Direct Trajectory Research Articles

EXTREME TRANSLATIONAL IMPACT OF TRIPLE-SHOCK CONFIGURATIONS OF BLAST WAVES IN A CONFINED VOLUME OF AN ORBITAL STATION

The translational effects of gas streams, which form after the triple-shock configurations at Mach reflection of blast waves with normal main shock (so-called stationary Mach configurations), were analyzed. Unlike in the case of an elevated explosions of fuel as rocket starts in initially stagnant air, which is considered here as a private case, it was supposed that this shock-wave structure moves in a preceding flow with arbitrary velocity (and corresponding flow Mach number). Analyzing relations of the dynamic pressures across the slipstream, which emanates from the triple point of the Mach reflection, it was shown that the flows after the triple-shock configuration usually differ much in their translational action on surrounding objects. It was found and discussed that some configurations drag the objects initially situated above and below the triple-point trajectory in opposite directions. Moreover, the “trigger” structure was found that remains previous flow drag action on the object above the triple-point trajectory, but switches it to exactly opposite one, if the object is situated below the triple point.

A reverse tracing of the water flow path algorithm for slope length extraction based on triangulated irregular network

Terrain factor is an important factor affecting soil erosion, in which slope length is an important indicator of terrain factor. In this paper, we model the regional topographic relief with triangulated irregular network TIN, use the slope aspect of the TIN triangular surface to determine the flow direction, and propose an algorithm (RT-WFP) for extracting the slope length by tracing the water flow trajectory in reverse direction. The slope cutoff point rule is set in the algorithm to improve the accuracy of the slope length extraction results. We calculated the slope length of the experimental area of the small watershed of Golden Hook-shaped collapsing hill in Bailu Township, Ganxian District, and the rationality of the algorithm proposed in this paper is verified through the comparison and analysis with the traditional slope length extraction algorithm. The experimental results show that, compared with the traditional D8 algorithm, the water flow path extracted by this algorithm in the experimental area more closely matches the water flow path based on contour mapping, and the slope length extracted by this algorithm has a lower sensitivity to the resolution of the data, and the percentage of cells with a slope length value of no more than 300 m (the limit standard of the RUSLE model) at a resolution of 30 m reaches 94.19%.

Modified stochastic diffusion particle-tracking model (MSDPTM) incorporating energy cascade theory and eddy intermittency for suspended sediment transport in open channel flow.

This study presents a modified stochastic diffusion particle tracking model (MSDPTM) that incorporates energy cascade theory to more accurately simulate suspended sediment transport. The impact of turbulent eddies on sediment particles is an intermittent process, which is also considered in this study. The study examines the time correlation between eddies using eddy turnover time and finds that closer-scale eddies exhibit higher correlations than those farther apart. The statistical properties of particle movement, such as the ensemble mean and variance of particle trajectories, have been calculated and compared with the stochastic diffusion particle tracking model (SDPTM) results. Notably, MSDPTM with intermittency demonstrates a significantly larger ensemble mean of particle trajectories in the streamwise direction than other particle tracking models. The proposed model is validated through comparison with available data, showing its enhanced performance. The results of the simulation indicate that MSDPTM outperforms SDPTM, especially when the intermittency effect of eddies is considered.

Post-mechanotherapy differences in postural control in patients with Achilles tendinopathy - A randomized controlled trial

BackgroundNeuromuscular deficits affecting functional ability can occur in patients with Achilles tendinopathy during difficult balance activities. This study aimed to assess postural control in patients with Achilles tendinopathy after shockwave and sonotherapy, using advanced analytical methods, including rambling-trembling signal decomposition and sample entropy. Research questionWhat are the differences in postural control between patients with Achilles tendinopathy after shockwave therapy, ultrasound therapy, and placebo ultrasound? MethodsThirty-nine patients were included in the study, and randomly assigned to 3 groups, i.e., shockwave therapy, ultrasound therapy and placebo ultrasound. Postural sway was assessed during quiet standing with eyes open and closed, with two force platforms, one for the affected and the other for the non-affected limb, at baseline and at weeks 1 and 6 after treatment. Rambling-trembling trajectories and sample entropy were calculated for the antero-posterior and medio-lateral directions. ResultsThe parameters of trembling trajectory in both directions were significantly smaller for the affected compared to non-affected limb. The ultrasound group had significantly larger rambling-trembling trajectories in the antero-posterior and medio-lateral sway directions than the shockwave therapy group. Also, all patients had more difficulty controlling their postural sway while standing with eyes closed compared to eyes open. Sample entropy was not significantly affected by the therapy type, timepoint and limb condition. SignificanceAs opposed to sample entropy, rambling-trembling decomposition can complement or replace traditional linear measures of COP time series in functional assessment of the Achilles tendon.

Kinetics and Dynamics of Cyclopentanone Thermal Decomposition in Gas Phase.

Cyclopentanone is a potential bio-fuel which can be produced from bio-mass. Its gas phase dissociation chemistry has attracted several experimental and theoretical investigations. In the photochemical and thermal decomposition studies of cyclopentanone, ethylene and carbon monoxide were found to be dominant reaction products along with several other compounds in smaller quantities. For the formation of ethylene and carbon monoxide, a concerted mechanism has been proposed as primary reaction pathway. In addition, a step-wise mechanism involving ring-opened radical intermediate has also been considered. The present work reports gas phase thermal decomposition of cyclopentanone at high temperatures investigated using electronic structure theory methods, Rice-Ramsperger-Kassel-Marcus (RRKM) rate constant calculations, and Born-Oppenheimer direct classical trajectory simulations. The trajectory calculations were performed on density functional PBE96/6-31+G* potential energy surface using initial conditions selected from fixed energy normal mode distributions. Simulations showed that ethylene and carbon monoxide formed primarily via the concerted mechanism confirming the earlier predictions. In addition, stepwise pathways were also observed for same products in lower fraction of trajectories. Furthermore, several other reaction products in smaller quantities and new mechanistic pathways were observed. The computed RRKM rate constants and simulation data are agreement with experimental results and detailed atomic level dissociation mechanisms presented.

Investigation of Aircraft Conflict Resolution Trajectories under Uncertainties.

As air traffic intensity increases and stochastic uncertainties, such as wind direction and speed, continue to impact air traffic controllers' workload significantly, airlines are increasingly pressured to reduce costs by flying via straighter/more direct trajectories. Due to these changes, it is important to search for new means/solutions for aircraft conflict resolution to ensure the required level of safety and rational flight trajectory. Such a solution could be the implementation of Dubin's method of flight trajectories. This paper aims to propose and deeply analyze a new mathematical model for two-aircraft conflict resolution where the Dubins method is applied in a dynamic conflict scenario. In this model, at a certain moment, the flight trajectory of one aircraft follows a path similar to a moving circle's tangential line. Upon that, the conflict detection and resolution (CDR) model considers wind uncertainty. The proposed CDR method could be applied when uncertainty such as wind direction and speed are inconstant (stochastic) throughout the simulation.

Sunflower-Inspired Superhydrophobic Surface with Composite Structured Microcone Array for Anisotropy Liquid/Ice Manipulation.

Precisely controlling the directional motion trajectories of droplets on anisotropic 3D functional surfaces has great application potential in self-cleaning, drug delivery, and droplet power generation, but it also faces huge challenges. Herein, inspired by the microcone structure in the heart of sunflowers, a nanoneedle-modified microcone array surface (NMAS)is reported. The surface is created using a combination of nanosecond laser direct engraving and electroforming and is subsequently fluorinated. Through programmable control of the laser spot, the geometric parameters and inclination angle of the microcone can be quickly and finely adjusted, thereby achieving precise control of the droplet bouncing trajectory. The results show that droplets can achieve programmable multiple bouncing behaviors on patterned functional surfaces, including gravity-defying hopping and directional water transport. It is worth noting that this functional surface has delayed freezing and anti-freezing effects. Furthermore, this functional surface has a wide range of potential applications, including surface self-cleaning, droplet capture, and droplet-based chemical microreactions, especially in the field of anti-icing operations. This opens up a new way for the directional transport of droplets on biomimetic functional surfaces.

Individualized Design Application of 3-Dimensional Printing Navigational Template for Pedicle Screw Installation: A Training Case Report.

BACKGROUND The proper installation for pedicle screws by the traditional method of surgeons dependent on experience is not guaranteed, and educational solutions have progressed from chalkboards to electronic teaching platforms. We designed a case of 3-dimensional printing drill guide template as a surgical application, which can accurately navigate implantation of pedicle screws, and assessed its effect for simulative training. MATERIAL AND METHODS We randomly selected a set of computed tomography data for spondylolisthesis. A navigational template of pedicles and screws was designed by software Mimics and Pro-E, where trajectories of directions and angles guiding the nail way were manipulated for screwing based on anatomy, and its solid model was fabricated by a BT600 3D printer. The screws were integrated and installed to observe their stability. RESULTS The navigational model and custom spine implants were examined to be compatibly immobilized, because they are tolerant to radiation and stable against hydrolysis. The screw size and template were fit accurately to the vertebrae intraosseously, because the pilot holes were drilled and the trajectories were guided by cannulas with visible routes. During the surgical workflow, the patient reported appreciation and showed substantial compliance, while having few complications with this approach. Compared with fluoroscopy-assisted or free-hand techniques, the effect of simulative training during processing was excellent. CONCLUSIONS The surgical biomodel is practical for the procedural accuracy of surgical guides or as an educational drill. This fostering a style of "practice substituting for teaching" sets a paragon of keeping up with time and is worthy of recommendation.

SupraPetrous InfraTemporal Approach: A Supplemental Approach to Supracerebellar Infratentorial for Inferior Amygdala and Hippocampal Head Access-A Cadaveric Study With Case Illustrations.

Access to the amygdala and hippocampus (A/H) is complex. To address the limitations and invasiveness of traditional approaches, including the Transsylvian, Subtemporal, and Supracerebellar infratentorial approaches, we developed the suprapetrous infratemporal (SPIT) approach. This study describes the nuances of this approach in both cadaveric studies and clinical cases. Three unilateral exposures were performed using microscopic and endoscopic methodologies in the SPIT approach. After cadaveric investigation, this approach was successfully implemented in representative clinical cases. The SPIT approach enabled direct access to the inferior A/H, circumventing the requirement for temporal lobe retraction and detachment of the temporal lobe from the dura through a subtemporal route by drilling the upper part of the mastoid, consequently mitigating tension on the vein of Labbé. This enabled a bottom-up view because one would gain with a zygomatic osteotomy and forward projection like a mini-posterior petrosal view by using a transmastoid view, without cutting down the zygomatic arch and opening the dura subtemporally, limiting patient pain and preventing case comorbidity. The SPIT approach was performed in 2 cases of mesial temporal cavernoma presenting with seizures. The lesion was visualized intraoperatively and was successfully removed in these cases. The postoperative course was excellent with no complications, and gross total resection was radiographically confirmed with Engel Class 1a seizure freedom. The SPIT approach is a complementary approach for inferior A/H disease, combining the combined middle fossa approach modified for intradural pathology. Limited drilling of the upper aspect of the mastoid with a medial dural opening at the level of the arcuate eminence provides a direct trajectory with minimal brain retraction. Additional research encompassing a larger patient cohort and extended follow-up periods is required to substantiate the advantages of SPIT in the management of inferior A/H lesions.

Exploring the Feasibility of Kuiper Belt Missions Supported by Centrifugal Nuclear Thermal Propulsion

Missions to the Kuiper belt have previously been carried out only as flybys and with very small payloads. Investigating launch windows for Kuiper belt missions supported by centrifugal nuclear thermal propulsion (CNTP) contributes to defining its operational use case. Results indicate that CNTP enables rendezvous missions to the Kuiper belt, both with direct transfer trajectories or planetary gravity assist trajectories, although there are many challenges to making these mission architectures feasible. The direct trajectories have transfer times of roughly 14 to 16 years while combining CNTP with gravity assists from Jupiter could lower transfer time to as low as 10 to 12 years to Kuiper belt objects such as Pluto and Quaoar. These missions are then shown to inform the architecture of the CNTP injection stage vehicle, which can be supported by heavy and super-heavy commercial launch vehicles with a single launch. Last, drawbacks of the mission and vehicle architectures are given that impose limits on the use case for CNTP on these missions.

Efficient Motion Primitives-Based Trajectory Planning for UAVs in the Presence of Obstacles

The achievement of full autonomy in Unmanned Aerial Vehicles (UAVs) is significantly dependent on effective motion planning. Specifically, it is crucial to plan collision-free trajectories for smooth transitions from initial to final configurations. However, finding a solution executable by the actual system adds complexity: the planned motion must be dynamically feasible. This involves meeting rigorous criteria, including vehicle dynamics, input constraints, and state constraints. This work addresses optimal kinodynamic motion planning for UAVs in the presence of obstacles by employing a hybrid technique instead of conventional search-based or direct trajectory optimization approaches. This technique involves precomputing a library of motion primitives by solving several Two-Point-Boundary-Value Problems (TPBVP) offline. This library is then repeatedly used online within a graph-search framework. Moreover, to make the method computationally tractable, continuity between consecutive motion primitives is enforced only on a subset of the state variables. This approach is compared with a state-of-the-art quadrotor-tailored search-based approach, which generates motion primitives online through control input discretization and forward propagation of the dynamic equations of a simplified model. The effectiveness of both methods is assessed through simulations and real-world experiments, demonstrating their ability to generate resolution-complete, resolution-optimal, collision-free, and dynamically feasible trajectories. Finally, a comparative analysis highlights the advantages, disadvantages, and optimal usage scenarios for each approach.

Trajectory-Based Time-Resolved Mechanism for Benzene Reductive Elimination from Cyclopentadienyl Mo/W Phenyl Hydride Complexes.

Calculated potential energy structures and landscapes are very often used to define the sequence of reaction steps in an organometallic reaction mechanism and interpret kinetic isotope effect (KIE) measurements. Underlying most of this structure-to-mechanism translation is the use of statistical rate theories without consideration of atomic/molecular motion. Here we report direct dynamics simulations for an organometallic benzene reductive elimination reaction, where nonstatistical intermediates and dynamic-controlled pathways were identified. Specifically, we report single spin state as well as mixed spin state quasiclassical direct dynamics trajectories in the gas phase and explicit solvent for benzene reductive elimination from Mo and W bridged cyclopentadienyl phenyl hydride complexes ([Me2Si(C5Me4)2]M(H)(Ph), M = Mo and W). Different from the energy landscape mechanistic sequence, the dynamics trajectories revealed that after the benzene C-H bond forming transition state (often called reductive coupling), σ-coordination and π-coordination intermediates are either skipped or circumvented and that there is a direct pathway to forming a spin flipped solvent caged intermediate, which occurs in just a few hundred femtoseconds. Classical molecular dynamics simulations were then used to estimate the lifetime of the caged intermediate, which is between 200 and 400 picoseconds. This indicates that when the η2-π-coordination intermediate is formed, it occurs only after the first formation of the solvent-caged intermediate. This dynamic mechanism intriguingly suggests the possibility that the solvent-caged intermediate rather than a coordination intermediate is responsible (or partially responsible) for the inverse KIE value experimentally measured for W. Additionally, this dynamic mechanism prompted us to calculate the kH/kD KIE value for the C-H bonding forming transition states of Mo and W. Surprisingly, Mo gave a normal value, while W gave an inverse value, albeit small, due to a much later transition state position.

A high-altitude geomagnetic matching area selection approach based on geomagnetic information entropy and geomagnetic direction entropy

Aiming at the obvious trend of the contours on the high-altitude geomagnetic map, this paper presents a method of high-altitude geomagnetic matching area selection combining geomagnetic information entropy and geomagnetic direction entropy based on the study of geomagnetic information entropy and geomagnetic direction entropy. The method first uses geomagnetic information entropy to select the region with rich geomagnetic information, and then determines the direction of the flight trajectory according to geomagnetic direction entropy to obtain the optimal matching trajectory. Finally, the method compares and analyzes the matching localization results of three flight trajectories in different directions on the geomagnetic map at an altitude of 30,000 m by using semi-physical simulation. The experimental results show that the flight navigation error along the trajectory with small information entropy is small, and its positioning error is 12.7% of the trajectory positioning error along the maximum information entropy direction. Selecting the flight trajectory according to the value of the geomagnetic direction entropy can greatly improve the precision and reliability of the geomagnetic matching localization. The method in this paper can provide a basis for path planning of the geomagnetic matching navigation.

The Application of Artificial Intelligence Technology in Shipping: A Bibliometric Review

Artificial intelligence (AI) technologies are increasingly being applied to the shipping industry to advance its development. In this study, 476 articles published in the Science Citation Index Expanded (SCI-EXPANDED) and the Social Sciences Citation Index (SSCI) of the Web of Science Core Collection from 2001 to 2022 were collected, and bibliometric methods were applied to conduct a systematic literature of the field of AI technology applications in the shipping industry. The review commences with an annual publication trend analysis, which shows that research in the field has been growing rapidly in recent years. This is followed by a statistical analysis of journals and a collaborative network analysis to identify the most productive journals, countries, institutions, and authors. The keyword “co-occurrence analysis” is then utilized to identify major research clusters, as well as hot research directions in the field, providing directions for future research in the field. Finally, based on the results of the keyword co-occurrence analysis and the content analysis of the papers published in recent years, the research gaps in AIS data applications, ship trajectory, and anomaly detection, as well as the possible future research directions, are discussed. The findings indicate that AIS data in the future research direction are mainly reflected in the analysis of ship behavior and AIS data repair. Ship trajectory in the future research direction is mainly reflected in the deep learning-based method research and the discussion of ship trajectory classification. Anomaly detection in the future research direction is mainly reflected in the application of deep learning technology in ship anomaly detection and improving the efficiency of ship anomaly detection. These insights offer guidance for researchers’ future investigations in this area. In addition, we discuss the implications of research in the field of shipping AI from both theoretical and practical perspectives. Overall, this review can help researchers understand the status and development trend of the application field of AI technology in shipping, correctly grasp the research direction and methodology, and promote the further development of the field.

Regional transformation pathways for the bioeconomy: A novel monitoring approach for complex transitions

AbstractAddressing the complexities of transitioning to a sustainable bioeconomy, this paper presents a novel approach for developing regional transformation pathways (RTPs) based on narratives derived from the shared socioeconomic pathways. The methodology emphasizes a comprehensive understanding of underlying perspectives and perceptions, incorporating socio‐economic, environmental, and political dimensions. The developed indicator framework captures a balanced representation of diverse interests by integrating insights from stakeholder analyses. The case study in the Rheinisches Revier region, Germany, exemplifies the approach's applicability, providing valuable insights for decision‐making processes in the context of regional transitions toward a low‐carbon economy. The results consist of five developed RTPs, offering a multitude of potential future trajectories of possible directions for regional transformations. Understanding potential pathways and related consequences is crucial for informed decision‐making concerning resource use optimization since transformations of that scale influence the composition of supply chains and resource networks. This informed approach contributes to strategic planning and helps ensure resources are utilized efficiently and sustainably. By emphasizing the crucial role of transparency and reflection of assumptions in addressing the complexities of societal transformation processes, our approach seeks to support the implementation of a sustainable and inclusive bioeconomy at the regional level.

Ultrafast transfer of low-mass payloads to Mars and beyond using aerographite solar sails

With interstellar mission concepts now being under study by various space agencies and institutions, a feasible and worthy interstellar precursor mission concept will be key to the success of the long shot. Here we investigate interstellar-bound trajectories of solar sails made of the ultra lightweight material aerographite. Due to its extremely low density (0.18kg m−3) and high absorptivity (A∼1), a thin shell can pick up an enormous acceleration from the solar irradiation. Payloads of up to 1kg can be transported rapidly throughout the solar system, e.g., to Mars and beyond. Our simulations consider various launch scenarios from a polar orbit around Earth including directly outbound launches as well as Sun-diver launches towards the Sun with subsequent outward acceleration. We use the poliastro Python library for astrodynamic calculations. For a spacecraft with a total mass of 1kg (including 720g aerographite) and a cross-sectional area of 104m2, corresponding to a shell with a radius of 56m, we calculate the positions, velocities, and accelerations based on the combination of gravitational and radiation forces on the sail. We find that the direct outward transfer to Mars near opposition to Earth results in a relative velocity of 65km s−1 with a minimum required transfer time of 26d. Using an inward transfer with solar sail deployment at 0.6AU from the Sun, the sail’s velocity relative to Mars is 118km s−1 with a transfer time of 126d, where Mars is required to be in one of the nodes of the two orbital planes upon sail arrival. Transfer times and relative velocities can vary substantially depending on the constellation between Earth and Mars and the requirements on the injection trajectory to the Sun diving orbit. The direct interstellar trajectory has a final velocity of 109km s−1. Assuming a distance to the heliopause of 120AU, the spacecraft reaches interstellar space after 5.3yr. When using an initial Sun dive to 0.6AU instead, the solar sail obtains an escape velocity of 148km s−1 from the solar system with a transfer time of 4.2yr to the heliopause. Values may differ depending on the rapidity of the Sun dive and the minimum distance to the Sun. The mission concepts presented in this paper are extensions of the 0.5kg tip mass and 196m2 design of the successful IKAROS mission to Venus towards an interstellar solar sail mission. They allow fast flybys at Mars and into the deep solar system. For delivery (rather than fly-by) missions of a sub-kg payload, for example medical supply or replenishment of essential materials, the biggest obstacle remains in the deceleration upon arrival.

Simulation and analysis of chest loads on crews during Lunar-Earth re-entry returns.

The safety of crews is the primary concern in the manned lunar landing project, particularly during re-entry as the manned spacecraft returns from a direct Lunar-Earth trajectory. This paper analyzed the crew's chest biomechanical response to assess potential injuries caused by acceleration loads during the re-entry phase. Initially, a sophisticated finite element model of the chest was constructed, whose effectiveness was verified by experiments involving vertebral range of motion, rib lateral rupture, and chest frontal impact. The model was then subjected to the return re-entry loads simulating the Apollo and Chang'e 5 T1 (CE-5T1) test returner to specifically analyze the correlation between the acceleration load and the injury of the crew's chest tissues and organs. The results indicate that the biomechanical response of crew chest bone tissue under the two return missions is within the threshold value and will not directly cause damage. Compared to the Apollo mission, the CE-5T1 mission's load poses a higher risk to internal organs. These findings can enhance the crew's safety and provide reliable assurance for future space exploration.

Theoretical Investigation of Bimolecular Carbon Chain Growth Reactions in the Interstellar Media.

Detection of molecular anions in interstellar media implies that negatively charged species play a prominent role in astrochemical reactions. Among the observed species, carbon chain anions are important, as they can be precursors for the production of complex organic molecules. These anions can form either via direct electron attachment to the corresponding neutral species or through chain growth reactions of smaller anions, resulting in longer chains. In a recent study, crossed beam experiments coupled with velocity map imaging techniques were used to investigate the carbon chain growth reaction C2n- + C2H2 → C2n+2Hm- + H2-m (n = 1-3, m = 0,1). Products and branching ratios were established from experimental data. In the present work, electronic structure calculations and on-the-fly direct dynamics simulations were used to study these reactions. Energy profiles were investigated by using different density functional methods. Direct trajectory simulations were performed at the experimental collision energies using the B3LYP/6-31+G* level of theory. Trajectory analysis showed a variety of reaction pathways, and detailed atomic-level reaction mechanisms are presented.

An artificial intelligent well trajectory design method combining both geological and engineering objectives

Conventional directional well trajectory is designed to connect the wellhead and target point or section with multiple engineering objectives including deflecting capacity, torsional strength, total length, etc. With the growing need of directional wells for complex geological conditions, only the target point or section provided by geologists and reservoir engineers may not be satisfied as the geological objective for well trajectory design. The whole geological profile along the well trajectory can be taken as the geological objective instead of the target point or section. Furthermore, the state-of-the-art of the artificial intelligence algorithm can be applied automatically evaluate the geological profile and form a new geology objective for well trajectory design. In this study, an algorithm is proposed to evaluate the geological profile and a new index, formation evaluation score (FES), is obtained as the geological target for well trajectory design together with conventional multiple engineering objectives. With the combined multiple geological and engineering target, a directional well trajectory is optimized. The results show that the hydrocarbon formation contact effectively increases under comparable engineering conditions, which confirms the benefit of the proposed method in this work. In addition, the proposed method can globally optimize well trajectory with the help of the geological profile, as opposed to locally satisfy the target point or section. The automation of geological formation analysis can also reduce the workload for geologist and reservoir engineers. The outcome of this work may pave the way to comprehensive combine the geological and engineering objectives for directional well design under higher automation levels.

Anatomizing online collaborative inquiry using directional epistemic network analysis and trajectory tracking

AbstractAccurate assessment and effective feedback are crucial for cultivating learners' abilities of collaborative problem‐solving and critical thinking in online inquiry‐based discussions. Based on quantitative content analysis (QCA), there has been a methodological evolvement from descriptive statistics to sequential mining and to network analysis for mining coded discourse data. Epistemic network analysis (ENA) has recently gained increasing recognition for modelling and visualizing the temporal characteristics of online discussions. However, due to methodological restraints, some valuable information regarding online discussion dynamics remains unexplained, including the directionality of connections between theoretical indicators and the trajectory of thinking development. Guided by the community of inquiry (CoI) model, this study extended generic ENA by incorporating directional connections and stanza‐based trajectory tracking. By examining the proposed extensions with discussion data of an online learning course, this study first verified that the extensions are comparable with QCA, indicating acceptable assessment validity. Then, the directional ENA revealed that two‐way connections between CoI indicators could vary over time and across groups, reflecting different discussion strategies. Furthermore, trajectory tracking effectively detected and visualized the fine‐grained progression of thinking. At the end, we summarize several research and practical implications of the ENA extensions for assessing the learning process.Practitioner notesWhat is already known about this topic Assessment and feedback are crucial for cultivating collaborative problem‐solving and critical thinking in online inquiry‐based discussions. Cognitive presence is an important construct describing the progression of thinking in online inquiry‐based discussions. Epistemic network analysis is gaining increasing recognition for modelling the temporal characteristics of online inquiries. What this paper adds Directional connections between discourses can reflect different online discussion strategies of groups and individuals. A pair of connected discourses coded with the community of inquiry model can have different meanings depending on their temporal order. A trajectory tracking approach can uncover the fine‐grained progression of thinking in online inquiry‐based discussions. Implications for practice and/or policy Besides the occurrences of individual discourses, examining the meanings of directional co‐occurrences of discourses in online discussions is worthwhile. Groups and individuals can employ different discussion strategies and follow diverse paths to thought development. Developmental assessment is crucial for understanding how participants achieve specific outcomes and providing adaptive feedback.