Pattern Speed Research Articles

Assessment on the influence of FDM process parameters on the mechanical properties of PLA samples

Abstract The manufacturing of functional parts from the fused deposition modeling 3D printer is limited due to poor mechanical properties, low surface finish, and huge production time. During 3D printing of prototypes, the time consumption of printing and mechanical properties of the model is directly proportional. The fused deposition modeling process parameters significantly impact the quality of printed parts. The prime objective of this research is to optimize the process parameters of a 3D printing machine (wall thickness, infill percentage, infill pattern, and infill speed) using polylactic acid material to enhance the mechanical properties with less printing time of the 3D printing model. The ultimate tensile strength and elongation of the 3D printed samples are used to evaluate the mechanical properties of the various slicing process parameters as per the standards. From the results, it is evident that the mechanical properties of the 3D printed materials increased significantly. The magnitude of ultimate tensile strength is reported as 39.972 MPa with a printing time of 28 min. From close observation, it is evident that lower infill speeds with gyroid infill pattern produce the highest ultimate tensile strength of all combinations. Also, optimal results are derived at higher wall thickness and higher infill percentage. In addition to that, finite element analysis was carried out for different infill percentages of the specimen to validate the actual result.

Numerical model of changes in current patterns due to reclamation around the Mireng River estuary, Gresik

Abstract The Mireng River is in Gresik Regency and empties into the Madura Strait. Around the mouth of the Mireng River, two industrial areas require construction facilities through reclamation. The consequences of reclamation will cause phenomena due to the interaction of marine and environmental dynamics, which can change current patterns, wave heights, and sedimentation processes, affecting the surrounding environment. This study explicitly discusses the changes in flow patterns that occur due to reclamation. The investigation was performed using numerical model simulations with Delft 3D software. The model results show the movement pattern and current speed during the highest and lowest low tides. There was a change in the average flow speed to 0.18 m/s around the reclamation area due to flow obstruction due to reclamation. This condition has the potential for sedimentation to occur in the area. Therefore, mitigation efforts are needed to reduce this impact.

How Does a Low Surface Brightness Galaxy Form Spiral Arms?

The formation and evolution of spiral arms in low surface brightness galaxies (LSBs) are not well understood. We study the dynamics of spiral arms in two prototypical LSBs, FGC 568-VI and FGC 568-01, using both analytical models and N-body + hydrodynamical simulations. We first consider the disk as a two-component system of gravitationally coupled stars and gas in the force field of a spherical dark matter halo, subjected to local, nonaxisymmetric perturbations. However, no local spirals are formed. We next assume the disk to be a one-component system of stars in the net gravitational potential of a galaxy with a spherical dark matter halo perturbed by a global m = 2 instability. In this case, the growth time for spiral formation was low, equal to 0.78 and 0.96 Gyr, respectively, corresponding to a few dynamical times of the galaxies. Finally, we simulate the LSBs using the N-body + hydrodynamical simulation code RAMSES. Our results show that a quadrupolar field associated with an oblate halo with an axial ratio of 0.7 is necessary to drive a long-lived global spiral in the LSB disks. Further, feedback corresponding to a supernova mass fraction of ∼0.05 is essential to comply with the observed stellar surface density. The simulated spirals survive for about 10 dynamical times and the average pattern speed lies between 10 and 15 km s−1 kpc−1. The spiral arms thus formed are therefore a transient global pattern driven by the tidal field of the oblate dark matter halo.

A new strategy for manufacturing, modeling, and optimization of 3D printed polylactide based on multiple nonlinear neuro regression analysis and stochastic optimization methods

Although there are many studies related to design, modeling, and optimization of fused deposition modeling (FDM) process parameters in the literature, the absence of a systematic approach to increase the reliability of model selection and optimization results is an important shortcoming that must be addressed. To make up for this deficiency, a new strategy was proposed to obtain desired quality on mechanical properties by adjusting FDM process parameters. This attempt involves manufacturing, modeling, and optimization point of view. The D-optimal method was employed to form experiment set, including process parameters. A hybrid approach neuro regression combining artificial neural network (ANN) and regression analysis together was used for modeling of FDM process. The most significant advantage of the neuro-regression approach compared to ANN is that the mathematical models can be used directly without needing any transformation. This is not possible in neural networks and, therefore, significantly limits and complicates the use of models obtained using ANN. The present study aims at optimization of the FDM process parameters, including infill density, infill pattern, layer thickness, and print speed on ultimate strength, fracture strength, and fracture strain for polylactide (PLA). In this regard, modified versions of the optimization algorithms Differential Evolution, Nelder Mead, and Simulated Annealing were used to find the best or elite designs. Linear or nonlinear models consisting of polynomial, trigonometric, and logarithmic expressions and their hybrid forms were employed to define the strength and strain behavior of PLA. It is concluded that (a) implementations of the optimization algorithms provide a 19% improving the minimum strain value if it is compared with the experimental results, (b) infill pattern types ( x2) were found as honeycomb, triangle, and cubic for the designs in terms of maximum fracture strength, minimum strain, and maximum ultimate tensile strength respectively, (c) many alternatives near optimum local designs could be obtained based on Nelder Mead algorithm for fracture strength and ultimate strength parameters. Thus, this allows work in a wide range of applications without depending on a single result for production.

Development of Driving Robot and Driver Model Applied Regenerative Brake Control of Electrified Vehicles

Real driving emissions (RDE) test procedures for type approval were initiated in Japan in 2022. In Japan, the test vehicle is driven on a test road (test course) by tracing the speed pattern prepared for each RDE test. The vehicle needs to trace the patterns in the same manner as in the conventional chassis dynamometer test. The use of a driving robot is effective for reproducibility in precisely tracing the target vehicle speed during these tests. In this study, we developed a driving robot for electrified vehicles (HEV, plug-in HEV, BEV, and FCV), which have regenerative brake-control systems. We applied a new logic to our robot that was developed in-house for conventional engine vehicles. We focused on braking deceleration of the regenerative brake control to change the operation timing from the accelerator pedal to the brake pedal. We verified the improvement of speed traceability of the driving robot installed with the proposed logic on the chassis dynamometer and test road.

Long-Term Wind and Air Temperature Patterns in the Southeastern Region of Iran through Model Simulation and Ground Observations

Dust storms are one of the important natural hazards that affect the lives of inhabitants all around the world, especially in North Africa and the Middle East. In this study, wind speed, wind direction, and air temperature patterns are investigated in one of the dustiest cities in Sistan Basin, Zahedan City, located in southeast Iran, over a 17-year period (2004–2020) using a WRF model and ground observation data. The city is located near a dust source and is mostly affected by local dust storms. The World Meteorology Organization (WMO) dust-related codes show that the city was affected by local dust, with 52 percent of the total dust events occurring during the period (2004–2021). The city’s weather station reported that 17.5% and 43% were the minimum and maximum dusty days, respectively, during 2004–2021. The summer and July were considered the dustiest season and month in the city. Since air temperature, wind speed, and wind direction are important factors in dust rising and propagation, these meteorological factors were simulated using the Weather Research and Forecasting (WRF) model for the Zahedan weather station. The WRF model’s output was found to be highly correlated with the station data; however, the WRF simulation mostly overestimated when compared with station data during the study period (2004–2020). The model had a reasonable performance in wind class frequency distribution at the station, demonstrating that 42.6% of the wind was between 0.5 and 2, which is in good agreement with the station data (42% in the range of 0.5–2). So, the WRF model effectively simulated the wind class frequency distribution and the wind direction at Zahedan station, despite overestimating the wind speed as well as minimum, maximum, and average air temperatures during the 17-year period.

Dynamic chaos unveiled: enhancing ship’s attitude time series prediction through spatiotemporal embedding and improved transformer model

Abstract During ship operations at sea, the vessel's attitude undergoes continuous changes due to various factors such as wind, waves, and its own motion. These influences are challenging to mathematically describe, and the changes in attitude are also influenced by multiple interconnected factors. Consequently, accurately predicting the ship's attitude presents significant challenges. Previous studies have demonstrated that phenomena like wind speed and wave patterns exhibit chaotic characteristics when affecting attitude changes. However, research on predicting ship attitudes lacks an exploration of whether chaotic characteristics exist and how they can be described and applied. This paper initially identifies the chaotic characteristics of ship attitude data through phase space reconstruction analysis and provides mathematical representations for them. Based on these identified chaotic characteristics, a
Transformer model incorporating feature embedding layers is employed for time series prediction. Finally, a comparison with traditional methods validates the superiority of our proposed approach.

Near‐surface wind profiles from numerical model predictions. Part II: Verifications against Australia‐wide surface wind observations

AbstractThe new scheme for deriving the near‐surface wind profiles discussed in Ma (in review) is applied to an Australian Bureau of Meteorology operational convective scale model over various domains. Both the new and conventional schemes' diagnostic 10‐m winds are then verified against Australia‐wide automatic weather station observations. Analyses of bulk statistics reveal that the new scheme's 10‐m wind forecasts have generally better accuracy than the current conventional scheme with a consistent reduction of biases over all domains. A widely recognised diurnal bias pattern of surface wind speed over the land is substantially reduced, and the inclusion of Ekman spiral effect on the 10‐m wind marginally improves statistics of the wind direction during the nighttime. The new scheme introduces no systemic bias, given the histogram of a bulk mean bias is analogiased to a Gaussian distribution, and moves the distribution of diagnostic wind speed closer to that observed.

Effects of Halo Spin on the Formation and Evolution of Bars in Disk Galaxies

The spin of dark halos has been shown to significantly affect bar formation and evolution in disk galaxies. To understand the physical role of halo spin in bar formation, we run N-body simulations of isolated, Milky Way–sized galaxies by varying the halo spin parameter in the range −0.16 ≤ λ ≤ 0.16 and the bulge mass. We find that our adopted halo alone is subject to swing amplification of an m = 2 nonaxisymmetric mode rotating in the same sense as the halo, which assists or inhibits the bar formation in a disk depending on its sense of rotation. The m = 2 mode in the disk, growing via swing amplification, interacts constructively (destructively) with the m = 2 mode in the prograde (retrograde) halo, promoting (delaying) bar formation. A bar grows by losing its angular momentum primarily to a halo. Since the halo particles inside (outside) the corotation resonance with the bar can emit (absorb) angular momentum to (from) the bar, the bar pattern speed decays more slowly for larger λ > 0, while it decreases relatively fast almost independent of λ ≤ 0. Models with a strong bar develop a boxy peanut-shaped bulge. In models without a bulge, this occurs rapidly via buckling instability, while bars with a bulge thicken gradually without undergoing buckling instability. Among the models considered in the present work, the bar in the λ = 0.06 model with a bulge of 10% of the disk mass best describes the Milky Way in terms of its length and pattern speed.

Revealing Gas Inflows Toward the Galactic Central Molecular Zone

We study the gas inflows toward the Galactic Central Molecular Zone (CMZ) based on the gas morphological and kinematic features from the Milky Way Imaging Scroll Painting in the region of l = 1.°2–19.°0 and ∣b∣ ≲ 3.°0. We find that the near dust lane appears to extend to l ∼ 15°, in which the end of the large-scale gas structure intersects with the 3 kpc ring at a distance of ∼5 kpc. Intriguingly, many filamentary molecular clouds (MCs), together with the bow-like/ballistic-like clouds and continuous CO features with notable velocity gradient, are finely outlined along the long structure. These MCs also have relatively large velocity dispersions, indicating the shocked gas generated by local continuous accretion and thus the enhanced turbulence along the entire gas structure. We suggest that the ∼3.1–3.6 kpc-long CO structure originates from the accretion molecular gas driven by the Galactic bar. The gas near the bar end at the 3 kpc ring region becomes an important reservoir for the large-scale accreting flows inward to the CMZ through the bar channel. The inclination angle of the bar is estimated to be ϕ bar = 23° ± 3°, while the pattern speed of the bar is Ωbar ≲ 32.5 ± 2.5 km s−1 kpc−1. The total mass of the whole near gas lane is about 1.3 ± 0.4 × 107 M ⊙ according to the calculated X CO ∼ 1.0 ± 0.4 × 1020 cm−2(K km s−1)−1 from the large-scale 12CO and 13CO data and the complementary H i data. We revisit the gas inflow rate as a mean value of 1.1 ± 0.3 M ⊙ yr−1, which seems to be comparable to the outflow's rate of the Galactic nuclear winds after applying the updated lower X-factor above.

KRATOS: A large suite of N-body simulations to interpret the stellar kinematics of LMC-like discs

Context. The Large and Small Magellanic Clouds (LMC and SMC, respectively) are the brightest satellites of the Milky Way (MW), and for the last thousand million years they have been interacting with one another. As observations only provide a static picture of the entire process, numerical simulations are used to interpret the present-day observational properties of these kinds of systems, and most of them have been focused on attempting to recreate the neutral gas distribution and characteristics through hydrodynamical simulations. Aims. We present KRATOS, a comprehensive suite of 28 open-access pure N-body simulations of isolated and interacting LMC-like galaxies designed for studying the formation of substructures in their discs after interaction with an SMC-mass galaxy. The primary objective of this paper is to provide theoretical models that help us to interpret the formation of general structures in an LMC-like galaxy under various tidal interaction scenarios. This is the first paper of a series dedicated to the analysis of this complex interaction. Methods. Simulations are grouped into 11 sets of up to three configurations, with each set containing (1) a control model of an isolated LMC-like galaxy; (2) a model that contains the interaction with an SMC-mass galaxy, and (3) a model where both an SMC-mass and a MW-mass galaxy may interact with the LMC-like galaxy (the most realistic model). In each simulation, we analysed the orbital history between the three galaxies and examined the morphological and kinematic features of the LMC-like disc galaxy throughout the interaction. This includes investigating the disc scale height and velocity maps. When a bar was found to develop, we characterised its strength, length, off-centredness, and pattern speed. Results. The diverse outcomes found in the KRATOS simulations, including the presence of bars, warped discs, and various spiral arm shapes, demonstrate the opportunities they offer to explore a range of LMC-like galaxy morphologies. These morphologies directly correspond to distinct disc kinematic maps, making them well-suited for a first-order interpretation of the LMC’s kinematic maps. From the simulations, we note that tidal interactions can: boost the disc scale height; both destroy and create bars; and naturally explain the off-centre stellar bars. The bar length and pattern speed of long-lived bars are not appreciably altered by the interaction. Conclusions. The high spatial, temporal, and mass resolution used in the KRATOS simulations has been shown to be appropriate for the purpose of interpreting the internal kinematics of LMC-like discs, as evidenced by the first scientific results presented in this work.

Predictive modeling and optimization of Rockwell hardness of additively manufactured PEEK using RSM, ANFIS and RNN integrated with PSO

The purpose of this research is to investigate the correlation between statistical and machine learning techniques and additive manufacturing, with a specific focus on predicting the Rockwell hardness of FDM-printed polyether ether ketone (PEEK) components. These components have a significant impact on various industries, such as aerospace, biomedical, and automobile. The study analyzes the hardness by conducting experimental analysis of four process parameters, including infill density, layer height, printing speed, and infill pattern. The research utilizes Response Surface Methodology (RSM), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Recurrent Neural Network (RNN) to accurately predict the Rockwell hardness of the printed parts, with an average deviation of less than 5% from the experimental value. The study also investigates how hardness varies with FDM process parameters using contour and surface plots. Furthermore, the study utilizes RNN integrated with the Particle Swarm Optimization (PSO) algorithm to optimize Rockwell hardness. This approach achieved a peak Rockwell hardness value of 66.89 RHN under conditions of 80% infill density, 0.1mm layer height, 25 mm sec−1 printing speed, and an octet infill pattern. Microstructural examinations and test results corroborate the findings derived from parametric analysis and optimization efforts.

Submerged surface texturing of AISI 304L using the pulsating water jet method

Submerged jets have a variety of practical applications due to their versatility in providing efficient and environmentally friendly options for treatment in various industries. The physical background is based on the continuous water jet (CWJ) application powered via stagnation pressure. However, it is known that impact pressure is much more effective than static pressure. When the impact pressure is repeated with a high frequency per time unit, the erosive effects of water can be used even at pressures below 100 MPa, which is attractive from the point of view of the low demands of the hydraulic system. Surface modification utilising impact pressure can be achieved by employing the pulsed water jet (PWJ) method. The combination of parameters such as the traverse speed and trajectory pattern can control the number of water clusters impacting the material surface. So far, the field of application of PWJ for surface treatment has mostly been investigated water atmospheric conditions. This article focuses on the possibility of the surface modification of AISI 304L stainless steel using the PWJ method under submerged conditions. The results are compared to those obtained under atmospheric conditions. The reference samples were treated by the same technological conditions using a continuous water jet (CWJ). The affected surfaces were characterised using areal surface roughness parameters Sa, Sz, Sp, and Sv, and the surface topography and mechanism of erosion wear were evaluated by scanning electron microscopy. A significant increase in all roughness parameters was confirmed using the PWJ compared to the CWJ method (both in atmospheric and submerged conditions), which confirms the importance of using impact pressure. The surface treatment by PWJ under submerged conditions resulted in a decrease of the surface roughness parameter Sa by approximately 97% compared to atmospheric conditions at a traverse speed of 2 mm/s for perpendicular interleaved trajectory, nevertheless, the homogeneity of treatment over a larger area was improved.

Dual-isotope ratios of carbonaceous aerosols for seasonal observation and their assessment as source indicators

Carbonaceous aerosols exhibit seasonal variations due to a complex interplay of emission sources, meteorological conditions, and chemical processes. This study presents the first year-round dual‑carbon isotopic analysis of carbonaceous aerosols in Northeastern Europe (Lithuania). The emphasis was placed on the processes affecting carbonaceous submicron particle (PM1) concentrations and their isotopic composition (δ13CTC, fc) during different seasons. Aerosol particles were collected in the two distinct sites: at an urban background site (Vilnius) and a coastal site (Preila). The concentrations of total carbon (TC) and black carbon (BC) varied both spatially and temporally. The annual average concentrations were 4 μg/m3 for TC and 2.3 μg/m3 for BC at the urban background site. They were considerably lower at the coastal site with 2.9 μg/m3 for TC and 0.74 μg/m3 for BC. The peak concentrations of TC and BC that occur during the cold season indicate a significant impact from residential heating. The δ13C in aerosols exhibited a distinct seasonal cycle with depleted δ13CTC values during the warm season (April–October). Through the integration of isotopic composition, contemporary carbon (fc), and BC source apportionment, we achieved precise predictions of isotopic parameter changes, encompassing pollution sources and the influence of meteorological parameters. To better understand the respective contributions of local and regional sources, air mass trajectories, wind patterns (speed and direction), and the polar conditional probability function (CPF) were studied in parallel. The study indicates that the isotopic composition of PM1 at both sites is primarily controlled by emission sources (local and regional), while meteorological conditions (temperature and mixing layer height) have less influence. These variations have important implications for regional air quality, climate dynamics, and public health, which are persistently subject to continuous research and monitoring.

Radial halo substructure in harmony with the Galactic bar

ABSTRACT Overdensities in the radial phase space $(r,v_{\rm r})$ of the Milky Way’s halo have previously been associated with the phase-mixed debris of a highly radial merger event such as Gaia Sausage–Enceladus. We present and test an alternative theory in which the overdense ‘chevrons’ are instead composed of stars trapped in resonances with the Galactic bar. We develop an analytic model of resonant orbits in the isochrone potential, and complement this with a test particle simulation of a stellar halo in a realistic barred Milky Way potential. These models are used to predict the appearance of action space $(J_\phi ,J_{\rm r})$ and radial phase space in the Solar neighbourhood. They are able to reproduce almost all salient features of the observed chevrons. In particular, both the analytic model and simulation predict that the chevrons are more prominent at $v_{\rm r}\ \lt\ 0$ when viewed near the Sun, as is observed by Gaia. This is inconsistent with formation by an ancient merger event. We also associate individual chevrons with specific resonances. At a bar pattern speed of $\Omega _\mathrm{b}=35$ km s$^{-1}$ kpc$^{-1}$, the two most prominent prograde chevrons align very closely with the corotation and outer Lindblad resonances. The former can be viewed as a highly eccentric extension of the Hercules stream. Finally, our model predicts that the $v_{\rm r}$ asymmetry changes sign as a function of Galactic radius and azimuth, and we find evidence that this is indeed the case in the Milky Way.

Optimal PLA+ 3D Printing Parameters through Charpy Impact Testing: A Response Surface Methodology

Additive manufacturing (AM) has revolutionized the manufacturing sector, particularly with the advent of 3D printing technology, which allows for the creation of customized, cost-effective, and waste-free products. However, concerns about the strength and reliability of 3D-printed products persist. This study focuses on the impact of three crucial variables—infill density, printing speed, and infill pattern—on the strength of PLA+ 3D-printed products. Our goal is to optimize these parameters to enhance product strength without compromising efficiency. We employed Charpy impact testing and Response Surface Methodology (RSM) to analyze the effects of these variables in combination. Charpy impact testing provides a measure of material toughness, while RSM allows for the optimization of multiple interacting factors. Our experimental design included varying the infill density from low to high values, adjusting printing speeds from 70mm/s to 100mm/s, and using different infill patterns such as cubic and others. Our results show that increasing infill density significantly boosts product strength but also requires more material and longer processing times. Notably, we found that when the infill density exceeds 50%, the printing speed can be increased to 100mm/s without a notable reduction in strength, offering a balance between durability and production efficiency. Additionally, specific infill patterns like cubic provided better strength outcomes compared to others. These findings provide valuable insights for developing stronger and more efficient 3D-printed products using PLA+ materials. By optimizing these parameters, manufacturers can produce high-strength items more efficiently, thereby advancing the capabilities and applications of 3D printing technology in various industries.

Self-consistent modelling of the Milky Way structure using live potentials

ABSTRACT To advance our understanding of the evolution of the interstellar medium (ISM) of our Galaxy, numerical models of Milky Way (MW) type galaxies are widely used. However, most models only vaguely resemble the MW (e.g. in total mass), and often use imposed analytic potentials (which cannot evolve dynamically). This poses a problem in asserting their applicability for the interpretation of observations of our own Galaxy. The goal of this work is to identify a numerical model that is not only an MW-type galaxy, but one that can mimic some of the main observed structures of our Galaxy, using dynamically evolving potentials, so that it can be used as a base model to study the ISM cycle in a galaxy like our own. This paper introduces a suite of 15 MW-type galaxy models developed using the arepo numerical code, that are compared to Galactic observations of $^{12}$CO and H i emission via longitude–velocity plots, from where we extract and compare the skeletons of major galactic features and the terminal gas velocities. We found that our best-fitting model to the overall structure, also reproduces some of the more specific observed features of the MW, including a bar with a pattern speed of $30.0 \pm 0.2$ km s$^{-1}$ kpc$^{-1}$, and a bar half-length of $3.2 \pm 0.8$ kpc. Our model shows large streaming motions around spiral arms, and strong radial motions well beyond the inner bar. This model highlights the complex motions of a dynamic MW-type galaxy and has the potential to offer valuable insight into how our Galaxy regulates the ISM and star formation.

Earthquake Seismicity Reveals the Location and Significance of the Shona Mantle Plume in the South Atlantic Ocean

AbstractThe South Atlantic Ocean hosts several well‐studied volcanic ridges and seamount chains, but the origin of their associated mantle plumes is debated. Reduced seismicity on the southern Mid‐Atlantic Ridge (MAR) suggests anomalously ductile thermomechanical conditions at 52°S and 47.5°S. These low seismicity patches extend 120–560 km along‐axis, and correspond with axial high spreading ridge morphology, geochemical anomalies, and mantle wave speed patterns likely associated with the Shona and Discovery plumes. Bathymetric data show that the northern extent of the Shona swell is associated with increased volcanism, elevated axial bathymetry, and a series of northward‐propagating rifts, with the overall swell geometry suggesting a buoyancy flux of 0.4–0.5 Mg s−1. The nearby Bouvet Island may be a product of a branch of the larger Shona plume swell, which has influenced crustal accretion on the southern MAR for the past 24 million years.

Predictive Modeling of Future Full-Ocean Depth SSPs Utilizing Hierarchical Long Short-Term Memory Neural Networks

The spatial-temporal distribution of underwater sound speed plays a critical role in determining the propagation mode of underwater acoustic signals. Therefore, rapid estimation and prediction of sound speed distribution are imperative for facilitating underwater positioning, navigation, and timing (PNT) services. While sound speed profile (SSP) inversion methods offer quicker response times compared to direct measurement methods, these methods often focus on constructing spatial sound velocity fields and heavily rely on sonar observation data, thus imposing stringent requirements on data sources. To delve into the temporal distribution pattern of sound speed and achieve SSP prediction without relying on sonar observation data, we introduce the hierarchical long short-term memory (H-LSTM) neural network for SSP prediction. Our method enables the estimation of sound speed distribution without the need for on-site data measurement, significantly enhancing time efficiency. Compared to other state-of-the-art approaches, the H-LSTM model achieves a root mean square error (RMSE) of less than 1 m/s in predicting monthly average sound speed distribution. Its prediction accuracy has improved several-fold over alternative methods, which validates the robust capability of our proposed model in predicting SSP.

Analysis of player speed and angle toward the ball in soccer

The study analyzes how the magnitude and angle of the speed of soccer players change according to the distance to the ball and the phases of the game, namely the defensive and attacking phases. We observed how the role played in the team (goalkeeper, defender, midfielder, or forward) strongly determines the speed pattern of players. As a general trend, the speed’s modulus is incremented as their position is closer to the ball, however, it is slightly decreased when arriving at it. Next, we studied how the angle of the speed with the direction to the ball is related to the distance to the ball and the game phases. We observed that, during the defensive phase, goalkeepers are the players that run more parallel to the ball, while forwards are the ones running more directly to the ball position. Importantly, this behavior changes dramatically during the attacking phase. Finally, we show how the proposed methodology can be used to analyze the speed-angle patterns of specific players to understand better how they move on the pitch according to the distance to the ball.