid-cheek junction in patients presenting with dark circles. Key factors within this framework included the importance of appropriate lighting when conducting a visual inspection, regional inspection of the cheek and tear trough, palpation of the orbital rim and soft tissues, determination of the orbital vector, and assessment of lower eyelid pigmentation and skin quality. Careful step-by-step assessment can reduce the challenges of treating dark circles by identifying patients in whom dark eye circles may be improved without the need to directly inject filler into the tear trough.

An Improved Acceleration Approach by Utilizing K-Band Range Rate Observations

During gravity field modeling, the conventional acceleration approach rarely incorporates KBR inter-satellite range rate data from the GRACE mission. To propose an improved acceleration method, this study introduces initial orbital position and velocity vectors to be estimated along with a combination of Cowell, KSG, and Adams integrators. In addition to achieving a full-rank design matrix regarding orbit corrections when constructing observation equations, the proposed method is capable of utilizing range rate observations for gravity field estimation. To verify the reliability of this approach, GRACE data from April 2002 to December 2016 was used to calculate a time series of monthly gravity solutions up to a degree and order of 96, referred to as Tongji-Acc RL06 in this paper. The computed time series are compared with the official models (i.e., CSR RL06, GFZ RL06, and JPL RL06) in terms of geoid degree variances, signal contents over distinct areas, and noise levels in desert regions. The investigations lead to the following conclusions: (a) the geoid degree variances indicate that Tongji-Acc RL06 exhibits comparable signal levels (approximately below 20 degrees) to the other three models while demonstrating lower noise at higher degrees (above 40 degrees); (b) the analysis over the globe, typical river basins, and land–ice regions illustrates that the solutions derived using the proposed acceleration method agree well with the official models based on the dynamic approach; (c) especially over the two large-scale river basins (i.e., Amazon and Zambezi) and another two small-scale river basins (i.e., Tennessee and Irrawaddy), Tongji-Acc RL06 significantly improves the SNR values; and (d) in the cases of the Sahara and Karakum deserts, Tongji-Acc RL06 achieves noise reductions of over 55.8% and 61.5% relative to CSR RL06, respectively. In general, the signal and noise analyses demonstrate that the proposed acceleration-based approach can effectively extract gravity field signals from KBR inter-satellite range rate observations with improved SNR, while significantly reducing the high-frequency noise.

Preventing Retraction With Use of Primary Eyelid Spacer Grafts in Cosmetic Lower Lid Blepharoplasty.

Lower eyelid retraction is a challenging complication that can develop after a cosmetic lower eyelid blepharoplasty. Factors such as proptosis and negative orbital vector may place patients at a higher risk for developing postblepharoplasty retraction. Rather than addressing this complication after it occurs postoperatively, this study focuses on preventing its occurrence through the use of primary eyelid spacer grafts during the initial blepharoplasty. The goal of this study was to review the outcomes of primary eyelid spacer graft placement during the initial cosmetic lower lid blepharoplasty. A retrospective chart review was performed at Emory Eye Center between January 1, 2014, and January 1, 2022. Patients that underwent lower eyelid blepharoplasty with primary eyelid spacer graft placement were identified and included in the study. Fifteen patients with Hertel measurements of >17 and adequate preoperative and postoperative photographs were analyzed. Fifteen patients with exophthalmometry measurements of >17 and adequate preoperative and postoperative photographs were analyzed. The mean change in marginal reflex distance 2 was 0.19 mm (range, -1.05 to 1.24 mm). Two patients developed eyelid retraction at their long-term follow-up. Both patients developed retraction about 2 years after the initial surgery. Although this study was limited by its retrospective nature and had a small sample size, none of these high-risk patients developed immediate post blepharoplasty retraction. Careful preoperative evaluation should be performed to identify these high-risk patients, and placement of a primary eyelid spacer graft during the initial lower eyelid blepharoplasty should be considered in this population.

Time-optimal maneuvers of a spacecraft between two arbitrary states in proximity of a circular reference orbit

The problem is considered to find the time-optimal control that transfers a fourth-order system that consists of a double integrator and a harmonic oscillator, coupled by one control channel, between two arbitrary states. That fourth-order system is equivalent to the Hill-Clohessy-Wiltshire model of the relative dynamics of an orbiting spacecraft in proximity of a second spacecraft on a circular reference orbit, subjected to a thrust parallel to the orbital velocity vector and having time-continuous amplitude. A new method is here introduced to determine the time-optimal control problem stated above. This method combines two previously discovered optimal control synthesis methods: the method by Romano and Curti (2020), that enables to find (analytically, in some case) the optimal control transferring a general Linear Time Invariant Normal system between two arbitrary states; and, the method by Belousova and Zarkh (1996), that enables to find the optimal control transferring a fourth-order system consisting of a double integrator and a harmonic oscillator, coupled by one control channel, from an arbitrary initial state to the origin of the state space, if the optimal control is a priori known, that transfers the same system from a reference state to the origin. The here proposed combined method utilizes two phases. During the first phase, a number of reference minimum-time controls are obtained that transfer the system from specific reference states to the state space origin; this is achieved by exploiting Pontryagin’s principle together with back-propagation from the origin of the state space. During the second phase, a search is run along a particular curve in the state space (named extremal search path) that depends on the boundary states of the problem at hand. In particular, a minimum-time control problem is iteratively solved to find the optimal control history that steers the system from a state on that curve to the origin, by exploiting Belousova and Zarkh method, until a particular state is found which satisfies an equivalency condition that, as demonstrated by Romano and Curti, guarantees that the optimal control history pertaining to the problem of transferring the system from that state to the origin is the same optimal control history that transfers the system between the arbitrarily set initial and final states. The new results, substantiated by numerical experiments, have both a theoretical and a practical value, as they could be applied for the optimal guidance of spacecraft performing autonomous proximity maneuvers.

Lower Eyelid Blepharoplasty: Minimizing Complications and Correction of Lower Eyelid Malposition.

Lid retraction is a feared complication of lower blepharoplasty. Anatomical variations like negative orbital vector, horizontal lid laxity, and preexisting lid retraction are more prone to lid malpositions. Meticulous and precise execution of a series of surgical steps is key to preventing complications. This includes minimizing surgical trauma, meticulous hemostasis, preserving innervation to the medial lid and pretarsal orbicularis, safe method of fat excision, septal tightening while maintaining lid traction, and conservative and titrated skin excision. Canthal fixation addresses lid laxity and maintains the lid stretched vertically while postoperative healing and fibrosis are taking place. Post-blepharoplasty lid retraction may occur due to failure to address lid laxity and the occurrence of middle lamellar fibrosis. Excessive skin excision may also result in anterior lamellar deficiency. The "sag and drag" concept is useful to evaluate the post-blepharoplasty retracted lid. The treatment of the retracted lid includes lid massage, replacing the anterior lamella, or releasing the middle lamellar fibrosis or a combination of techniques. In conclusion, understanding the mechanisms of lid retraction, careful preoperative assessment, and surgical precision will help surgeons to prevent and manage this complication.

Excitation of vertical breathing motion in disc galaxies by tidally-induced spirals in fly-by interactions

ABSTRACT It is now clear that the stars in the Solar neighbourhood display large-scale coherent vertical breathing motions. At the same time, Milky Way-like galaxies experience tidal interactions with satellites/companions during their evolution. While these tidal interactions can excite vertical oscillations, it is still not clear whether vertical breathing motions are excited directly by the tidal encounters or are driven by the tidally-induced spirals. We test whether excitation of breathing motions are directly linked to tidal interactions by constructing a set of N-body models (with mass ratio 5:1) of unbound single fly-by interactions with varying orbital configurations. We first reproduce the well-known result that such fly-by interactions can excite strong transient spirals (lasting for ${\sim}2.9{-}4.2\,{\rm Gyr}$) in the outer disc of the host galaxy. The generation and strength of the spirals are shown to vary with the orbital parameters (the angle of interaction, and the orbital spin vector). Furthermore, we demonstrate that our fly-by models exhibit coherent breathing motions whose amplitude increases with height. The amplitudes of breathing motions show characteristic modulation along the azimuthal direction with compressing breathing motions coinciding with the peaks of the spirals and expanding breathing motions falling in the inter-arm regions – a signature of a spiral-driven breathing motion. These breathing motions in our models end when the strong tidally-induced spiral arms fade away. Thus, it is the tidally-induced spirals which drive the large-scale breathing motions in our fly-by models, and the dynamical role of the tidal interaction in this context is indirect.

Evaluation of Orbit Vector Relationships in Different Types of Skeletal Malocclusions

Evaluation of Orbit Vector Relationships in Different Types of Skeletal Malocclusions

Mission ORCA: Orbit Refinement for Collision Avoidance

Forecasting of collisions between resident space objects (RSOs) is becoming critical for the future exploitation of near-Earth space. A constellation of 28 spacecrafts (plus in-orbit spares) in sun synchronous orbits is proposed as a solution for improving the current space situational awareness capabilities. Each satellite uses an optical payload to track target RSOs, with the satellite's position precisely determined. Multiple pictures of the RSO are taken, and the spacecraft attitude used to calculate the target's position relative to the spacecraft. The target's orbit is then determined from the movement of the target through the field of view over time. The system outputs orbit state vectors of the tracked object, allowing precise orbit characterisation and collision forecasting to be delivered. The constellation's design allows high temporal resolution, so reliable information can be supplied to end-users. The paper shows the results of the system design of a demonstration mission meant to verify the feasibility of the concept, performed by a team of students of Cranfield University. The exercise addresses all the aspects of the preliminary design, including the definition of the mission and system requirements, the selection of the overall mission architecture, operations, and mission phases. A cap on the overall cost allows for the realisation of the platform within a university budget. The outline of the design includes not only the selection and sizing of all the subsystems and payload but also suggests a new strategy for deploying the constellation if the demonstration mission is successful. The utilisation of high TRL and COTS components, as well as mass, power, and link budgets, demonstrate the feasibility of the overall mission concept.

Orbit error removal in InSAR/MTInSAR with a patch-based polynomial model

The orbit error caused by the inaccuracy of the orbit state vector can lead to fringes in differential interferograms, which can impede the estimation of deformation in differential SAR interferometry (DInSAR) applications. Usually, a set of polynomial coefficients for an entire SAR image is obtained for orbit error removal. However, the orbit error plane is influenced by overfitting in the case that the SAR satellites do not have a precise orbit. In this paper, a patch-based polynomial method is proposed to fit the orbit error plane. The new method divides an SAR image into several overlapping patches in the azimuth and range directions. Every patch obtains its own polynomial coefficients, and an iterative least-square method is used to mosaic the orbit plane. This method is tested and validated via a simulated dataset and then applied to ALOS1/2 PALSAR and Sentinel-1A datasets. The accuracy of deformation is evaluated by in situ GPS datasets. The results show that the patch-based method can fit the orbit phase plane more accurately than the traditional polynomial model with millimeter-level displacement improvement, especially in the margin areas of ALOS1/2 and for the wide-coverage Sentinel-1A datasets. Moreover, in the MTInSAR parameter calculations, the new method improves the accuracy of mean velocity calculations for ALOS1 time series, with a reduction of RMSE from 4.47 mm/yr to 3.17 mm/yr. Additionally, the new method reduces the spatial correlation of the residual topographic phase, with a mean value reduction from 0.32 m to 0.13 m.

The origin of metal-poor stars on prograde disc orbits in FIRE simulations of Milky Way-mass galaxies

ABSTRACT In hierarchical structure formation, metal-poor stars in and around the Milky Way (MW) originate primarily from mergers of lower mass galaxies. A common expectation is therefore that metal-poor stars should have isotropic, dispersion-dominated orbits that do not correlate strongly with the MW disc. However, recent observations of stars in the MW show that metal-poor ($\rm {[Fe/H]}\lesssim -2$) stars are preferentially on prograde orbits with respect to the disc. Using the Feedback In Realistic Environments 2 (FIRE-2) suite of cosmological zoom-in simulations of MW/M31-mass galaxies, we investigate the prevalence and origin of prograde metal-poor stars. Almost all (11 of 12) of our simulations have metal-poor stars on preferentially prograde orbits today and throughout most of their history: we thus predict that this is a generic feature of MW/M31-mass galaxies. The typical prograde-to-retrograde ratio is ∼2:1, which depends weakly on stellar metallicity at $\rm {[Fe/H]}\lesssim -1$. These trends predicted by our simulations agree well with MW observations. Prograde metal-poor stars originate largely from a single Large/Small Magellanic Cloud (LMC/SMC)-mass gas-rich merger $7\!-\!12.5\, \rm {Gyr}$ ago, which deposited existing metal-poor stars and significant gas on an orbital vector that sparked the formation of and/or shaped the orientation of a long-lived stellar disc, giving rise to a prograde bias for all low-metallicity stars. We find subdominant contributions from in situ stars formed in the host galaxy before this merger, and in some cases, additional massive mergers. We find few clear correlations between any properties of our MW/M31-mass galaxies at z = 0 and the degree of this prograde bias as a result of diverse merger scenarios.

Broadband Structured Light Multiplexing With Dielectric Meta-Optics

Structured light beams (SLBs), mainly including vortex beams (VBs) and cylindrical vector beams (CVBs), have received significant attention in optical communications due to orthogonal orbital angular momentum (OAM) or vector modes. However, the mode conversion between OAM and vector modes and the working bandwidth are always challenges restricting the practical applications. Here, we demonstrate broadband SLB multiplexing in optical communication with dielectric Pancharatnam-Berry phase-based metasurfaces (PBMs). By virtue of the dispersion-free characteristic and spin-orbital interaction, the designed metasurfaces have a broad working wavelength ranging from C- to L-bands and can flexibly convert VBs and CVBs. With these properties, SLBs are successfully multiplexed with conventional physical dimensions (including wavelengths and polarization states) to construct complex multiplexing formats. In a back-to-back free-space transmission experiment, 50 Gbit/s quadrature-phase shift-keying (QPSK) signals are used for multiplexing with four OAM modes, seven wavelengths, and two polarization states. When the transmission rate reaches 2.73 Tbit/s, the bit-error rate (BER) is below 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> at an optical signal-to-noise ratio (OSNR) of 17 dB. By changing the polarization states of the incident light, CVB multiplexing is realized, and the BER is below 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> at an OSNR of 19 dB. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Owing to the silica substrate, PBM is capable of photonic integration, and it is anticipated that this PBM may provide a new avenue for high-order multiplexing and all-optical signal processing of SLBs.

Mangrove Park of Recife: A century of extreme uses and abuses (?)

Recife, in Northeast Brazil, was surrounded by the Atlantic Rainforest and its associated ecosystems (e.g., flooded mangrove forests and vegetated dune), intertwined with numerous channels and other naturally occurring water features, until the mid-1800s. Today, it is the core of a metropolitan area with the usual urban problems that affect all coastal cities, including conflicts with the remaining mangrove forest. It is possible to analyse the conflicts between the urban growth of coastal cities and their environment and ecosystems through three dimensions: urban–physical, socio-demographic, and socio-environmental. We present an analysis of the urban area expansion density variation in Recife over nearly a century (1951–2014) in terms of its conflicts with the remaining mangrove forest patch. Improved GIS data (compilation of orbital images, aerial photography, aerial mapping, and vector data) and qualitative analysis of the master plan were used. The results indicate an unexpected expansion (in area) of flooded mangrove forests, with the replacement of other wetland areas or channels with urban growth. The fact that the mangrove park is surrounded by urban areas represent an increasing risk of being occupied. There is a great real estate interest on the edge of the park facing the neighbourhoods of Boa Viagem and Imbiribeira. Knowing how urban development interfered with natural areas to provide space for coastal cities can help researchers understand how ecosystems are characterised by different growth models. Thus, it will be possible to contribute to the development of new approaches to coastal development that include the better use of ecosystem services that guarantee better living conditions in cities by reducing conflicts and increasing the exploitation of flow control, thermal regulation and the possibility of co-existing with a flooded urban forest and all its associated biodiversity.

Fate of stellar bars in minor merger of galaxies

ABSTRACT Minor merger of galaxies is common during the evolutionary phase of galaxies. Here, we investigate the dynamical impact of a minor merger (mass ratio 1:10) event on the final fate of a stellar bar in the merger remnant. To achieve that, we choose a set of minor merger models from the publicly available GalMer library of galaxy-merger simulations. The models differ in terms of their orbital energy, orientation of the orbital spin vector, and morphology of the satellite galaxy (discy/spheroidal). We demonstrate that the central stellar bar, initially present in the host galaxy, undergoes a transient bar amplification phase after each pericentre passage of the satellite; in concordance with past studies of bar excitation due to tidal encounter. However, once the merger happens, the central stellar bar weakens substantially in the post-merger remnants. The accumulation of satellite’s stars in the central region of merger remnant plays a key role in the bar-weakening process; causing a net increase in the central mass concentration as well as in the specific angular momentum content. We find that the efficiency of mass accumulation from the satellite in the central parts of merger remnants depends on the orbital parameters as well as on the satellite’s morphology. Consequently, different minor merger models display different degrees of bar-weakening event. This demonstrates that minor merger of galaxies is a plausible avenue for bar weakening in disc galaxies.

A KK-theoretic perspective on deformed Dirac operators

We study the index theory of a class of perturbed Dirac operators on non-compact manifolds of the form D+ic(X), where c(X) is a Clifford multiplication operator by an orbital vector field with respect to the action of a compact Lie group. Our main result is that the index class of such an operator factors as a KK-product of certain KK-theory classes defined by D and X. As a corollary we obtain the excision and cobordism-invariance properties first established by Braverman. An index theorem of Braverman relates the index of D+ic(X) to the index of a transversally elliptic operator. We explain how to deduce this theorem using a recent index theorem for transversally elliptic operators due to Kasparov.

Fault-tolerant estimation of satellite orbital states

This paper is devoted to global positioning system (GPS)-based fault-tolerant satellite orbital states estimation which is used for the pseudo-ranging model. GPS is widely used by many researchers to determine the orbit state vectors of satellites, but errors in GPS measurements can cause major errors in satellite location detection. Therefore, there is a need for an architecture that will resist possible measurement errors and GPS malfunctions. This study aims to present the novel approaches to tolerate the errors that may take place in GPS measurements. The satellite localisation has been detected via a pseudo-ranging model between four GPS satellites and the target satellite. The Keplerian equations and orbit elements are used for the satellite dynamic model with orbital J2 perturbation which is due to the flattened shape of the earth is taken into account via the extended Kalman filter (EKF) algorithms. The reconfigurable and the adaptive version of fault-tolerant localisation architecture eliminate the GPS measurement errors during estimating satellite position vectors. The comparison of the prediction architectures of the fault tolerant satellite state vectors originally proposed. At the same time, it is possible to use fault tolerant architectures designed to detect whether GPS satellites are malfunctioning or not.

Diabatization by Machine Intelligence.

Understanding nonadiabatic dynamics is important for chemical and physical processes involving multiple electronic states. Direct nonadiabatic dynamics simulations are often employed to observe such processes on a femtosecond time scale. One often needs to do the simulation on a longer time scale, but direct simulation based on electronic structure calculations of the surfaces and couplings is expensive due to the large number of electronic structure calculations needed for ensemble averaging or simulation of longer-time processes. An alternative approach is to construct an analytical representation of potential energy surfaces (PESs) and couplings, which allows for faster dynamics calculations. Diabatic representations are preferred for such purposes because of the smoothness of the surfaces and couplings and the scalar nature of the couplings. However, many diabatization procedures are complicated by the need to consider orbitals or vector coupling elements, and these can make the process very labor-intensive. To circumvent these difficulties, we here propose diabatization by a deep neural network (DDNN) based on a new architecture for a deep neural network that requires neither orbital input nor vector input. The DDNN method allows convenient and semiautomatic diabatization, and it is demonstrated here for a model problem and for producing diabatic potential energy matrices for thiophenol.

The Impact of SAR Parameter Errors on the Ionospheric Correction Based on the Range-Doppler Model and the Split-Spectrum Method

Interferometric synthetic aperture radar (InSAR) products may be significantly distorted by microwave signals traveling through the ionosphere, especially with long wavelengths. The split-spectrum method (SSM) is used to separate the ionospheric and the nondispersive phase terms with lower and higher spectral sub-band interferogram images. However, the ionospheric path delay phase is very delicate to the synthetic aperture radar (SAR) parameters including orbit vectors, slant range, and target height. In this paper, we get the impact of SAR parameter errors on the ionospheric phase by two steps. The first step is getting the derivates of geolocation with reference to SAR parameters based on the range-Doppler (RD) imaging model and the second step is calculating the derivates of the ionospheric phase delay with respect to geometric positioning. Through the numerical simulation, we demonstrate that the deviation of ionospheric phase has a linear relationship with SAR parameter errors. The experimental results show that the estimation of SAR parameters should be accurate enough since the parameter errors significantly affect the performance of ionospheric correction. The root mean square error (RMSE) between the corrected differential interferometric SAR (DInSAR) phase with SAR parameter errors and the corrected DInSAR phase without parameter errors varies from centimeter to decimeter level with the L-band data acquired by the Advanced Land Observing Satellite (ALOS) Phased Array type L-band SAR (PALSAR) over Antofagasta, Chile. Furthermore, the effectiveness of SSM can be improved when SAR parameters are accurately estimated.

Prediction of Lower Eyelid Malpositioning After Surgical Correction of Orbital Fracture Using the Subciliary Approach Through the Canthal Area and Orbital Vector Analysis.

A subciliary incision has been widely used not only for blepharoplasty but also for facial fracture surgery. However, lower eyelid malpositioning is one of the most common complications after fracture surgery. A limited number of studies have been conducted on the relationships among evaluation of the canthal area, orbital vector analysis, and lower eyelid malpositioning following the subciliary approach for surgical repair of fractures. The primary goal of this study was to identify and analyze the possible risk factors, including incidence of lower eyelid malpositioning and orbital vector after surgical correction of the orbital fracture. A total of 241 cases of orbital fracture surgery was retrospectively reviewed. Data related to the patient and surgery were collected. Orbital vector and angle that reflects the vector, distance between soft tissue and bone in the lateral canthal area were measured for orbital vector analysis. The relationship between the prevalence of the malpositioning of the lower eyelid and each factor was statistically analyzed. The distance between the soft tissue and bone at the lateral canthal area was statistically significant (P = 0.031). The distance between the soft tissue and bone at lateral canthal area illustrates the lateral side or periorbital anatomical morphology. It could be inferred that patients with a negative orbital vector were relatively more vulnerable to scar formation or lower eyelid malpositioning caused by iatrogenic factors. Therefore, it could be analyzed as a risk factor to predict the malpositioning of the lower eyelid postoperatively.