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Search Results (27,013)

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25 pages, 3691 KiB  
Article
Research on Motion Control Method of Wheel-Legged Robot in Unstructured Terrain Based on Improved Central Pattern Generator (CPG) and Biological Reflex Mechanism
by Jian Gao, Ruilin Fan, Hongtao Yang, Haonan Pang and Hangzhou Tian
Appl. Sci. 2025, 15(15), 8715; https://doi.org/10.3390/app15158715 (registering DOI) - 6 Aug 2025
Abstract
With the development of inspection robot control technology, wheel-legged robots are increasingly used in complex underground space inspection. To address low stability during obstacle crossing in unstructured terrains, a motion control strategy integrating an improved CPG algorithm and a biological reflex mechanism is [...] Read more.
With the development of inspection robot control technology, wheel-legged robots are increasingly used in complex underground space inspection. To address low stability during obstacle crossing in unstructured terrains, a motion control strategy integrating an improved CPG algorithm and a biological reflex mechanism is proposed. It introduces an adaptive coupling matrix, augmented with the Lyapunov function, and vestibular/stumbling reflex models for real-time motion feedback. Simulink–Adams virtual prototypes and single-wheeled leg experiments (on the left front leg) were used to verify the system. Results show that the robot’s turning oscillation was ≤±0.00593 m, the 10° tilt maintained a stable center of mass at 10.2° with roll angle fluctuations ≤±5°, gully-crossing fluctuations ≤±0.01 m, and pitch recovery ≤2 s. The experiments aligned with the simulations, proving that the strategy effectively suppresses vertical vibrations, ensuring stable and high-precision inspection. Full article
22 pages, 4194 KiB  
Article
Grain Boundary Regulation in Aggregated States of MnOx Nanofibres and the Photoelectric Properties of Their Nanocomposites Across a Broadband Light Spectrum
by Xingfa Ma, Xintao Zhang, Mingjun Gao, Ruifen Hu, You Wang and Guang Li
Coatings 2025, 15(8), 920; https://doi.org/10.3390/coatings15080920 (registering DOI) - 6 Aug 2025
Abstract
Improving charge transport in the aggregated state of nanocomposites is challenging due to the large number of defects present at grain boundaries. To enhance the charge transfer and photogenerated carrier extraction of MnOx nanofibers, a MnOx/GO (graphene oxide) nanocomposite was [...] Read more.
Improving charge transport in the aggregated state of nanocomposites is challenging due to the large number of defects present at grain boundaries. To enhance the charge transfer and photogenerated carrier extraction of MnOx nanofibers, a MnOx/GO (graphene oxide) nanocomposite was prepared. The effects of GO content and bias on the optoelectronic properties were studied. Representative light sources at 405, 650, 780, 808, 980, and 1064 nm were used to examine the photoelectric signals. The results indicate that the MnOx/GO nanocomposites have photocurrent switching behaviours from the visible region to the NIR (near-infrared) when the amount of GO added is optimised. It was also found that even with zero bias and storage of the nanocomposite sample at room temperature for over 8 years, a good photoelectric signal could still be extracted. This demonstrates that the MnOx/GO nanocomposites present a strong built-in electric field that drives the directional motion of photogenerated carriers, avoids the photogenerated carrier recombination, and reflect a good photophysical stability. The strength of the built-in electric field is strongly affected by the component ratios of the resulting nanocomposite. The formation of the built-in electric field results from interfacial charge transfer in the nanocomposite. Modulating the charge behaviour of nanocomposites can significantly improve the physicochemical properties of materials when excited by light with different wavelengths and can be used in multidisciplinary applications. Since the recombination of photogenerated electron–hole pairs is the key bottleneck in multidisciplinary fields, this study provides a simple, low-cost method of tailoring defects at grain boundaries in the aggregated state of nanocomposites. These results can be used as a reference for multidisciplinary fields with low energy consumption. Full article
27 pages, 4680 KiB  
Article
Gecko-Inspired Robots for Underground Cable Inspection: Improved YOLOv8 for Automated Defect Detection
by Dehai Guan and Barmak Honarvar Shakibaei Asli
Electronics 2025, 14(15), 3142; https://doi.org/10.3390/electronics14153142 - 6 Aug 2025
Abstract
To enable intelligent inspection of underground cable systems, this study presents a gecko-inspired quadruped robot that integrates multi-degree-of-freedom motion with a deep learning-based visual detection system. Inspired by the gecko’s flexible spine and leg structure, the robot exhibits strong adaptability to confined and [...] Read more.
To enable intelligent inspection of underground cable systems, this study presents a gecko-inspired quadruped robot that integrates multi-degree-of-freedom motion with a deep learning-based visual detection system. Inspired by the gecko’s flexible spine and leg structure, the robot exhibits strong adaptability to confined and uneven tunnel environments. The motion system is modeled using the standard Denavit–Hartenberg (D–H) method, with both forward and inverse kinematics derived analytically. A zero-impact foot trajectory is employed to achieve stable gait planning. For defect detection, the robot incorporates a binocular vision module and an enhanced YOLOv8 framework. The key improvements include a lightweight feature fusion structure (SlimNeck), a multidimensional coordinate attention (MCA) mechanism, and a refined MPDIoU loss function, which collectively improve the detection accuracy of subtle defects such as insulation aging, micro-cracks, and surface contamination. A variety of data augmentation techniques—such as brightness adjustment, Gaussian noise, and occlusion simulation—are applied to enhance robustness under complex lighting and environmental conditions. The experimental results validate the effectiveness of the proposed system in both kinematic control and vision-based defect recognition. This work demonstrates the potential of integrating bio-inspired mechanical design with intelligent visual perception to support practical, efficient cable inspection in confined underground environments. Full article
(This article belongs to the Special Issue Robotics: From Technologies to Applications)
20 pages, 360 KiB  
Article
Parabolic and Linear Rotational Motions on Cones and Hyperboloids
by Harun Barış Çolakoğlu, Mehmet Duru and Ayşe Yılmaz Ceylan
Axioms 2025, 14(8), 612; https://doi.org/10.3390/axioms14080612 - 6 Aug 2025
Abstract
In this study, we consider the Lorentzian rotation about a lightlike axis. First, we introduce a geometric characterization for the rotation angle between two vectors that can overlap each other under a Lorentzian rotation about a lightlike axis. Then, we give a definition [...] Read more.
In this study, we consider the Lorentzian rotation about a lightlike axis. First, we introduce a geometric characterization for the rotation angle between two vectors that can overlap each other under a Lorentzian rotation about a lightlike axis. Then, we give a definition for the angle measurement between two spacelike vectors whose vector product is lightlike. Later, we generalize the Lorentzian rotation about a lightlike axis, and determine matrices of these transformations using the Cartan frame and the well-known Rodrigues formula, then using the Cayley map, and finally using the generalized split quaternions. We see that such transformations give parabolic rotational motions on general cones or general hyperboloids of one or two sheets, while they also give linear rotational motions on general hyperboloids of one sheet. Full article
(This article belongs to the Section Geometry and Topology)
24 pages, 8377 KiB  
Article
Investigation of Wind Pressure Dynamics on Low-Rise Buildings in Sand-Laden Wind Environments
by Di Hu, Teng Zhang and Qiang Jin
Buildings 2025, 15(15), 2779; https://doi.org/10.3390/buildings15152779 - 6 Aug 2025
Abstract
To enhance the structural safety in wind-sand regions, this study employs the Euler-Lagrange numerical method to investigate the wind pressure characteristics of typical low-rise auxiliary buildings in a strong wind-blown sand environment. The results reveal that sand particle motion dissipates wind energy, leading [...] Read more.
To enhance the structural safety in wind-sand regions, this study employs the Euler-Lagrange numerical method to investigate the wind pressure characteristics of typical low-rise auxiliary buildings in a strong wind-blown sand environment. The results reveal that sand particle motion dissipates wind energy, leading to a slight reduction in average wind speed, while the increase in small-scale vortex energy enhances fluctuating wind speed. In the sand-laden wind field, the average wind pressure coefficient shows no significant change, whereas the fluctuating wind pressure coefficient increases markedly, particularly in the windward region of the building. Analysis of the skewness and kurtosis of wind pressure reveals that the non-Gaussian characteristics of wind pressure are amplified in the sand-laden wind, thereby elevating the risk of damage to the building envelope. Consequently, it is recommended that the design fluctuating wind load for envelopes and components of low-rise buildings in wind-sand regions be increased by 10% to enhance structural resilience. Full article
(This article belongs to the Section Building Structures)
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6 pages, 197 KiB  
Editorial
Contact Line Dynamics and Droplet Spreading
by Alireza Mohammad Karim
Fluids 2025, 10(8), 206; https://doi.org/10.3390/fluids10080206 - 6 Aug 2025
Abstract
Contact line motion occurs when a liquid encounters a solid surface [...] Full article
(This article belongs to the Special Issue Contact Line Dynamics and Droplet Spreading)
25 pages, 10639 KiB  
Article
Sliding Mode Control of the MY-3 Omnidirectional Mobile Robot Based on RBF Neural Networks
by Huaiyong Li, Changlong Ye, Song Tian and Suyang Yu
Machines 2025, 13(8), 695; https://doi.org/10.3390/machines13080695 - 6 Aug 2025
Abstract
Omnidirectional mobile robots have gained extensive application across diverse fields due to their exceptional maneuverability and adaptability in confined spaces. However, structural and systemic uncertainties significantly compromise motion accuracy. To enhance motion control precision, this paper proposes a sliding mode control (SMC) method [...] Read more.
Omnidirectional mobile robots have gained extensive application across diverse fields due to their exceptional maneuverability and adaptability in confined spaces. However, structural and systemic uncertainties significantly compromise motion accuracy. To enhance motion control precision, this paper proposes a sliding mode control (SMC) method integrated with a radial basis function (RBF) neural network. The approach aggregates model uncertainties, nonlinear dynamics, and unknown disturbances into a composite disturbance term. An RBF neural network is employed to approximate this disturbance, with compensation embedded within the SMC framework. An online adaptive law for neural network optimization is derived using the Lyapunov stability theorem, thereby improving the disturbance rejection capability. Comparative simulations and experiments validate the proposed method against modern control strategies. Results demonstrate superior tracking performance and robustness, significantly enhancing trajectory tracking accuracy for the MY3 wheeled omnidirectional mobile robot. Full article
(This article belongs to the Section Robotics, Mechatronics and Intelligent Machines)
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16 pages, 2067 KiB  
Article
Ankle Joint Kinematics in Expected and Unexpected Trip Responses with Dual-Tasking and Physical Fatigue
by Sachini N. K. Kodithuwakku Arachchige, Harish Chander and Adam C. Knight
Biomechanics 2025, 5(3), 62; https://doi.org/10.3390/biomechanics5030062 - 6 Aug 2025
Abstract
Concurrent cognitive tasks, such as avoiding visual, auditory, chemical, and electrical hazards, and concurrent motor tasks, such as load carriage, are prevalent in ergonomic settings. Trips are extremely common in the workplace, leading to fatal and non-fatal fall-related injuries. Intrinsic factors, such as [...] Read more.
Concurrent cognitive tasks, such as avoiding visual, auditory, chemical, and electrical hazards, and concurrent motor tasks, such as load carriage, are prevalent in ergonomic settings. Trips are extremely common in the workplace, leading to fatal and non-fatal fall-related injuries. Intrinsic factors, such as attention, fatigue, and anticipation, as well as extrinsic factors, including tasks at hand, affect trip recovery responses. Objective: The purpose of this study was to investigate the ankle joint kinematics in unexpected and expected trip responses during single-tasking (ST), dual-tasking (DT), and triple-tasking (TT), before and after a physically fatiguing protocol among young, healthy adults. Methods: Twenty volunteers’ (10 females, one left leg dominant, age 20.35 ± 1.04 years, height 174.83 ± 9.03 cm, mass 73.88 ± 15.55 kg) ankle joint kinematics were assessed using 3D motion capture system during unperturbed gait (NG), unexpected trip (UT), and expected trip (ET), during single-tasking (ST), cognitive dual-tasking (CDT), motor dual-tasking (MDT), and triple-tasking (TT), under both PRE and POST fatigue conditions. Results: Greater dorsiflexion angles were observed during UT compared to NG, MDT compared to ST, and TT compared to ST. Significantly greater plantar flexion angles were observed during ET compared to NG and during POST compared to PRE. Conclusions: Greater dorsiflexion angles during dual- and triple-tasking suggest that divided attention affects trip recovery. Greater plantar flexion angles following fatigue are likely an anticipatory mechanism due to altered muscle activity and increased postural control demands. Full article
(This article belongs to the Section Gait and Posture Biomechanics)
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19 pages, 14381 KiB  
Article
Temperature and Humidity Anomalies During the Summer Drought of 2022 over the Yangtze River Basin
by Dengao Li, Er Lu, Dian Yuan and Ruisi Liu
Atmosphere 2025, 16(8), 942; https://doi.org/10.3390/atmos16080942 (registering DOI) - 6 Aug 2025
Abstract
In the summer of 2022, central and eastern China experienced prolonged extreme high temperatures and severe drought, leading to significant economic losses. To gain a more profound understanding of this drought event and furnish a reference for forecasting similar events in the future, [...] Read more.
In the summer of 2022, central and eastern China experienced prolonged extreme high temperatures and severe drought, leading to significant economic losses. To gain a more profound understanding of this drought event and furnish a reference for forecasting similar events in the future, this study examines the circulation anomalies associated with the drought. Employing a diagnostic method focused on temperature and moisture anomalies, this study introduces a novel approach to quantify and compare the relative significance of moisture transport and warm air dynamics in contributing to the drought. This study examines the atmospheric circulation anomalies linked to the drought event and compares the relative contributions of water vapor transport and warm air activity in causing the drought, using two parameters defined in the paper. The results show the following: (1) The West Pacific Subtropical High (WPSH) was more intense than usual and extended westward, consistently controlling the Yangtze River Basin. Simultaneously, the polar vortex area was smaller and weaker, the South Asian High area was larger and stronger, and it shifted eastward. These factors collectively led to weakened water vapor transport conditions and prevailing subsiding air motions in the Yangtze River Basin, causing frequent high temperatures. (2) By defining Iq and It to represent the contributions of moisture and temperature to precipitation, we found that the drought event in the Yangtze River Basin was driven by both reduced moisture supplies in the lower troposphere and higher-than-normal temperatures, with temperature playing a dominant role. Full article
(This article belongs to the Section Meteorology)
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26 pages, 1698 KiB  
Article
Photoplethysmography-Based Blood Pressure Calculation for Neonatal Telecare in an IoT Environment
by Camilo S. Jiménez, Isabel Cristina Echeverri-Ocampo, Belarmino Segura Giraldo, Carolina Márquez-Narváez, Diego A. Cortes, Fernando Arango-Gómez, Oscar Julián López-Uribe and Santiago Murillo-Rendón
Electronics 2025, 14(15), 3132; https://doi.org/10.3390/electronics14153132 - 6 Aug 2025
Abstract
This study presents an algorithm for non-invasive blood pressure (BP) estimation in neonates using photoplethysmography (PPG), suitable for resource-constrained neonatal telecare platforms. Using the Windkessel model, the algorithm processes PPG signals from a MAX 30102 sensor, (Analog Devices (formerly Maxim Integrated), based in [...] Read more.
This study presents an algorithm for non-invasive blood pressure (BP) estimation in neonates using photoplethysmography (PPG), suitable for resource-constrained neonatal telecare platforms. Using the Windkessel model, the algorithm processes PPG signals from a MAX 30102 sensor, (Analog Devices (formerly Maxim Integrated), based in San Jose, CA, USA) filtering motion noise and extracting cardiac cycle time and systolic time (ST). These parameters inform a derived blood flow signal, the input for the Windkessel model. Calibration utilizes average parameters based on the newborn’s post-conceptional age, weight, and gestational age. Performance was validated against readings from a standard non-invasive BP cuff at SES Hospital Universitario de Caldas. Two parameter estimation methods were evaluated. The first yielded root mean square errors (RMSEs) of 24.14 mmHg for systolic and 19.13 mmHg for diastolic BP. The second method significantly improved accuracy, achieving RMSEs of 2.31 mmHg and 5.13 mmHg, respectively. The successful adaptation of the Windkessel model to single PPG signals allows for BP calculation alongside other physiological variables within the telecare program. A device analysis was conducted to determine the appropriate device based on computational capacity, availability of programming tools, and ease of integration within an Internet of Things environment. This study paves the way for future research that focuses on parameter variations due to cardiovascular changes in newborns during their first month of life. Full article
(This article belongs to the Section Circuit and Signal Processing)
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12 pages, 1706 KiB  
Article
Modulating Enzyme–Ligand Binding with External Fields
by Pedro Ojeda-May
Biophysica 2025, 5(3), 33; https://doi.org/10.3390/biophysica5030033 - 6 Aug 2025
Abstract
Protein enzymes are highly efficient catalysts that exhibit adaptability and selectivity under diverse biological conditions. In some organisms, such as bacteria, structurally similar enzymes, for instance, shikimate kinase (SK) and adenylate kinase (AK), coexist and act on chemically related ligands. This raises the [...] Read more.
Protein enzymes are highly efficient catalysts that exhibit adaptability and selectivity under diverse biological conditions. In some organisms, such as bacteria, structurally similar enzymes, for instance, shikimate kinase (SK) and adenylate kinase (AK), coexist and act on chemically related ligands. This raises the question of whether these enzymes can accommodate and potentially react with each other’s ligands. In this study, we investigate the stability of non-cognate ligand binding in SK and explore whether external electric fields (EFs) can modulate this interaction, leading to cross-reactivity in SK. Using molecular dynamics simulations, we assess the structural integrity of SK and the binding behavior of ATP and AMP under EF-off and EF-on cases. Our results show that EFs enhance protein structure stability, stabilize non-cognate ligands in the binding pocket, and reduce local energetic frustration near the R116 residue located in the binding site. In addition to this, dimensionality reduction analyses reveal that EFs induce more coherent protein motions and reduce the number of metastable states. Together, these findings suggest that external EFs can reshape enzyme–ligand interactions and may serve as a tool to modulate enzymatic specificity and functional promiscuity. Thus, we provide computational evidence that supports the concept of using an EF as a tunable parameter in enzyme engineering and synthetic biology. However, further experimental investigation would be valuable to assess the reliability of our computational predictions. Full article
(This article belongs to the Collection Feature Papers in Biophysics)
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11 pages, 222 KiB  
Essay
Beyond Space and Time: Quantum Superposition as a Real-Mental State About Choices
by Antoine Suarez
Condens. Matter 2025, 10(3), 43; https://doi.org/10.3390/condmat10030043 - 6 Aug 2025
Abstract
This contribution aims to honour Guido Barbiellini’s profound interest in the interpretation and impact of quantum mechanics by examining the implications of the so-called before–before Experiment on quantum entanglement. This experiment was inspired by talks and discussions with John Bell at CERN. This [...] Read more.
This contribution aims to honour Guido Barbiellini’s profound interest in the interpretation and impact of quantum mechanics by examining the implications of the so-called before–before Experiment on quantum entanglement. This experiment was inspired by talks and discussions with John Bell at CERN. This was during the years when John and Guido co-worked, promoting the mission of the laboratory: “to advance the boundaries of human knowledge”. As the experiment uses measuring devices in motion, it can be considered a complement to entanglement experiments using stationary measuring devices, which have meanwhile been awarded the 2022 Nobel Prize in Physics. The before–before Experiment supports the idea that the quantum realm exists beyond space and time and that the quantum state is a real mental entity concerning choices. As it also leads us to a better understanding of the ‘quantum collapse’ and the measurement process, we pay homage to Guido’s work on detectors, such as his collaborations on the DELPHI experiment at CERN, on cosmic ray detection at the International Space Station, and gamma-ray astrophysics during a large NASA space mission. Full article
19 pages, 487 KiB  
Review
Smart Clothing and Medical Imaging Innovations for Real-Time Monitoring and Early Detection of Stroke: Bridging Technology and Patient Care
by David Sipos, Kata Vészi, Bence Bogár, Dániel Pető, Gábor Füredi, József Betlehem and Attila András Pandur
Diagnostics 2025, 15(15), 1970; https://doi.org/10.3390/diagnostics15151970 - 6 Aug 2025
Abstract
Stroke is a significant global health concern characterized by the abrupt disruption of cerebral blood flow, leading to neurological impairment. Accurate and timely diagnosis—enabled by imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI)—is essential for differentiating stroke types and [...] Read more.
Stroke is a significant global health concern characterized by the abrupt disruption of cerebral blood flow, leading to neurological impairment. Accurate and timely diagnosis—enabled by imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI)—is essential for differentiating stroke types and initiating interventions like thrombolysis, thrombectomy, or surgical management. In parallel, recent advancements in wearable technology, particularly smart clothing, offer new opportunities for stroke prevention, real-time monitoring, and rehabilitation. These garments integrate various sensors, including electrocardiogram (ECG) electrodes, electroencephalography (EEG) caps, electromyography (EMG) sensors, and motion or pressure sensors, to continuously track physiological and functional parameters. For example, ECG shirts monitor cardiac rhythm to detect atrial fibrillation, smart socks assess gait asymmetry for early mobility decline, and EEG caps provide data on neurocognitive recovery during rehabilitation. These technologies support personalized care across the stroke continuum, from early risk detection and acute event monitoring to long-term recovery. Integration with AI-driven analytics further enhances diagnostic accuracy and therapy optimization. This narrative review explores the application of smart clothing in conjunction with traditional imaging to improve stroke management and patient outcomes through a more proactive, connected, and patient-centered approach. Full article
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20 pages, 7016 KiB  
Article
Design, Analysis and Control of Tracked Mobile Robot with Passive Suspension on Rugged Terrain
by Junfeng Gao, Yi Li, Jingfu Jin, Zhicheng Jia and Chao Wei
Actuators 2025, 14(8), 389; https://doi.org/10.3390/act14080389 - 6 Aug 2025
Abstract
With the application of tracked mobile robots in detection and rescue, how to improve their stability and trafficability has become the research focus. In order to improve the driving ability and trafficability of tracked mobile robots in rugged terrain, this paper proposes a [...] Read more.
With the application of tracked mobile robots in detection and rescue, how to improve their stability and trafficability has become the research focus. In order to improve the driving ability and trafficability of tracked mobile robots in rugged terrain, this paper proposes a new type of tracked mobile robot using passive suspension. By adding a connecting rod differential mechanism between the left and right track mechanisms, the contact stability between the track and terrain is enhanced. The kinematics model and attitude relationship of the suspension are analyzed and established, and the rationality of the passive suspension scheme is verified by dynamic simulation. The simulation results show that the tracked robot with passive suspension shows good obstacle surmounting performance, but there will be a heading deflection problem. Therefore, a track drive speed of the driving state compensation control is proposed based on the driving scene, which can effectively solve the problem of slip and heading deflection. Through the field test of the robot prototype, the effectiveness of the suspension scheme and control system is verified, which provides a useful reference for the scheme design and performance improvement of the tracked mobile robot in complex field scenes. Full article
(This article belongs to the Section Actuators for Robotics)
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57 pages, 647 KiB  
Article
A Unified Perspective on Poincaré and Galilei Relativity: II. General Relativity: A. Kinematics
by Christian Y. Cardall
Symmetry 2025, 17(8), 1245; https://doi.org/10.3390/sym17081245 - 5 Aug 2025
Abstract
Building on the first paper in this series (Paper I), a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting is further pursued through a consideration of the kinematics of general relativity, with the gravitational dynamics to be addressed separately. [...] Read more.
Building on the first paper in this series (Paper I), a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting is further pursued through a consideration of the kinematics of general relativity, with the gravitational dynamics to be addressed separately. The metric of the 5-dimensional affine spacetimes governed by the Bargmann groups considered in Paper I (central extensions of the Poincaré and Galilei groups) is generalized to curved spacetime by extending the usual 1 + 3 (traditionally `3 + 1’) formalism of general relativity on 4-dimensional spacetime to a 1 + 3 + 1 formalism, whose spacetime kinematics is shown to be consistent with that of the usual 1 + 3 formalism. Spacetime tensor laws governing the motion of an elementary classical material particle and the dynamics of a simple fluid are presented, along with their 1 + 3 + 1 decompositions; these reference the foliation of spacetime in a manner that partially reverts the Einstein perspective (accelerated fiducial observers, and geodesic material particles and fluid elements) to a Newton-like perspective (geodesic fiducial observers, and accelerated material particles and fluid elements subject to a gravitational force). These spacetime laws of motion for particles and fluids also suggest that a strong-field Galilei general relativity would involve a limit in which not only c but also G, such that G/c2 remains constant. Full article
(This article belongs to the Special Issue Recent Advance in Mathematical Physics II)
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