Trajectory Method Research Articles

Identifying the Most Successful Formula 1 Drivers in the Turbo Era

Background: Formula 1 is the world’s fastest auto racing circuit and one that is among the most-watched of all televised sports. With its international flair and glamor and the glitz it brings to viewers and spectators, it is no surprise that fans, commentators, and media covering the races enjoy ranking the most successful teams and especially the most successful drivers of all time. Yet, there are few empirical studies that have developed and/or applied rigorous methodological techniques to examine which drivers are the most successful within the recent turbo-hybrid era. Objective: This study uses novel group-based trajectory methods to rank the most successful drivers within the turbo area, 2014-2019. Methods: Group-based trajectory methods are used to identify distinct groups of drivers according to accumulated points. Results: Using total points accumulated during each respective season as our measure of success, results showed that the 45 drivers who competed during this time period could be classified into three groups, with the top-performing group of drivers being Lewis Hamilton and Nico Rosberg. A second better-performing group of six drivers followed and included Bottas, LeClerc, Räikkönen, Ricciardo, Verstappen, and Vettel. The remaining 37 drivers were classified into a third low-performing group, a great number of which scored zero points during the time period. Conclusion: The most successful Formula 1 drivers during the turbo era were able to be identified using group-based trajectory modeling, with Lewis Hamilton and Nico Rosberg identified as the best drivers based on accumulated points.

Globally Accurate Potential Energy Surface for BH2+2(13A') Using the Switching Function Formalism.

A great number of ab initio energy points are calculated using the aug-cc-pV(Q,5)Z basis sets at the multireference configuration interaction level and extrapolated to the complete basis set limit. An exact three-dimensional potential energy surface of the ground-state BH2+ is obtained. A switching function is developed to model the transition of B+(3P) to B+(1S) to guarantee the reliable behavior at B+(3P) + H2(X1∑g+) and BH+(X2∑+) + H(2S) dissociation limits. The various topographic features of the new global potential energy surface are discussed in detail, showing a good agreement with the previous results from the theory. The quasi-classical trajectory method is utilized to calculate the integral cross sections of the B+(3P) + H2(X1∑g+) (v = 0, j = 0) → BH+(X2∑+) + H(2S) reaction, which can provide another support for reliability of the title potential energy surface.

Can the cortical bone trajectory screw technique be an alternative method to the pedicle screw in posterior lumbar fusion? A systematic review and metaanalysis.

The aim of this study was to verify the practicability of the cortical bone trajectory (CBT) method by comparing the clinical outcomes including the complications between the CBT method and pedicle screws (PSs). MEDLINE, EMBASE, Cochrane Central Register of Controlled Trials (CENTRAL), web of Science, and SCOPUS electronic databases were searched for relevant articles published through March 2021 that compared the outcomes of the CBT and PSs. The data search, extraction, analysis, and quality assessment were performed according to the Cochrane Collaboration guidelines. The clinical and radiological outcomes of both techniques were evaluated using various outcome measures. Sixteen studies with a total of 1173 patients were included in the study. The outcomes in the meta-analysis indicated that the use of CBT fixation showed better results for overall complications (P < 0.0001), symptomatic adjacent segment disease (sASD) (P = 0.007), superior facet joint violation (SFJV) rate (P = 0.007), operating time (P = 0.007), intraoperative blood loss (P < 0.00001), incision length (P = 0.002), length of hospital stay (P = 0.0006), and revision rates (P = 0.02). However, there were no statistically significant differences in fusion rates or detailed complications including hardware complications, wound infections (all P > 0.05) between the CBT method and PS fixation groups. The present study revealed that the CBT method was associated with higher functional recovery, lower surgical morbidity rates, lower revision rates, and lower overall complication rates including sASD and SFJV rates. However, both the CBT method and PSs had similar fusion rates, complications including hardware complications (screw malposition, screw loosening, and screw pullout) and wound infections. Thus, the CBT method did not outperform the PSs in all aspects. Therefore, it is recommended to select a surgical method in consideration of the patient's bone mineral density, the condition of the pars interarticularis, or the skill level of the surgeon. Prognostic evaluation through long-term follow-up is required, and more high-quality randomized controlled trials are required to verify and strengthen our results. Level III, Therapeutic Study.

Multi-CRAFTI: Relative Collision Cross Sections from Fourier Transform Ion Cyclotron Resonance Mass Spectrometric Line Width Measurements.

Determination of collision cross sections (CCS) using the cross-sectional areas by the Fourier transform ion cyclotron resonance (CRAFTI) technique is limited by the requirement that accurate pressures in the trapping cell of the mass spectrometer must be known. Experiments must also be performed in the energetic hard-sphere regime such that ions decohere after single collisions with neutrals; this limits application to ions that are not much more massive than the neutrals. To mitigate these problems, we have resonantly excited two (or more) ions of different m/z to the same center-of-mass kinetic energy in a single experiment, subjecting them to identical neutral pressures. We term this approach "multi-CRAFTI". This facilitates measurement of relative CCS without requiring knowledge of the pressure and enables determination of absolute CCS using internal standards. Experiments with tetraalkylammonium ions yield CCS in reasonable agreement with the one-ion-at-a-time CRAFTI approach and with ion mobility spectrometry (IMS) when differences in collision energetics are taken into account (multi-CRAFTI generally yields smaller CCS than does IMS due to the higher collision energies employed in multi-CRAFTI). Comparison of multi-CRAFTI and IMS results with CCS calculated from structures computed at the M06-2X/6-31+G* level of theory using projection approximation or trajectory method values, respectively, indicates that the computed structures have CCS increasingly smaller than the experimental CCS as m/z increases, implying the computational model overestimates interactions between the alkyl arms. For ions that undergo similar collisional decoherence processes, relative CCS reach constant values at lower collision energies than do absolute CCS values, suggesting a means of increasing the accessible upper m/z limit by employing multi-CRAFTI.

Collisions of antiprotons with excited positronium atoms

A detailed theoretical investigation of the fundamental three-body antiproton-positronium system is presented, utilizing both quantum convergent close coupling and classical trajectory methods. We evaluate scattering cross sections for all major processes, including charge transfer and breakup, over a wide range of positronium kinetic energies and states with principal quantum number ${n}_{\mathrm{Ps}}\ensuremath{\le}6$. The study has significantly extended previous work, and the direct quantum-classical comparison has revealed a systematic approach to obtaining cross sections for arbitrarily high ${n}_{\mathrm{Ps}}$. This is of major significance for prospective applications of collisions of excited positronium atoms in cold (anti-)atomic physics.

A new application of multi-criteria decision making in identifying critical dust sources and comparing three common receptor-based models

Dust storms are a common phenomenon in arid and semi-arid regions in West Asia, which has led to high levels of PM10 in local and remote area. The Yazd city in Iran with a high PM10 level located downstream of dust sources in the Middle East and Central Asia. In this study, based on meteorological and PM10 monitoring data, backward trajectory modeling of air parcels related to dust events at Yazd station was performed using the HYSPLIT model in 2012–2019. The trajectory cluster analysis was used to identify the main dust transport pathways and wind systems. Three methods of Cross-referencing Backward Trajectory (CBT), Potential Source Contribution Function (PSCF) and Concentration Weighted Trajectory (CWT) were used to identify the most critical dust sources. Multi-Criteria Decision Making (MCDM) methods were also used to integrate the results. Nine dust sources affecting central Iran were determined, and six criteria from different aspects were considered. To prioritize the dust sources affecting central Iran from four new MCDM methods, including WASPAS, EDAS, ARAS and TOPSIS were used. The results showed that the Levar wind system (51%), the Shamal wind system (32%) and the Prefrontal wind system (18%) were the most important wind systems to cause dust events in central Iran. The MCDM approach to identify dust sources also showed that Dasht-e-Kavir in central Iran was the most critical dust source. The results also showed that in hot seasons (spring and summer), local and Central Asia dust sources and cold seasons (autumn and winter), Middle East dust sources have the greatest impact on dust events in central Iran. Also, a comparison of common receptor-based methods for identifying dust sources showed that CBT, CWT and PSCF were the most appropriate methods for identifying dust sources, respectively.

The numerical simulation of the generation of lower-band VLF chorus using a quasi-broadband Vlasov Hybrid Simulation code

In this paper, we perform the numerical modelling of lower-band VLF chorus in the earth’s magnetosphere. Assuming parallel propagation the 1d3v code has one spatial dimension z along the ambient magnetic field, which has a parabolic z dependence about the equator. The method used is Vlasov Hybrid Simulation (VHS) also known in the literature as the method of Kinetic Phase Point Trajectories (Nunn in Computer Physics Comms 60:1–25, 1990, J Computational Phys 108(1):180–196, 1993; Kazeminezhad et al. in Phys Rev E67:026704, 2003). The method is straightforward and easy to program, and robust against distribution function filamentation. Importantly, VHS does not invoke unphysical smoothing of the distribution function. Previous versions of the VLF/VHS code had a narrow bandwidth ~ 100 Hz, which enabled simulation of a wide variety of discrete triggered emissions. The present quasi-broadband VHS code has a bandwidth of ~ 3000 Hz, which is far more realistic for the simulation of chorus in its entirety. Further, the quasi-broadband code does not require artificial saturation, and does not need to employ matched filtering to accommodate large spatial frequency gradients. The aim of this paper which has been achieved is to produce VLF chorus Vlasov simulations employing a systematic variety of triggering input signals, namely key down, single pulse, PLHR, and broadband hiss.Graphical

Squeezed-vacuum-induced optical tristability in an atom-cavity system

In this paper we investigate the model of $N$ two-level atoms coupled to a squeezed vacuum inside a coherently driven cavity. By a linear stability analysis in the semiclassical description, we find that the optical tristability emerges in our system owing to the presence of the squeezed vacuum. Moreover, the transition among monostable, bistable, and tristable states can be realized by manipulating the squeezing phase or the squeezing strength of the squeezed vacuum. We also show the signatures of quantum tristability by using the $Q$ function and quantum trajectory methods for the situation of a single atom and low cavity photon number. Our paper offers a way to realize optical tristability in a two-level atomic system.

An Improved Similarity Trajectory Method Based on Monitoring Data under Multiple Operating Conditions

With the complexity of the task requirement, multiple operating conditions have gradually become the common scenario for equipment. However, the degradation trend of monitoring data cannot be accurately extracted in life prediction under multiple operating conditions, which is because some monitoring data is affected by the operating conditions. Aiming at this problem, this paper proposes an improved similarity trajectory method that can directly use the monitoring data under multiple operating conditions for life prediction. The morphological pattern and symbolic aggregate approximation-based similarity measurement method (MP-SAX) is first used to measure the similarity between the monitoring data under multiple operating conditions. Then, the similar life candidate set, and corresponding weight are obtained according to the MP-SAX. Finally, the life prediction results of equipment under multiple operating conditions can be calculated by aggregating the similar life candidate set. The proposed method is validated by the public datasets from NASA Ames Prognostics Data Repository. The results show that the proposed method can directly and effectively use the original monitoring data for life prediction without extracting the degradation trend of the monitoring data.

Photon statistics of the light transmitted and reflected by a two-dimensional atomic array

This work proposes to investigate the photon statistics of the light transmitted and reflected by a two-dimensional array of interacting atoms. The reflected beam is characterized by photon antibunching. On the other hand, in the transmitted beam the indistinguishability between the driving laser photons and the photons re-emitted by the atoms results in photon bunching. The overlap between the driving and scattered fields is enhanced by the cooperative optical response of the atomic array. In the examples used in this paper, up to 25\% of the transmitted photons are grouped in pairs. The simulations are carried out using the stochastic method of quantum trajectories.

Quantum and quasiclassical dynamics of Coriolis coupling effects and stereodynamics

The dynamics of C + H2 → H + CH reaction is theoretically studied using the quasiclassical trajectory and quantum mechanical wave packet methods. The analysis of reaction probabilities, integral cross sections, and rate coefficients reveal the essential Coriolis coupling effects in the quantum mechanical wave packet calculations. The calculated polarization-dependent differential cross section, P(θr ) and P(ϕr ) show that the j ′ of product rotational angular momentum is not only aligned along the y axis and the direction of the vector x + z , but also strongly oriented along the positive y axis.

Using fireball networks to track more frequent reentries: Falcon 9 upper-stage orbit determination from video recordings

On February 16, 2021, an artificial object was recorded by the Spanish Meteor Network (SPMN) moving slowly over the Mediterranean. From the astrometric measurements, we identify this event as the reentry engine burn of a SpaceX Falcon 9 launch vehicle's upper stage. To study this event in detail, we adapted the plane intersection method for near-straight meteoroid trajectories to analyze slow and curved orbits associated with artificial objects. To corroborate our results, we approximated the orbital elements for the upper stage using four pieces of "debris" cataloged by the U.S. Government Combined Space Operations Center (CSpOC). Based on these calculations, we also estimated the possible deorbit hazard zone using the MSISE90 model atmosphere. We warn of the interference that these artificial bolides might have in fireball studies. In addition, given that artificial bolides will be probably more frequent in the future, we point out the new role that ground-based detection networks can play in the monitoring of potentially hazardous artificial objects in near-Earth space and determining the strewn field of artificial space debris.

Iterative synthesis of binary inline Fresnel holograms for high-quality reconstruction in divergent beams with DMD

Aim of this paper is formation of single focused diffraction order using binary amplitude modulation for digital micromirror device (DMD) applications. This can be achieved by using inline binary Fresnel holograms with divergent incident beam. However, extremely low reconstruction quality and diffraction efficiency of such holograms, synthesized by conventional means, prevent it. Here, we present new iterative method of synthesis of binary inline Fresnel holograms with much higher image reconstruction quality and diffraction efficiency compared to standard technique of hologram direct calculation. Synthesis procedure was carried out in two stages. The first stage of the new technique is based on Gerchberg-Saxton algorithm with two principal differences. First one is that synthesized diffractive optical element (DOE) is not a phase one, but an inline binary amplitude hologram. And second difference is that incident wavefront is spherical instead of a plane one. The second stage includes an application of the direct search with random trajectory method which greatly improves hologram characteristics by consequent processing of every pixel in it. The resulting binary inline Fresnel holograms in comparison to ones, synthesized using direct calculation method, have up to 11 times lower reconstruction error and up to 4 times higher diffraction efficiency. Results of optical reconstruction using DMD also demonstrate superiority of the new approach.

ConvLSTM based Estimation Method of Incision Trajectory with Electric Knife by Connecting Restored Thermal Sources.

Surgical navigation for understanding the internal structure of an organ is being actively studied, and it is necessary to estimate the incision trajectory to update the structure information dynamically. In this study, we focused on the fact that the region incised by the electric knife becomes high in temperature. Thus, we propose an estimation method of incision trajectory by restoring thermal source from diffused thermal images using a ConvLSTM and connecting the restored thermal sources. We first verified the possibility of thermal source restoration, and confirmed that the method enabled to restore the thermal source with high PSNR equivalent to 42.61. Next, we verified the accuracy of the incision trajectory from proposed method by comparing with the traditional method. The results suggested a better performance compared with the traditional method.

Pen-point Trajectory Analysis During Trail Making Test Based on a Time Base Generator Model.

The Trail Making test (TMT) is a widely used neuropsychological test to assess the cognitive function of patients. This paper presents the analysis method of pen-point trajectory during the TMT based on a time base generator (TBG). In the proposed method, the movement segments between targets are first extracted from pen-point trajectories, which are measured during performance of the TMT on an iPad. By fitting the extracted trajectories with a TBG-based trajectory generation model, the proposed method can then calculate quantitative indices representing the shape and collapse of the velocity profile. In the experiment, we analyzed TMT data from 25 stroke patients who were classified into three groups according to their scores on the Mini-Mental State Examination (MMSE). The results revealed that most of the measured inter-target trajectories had unimodal bell-shaped velocity profiles, as seen in reaching movements. Furthermore, we found that the degree of collapse in the velocity profile shape increased significantly when the cognitive function decreased.

Small-signal modeling and stability analysis of grid-connected offshore wind power based on virtual synchronous generator control

With the increasing installed capacity of offshore wind power, the grid-connected of offshore wind power technology based on virtual synchronous generators (VSG) control can simulate the inertia and damping characteristics of synchronous generator, which is helpful to improve the networking ability and inertial supportability of grid-connected inverter. However, VSG control also inevitably causes system oscillation, endangers the safe and stable operation of the power grid. Hence, the main circuit and control circuit of offshore wind power grid connection are firstly modeled, and the small-signal model of offshore wind power grid-connected inverter based on VSG control is obtained. Then the correctness of the model is verified by Matlab/Simulink software. Finally, the root trajectory method is used to identify the effects of VSG control parameters and line parameters on the system stability. The results show that VSG control has a significant influence on the stability of the grid-connected system, and reasonable design parameters are needed to ensure the safe and stable operation of the power grid.

A New 3D Shaping Method for Low-Thrust Trajectories between Non-Intersect Orbits

This paper proposes a new shape-based method in spherical coordinates to solve three-dimensional rendezvous problems. Compared with the existing shape-based methods, the proposed method does not need parameter optimization. Moreover, it improves the flexibility of orbit fitting, greatly reduces the velocity increment and maximum thrust acceleration, and ensures the orbit safety to a certain extent. The shaping function can provide the initial estimate for numerical trajectory optimization and improve the convergence rate in a certain range when combined with the normalization method. The superiority of the proposed method over the existing methods is demonstrated by two numerical examples. Its effectiveness at initial estimation generation in the indirect optimization of a low-thrust trajectory is demonstrated by the third example.

Electron trajectory backanalysis for spectral profile in two-color terahertz generation

The gas-phase medium ionized by two-color femtosecond field produces supercontinuum radiation ranging from the terahertz to midinfrared band. Under the strong-field approximation, the electron trajectory backanalysis is exploited to interpret the spectral profile of terahertz radiation. Meanwhile, the electron trajectory method can correlate terahertz spectral profiles and photoelectron momentum distributions (PEMDs). The coherent superposition of electron trajectories released from the consecutive cycles is found to induce the high-frequency cutoff and sharpen the spectral bandwidth of supercontinuum radiation, tightly coinciding with the intercycle interference fringes in PEMDs. The trajectory analysis exhibits that single electron interference plays an important role in the terahertz generation process. Our method provides an intuitive interpretation in terms of electron trajectory perspective and sheds light on the microscopic mechanisms of terahertz generation.

Development of a Model for Individual Educational Pathways in Engineering Education

Introduction. Individual educational pathways are widely used in higher education to optimize the educational process and harmonize the personal needs of students. The problem of their further development consists in improving scientific and methodological support and meeting the requirements of documents regulating educational activities. The purpose of the article is to present the results of theoretical substantiation, development and implementation of a model for individual educational pathways in engineering education. Materials and Methods. As a research toolkit, a methodological system, including an integrated and interdisciplinary (combine all components of the model of individual educational trajectories into a system), systemic, substrate and structured (for designing new models of individual educational trajectories) approaches was used; hypothetical-deductive, analysis-synthesis, morphology and classification (to analyze all possible models of individual educational trajectories), modeling and design (to create various individual educational trajectories) methods were also utilized. Results. In the course of the study, the definition of an individual educational pathway was formulated. As a result of the joint work of the authors from Mordovia State University and the engineering universities of the Republic of Kyrgyzstan, individual educational trajectories were developed for students of engineering specialisms at these universities. A generalized combinatorial model of possible individual educational pathways of engineering specialism has been developed. Discussion and Сonclusion. The results obtained contribute to the development of the curriculum design theory in the context of individual educational pathways. The materials of the article will be useful to researchers dealing with the problems of personalization of learning based on the use of individual educational trajectories.

Quasiclassical Trajectory Study of the O(3P) + CO2(1Σg+) Reaction at Hyperthermal Energies

This paper presents the reaction mechanism, cross sections, and product energy partitioning for the O + CO2 reaction, calculated using Born-Oppenheimer molecular dynamics simulations with the quasiclassical trajectory (BOMD-QCT) method. At collision energies up to 9.5 eV, three reactions, oxygen exchange (above ∼1.5 eV), abstraction (above ∼5.5 eV), and dissociation (above ∼7.5 eV) occur, with abstraction and dissociation involving either an insertion-elimination mechanism or a stripping mechanism. The insertion-elimination mechanism involves the formation of a planar CO3 intermediate which lies 0.52 eV above the ground-state CO2; the energetic barrier for oxygen abstraction via this mechanism is 3.52 eV. Interestingly, the insertion-elimination mechanism predominately contributes to the cross sections at collision energies just above the effective energetic threshold for the abstraction and dissociation reactions; at higher collision energies, the contribution from the stripping mechanism increases and eventually dominates. At a collision energy of 9.5 eV, the cross sections for oxygen exchange, abstraction, and dissociation are 4.17 a02, 1.58 a02, and 0.68 a02, respectively. The lower reaction cross sections, higher effective reaction barrier, and product energy distribution of the stripping mechanism were attributed to the short lifetime (28 fs) of the OCOO species compared with that of the CO3 species (45 fs) that arises in the insertion-elimination mechanism. For the exchange reaction, it is found that roughly 40% of the reactant translational energy ends up in CO2 vibration, which provides a single-collision mechanism to produce highly excited CO2. We also studied intersystem crossing effects using trajectory surface hopping calculations and find no changes compared to single surface (triplet) calculations at energies below 7.5 eV; however, at 7.5 eV and higher the abstraction cross sections are changed by as much as 20%, and the (very small) dissociation cross sections are changed by factors of four or more.