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We present a derivation from the first principles of the coupled equations of motion of an active self-diffusiophoretic Janus motor and the hydrodynamic densities of its fluid environment that are nonlinearly displaced from equilibrium. The derivation makes use of time-dependent projection operator techniques defined in terms of slowly varying coarse-grained microscopic densities of the fluid species number, total momentum, and energy. The exact equations of motion are simplified using time scale arguments, resulting in Markovian equations for the Janus motor linear and angular velocities with average forces and torques that depend on the fluid densities. For a large colloid, the fluid equations are separated into bulk and interfacial contributions, and the conditions under which the dynamics of the fluid densities can be accurately represented by bulk hydrodynamic equations subject to boundary conditions on the colloid are determined. We show how the results for boundary conditions based on continuum theory can be obtained from the molecular description and provide Green–Kubo expressions for all transport coefficients, including the diffusiophoretic coupling and the slip coefficient. [ABSTRACT FROM AUTHOR]

Blue compact galaxies, also known as H  ii galaxies, are dwarf, star-forming objects with relatively simple dynamics, which allows for the investigation of star formation mechanisms in a cleaner manner compared to late-type objects. In this study, we have examined various characteristics of the interstellar medium, in connection with the kinematics and dynamics of ionized gas, in Tol 1004-296 and Tol 0957-278. These two objects were observed using the SOAR Integral Field Spectrometer (SIFS) attached to the Southern Observatory for Astrophysical Research (SOAR). Both galaxies were observed with two gratings: one with medium resolution for monochromatic and abundance maps, and another with high resolution for kinematics and profile analysis. Additionally, we conducted an analysis on the velocity and velocity dispersion maps using intensity–velocity dispersion (I-σ) and velocity–velocity dispersion (Vr-σ) diagrams. Neither object exhibits a rotation pattern, and only Tol 1004-296 shows a velocity gradient between the two principal knots. However, the study reveals the significant role played by velocity dispersion in the star formation process. Specifically, we identified a relationship between monochromatic intensity, metallicity, and velocity dispersion, where high emission corresponds to low metallicity and low velocity dispersion. Tol 1004-296, in particular, exhibits a distinctive linear high velocity dispersion pattern between the two main knots, suggesting that both star formation sites are pushing the gas in opposite directions. [ABSTRACT FROM AUTHOR]

Many mobile robotics applications require robots to navigate around humans who may interpret the robot's motion in terms of social attitudes and intentions. It is essential to understand which aspects of the robot's motion are related to such perceptions so that we may design appropriate navigation algorithms. Current works in social navigation tend to strive towards a single ideal style of motion defined with respect to concepts such as comfort, naturalness, or legibility. These algorithms cannot be configured to alter trajectory features to control the social interpretations made by humans. In this work, we firstly present logistic regression models based on perception experiments linking human perceptions to a corpus of linear velocity profiles, establishing that various trajectory features impact human social perception of the robot. Secondly, we formulate a trajectory planning problem in the form of a constrained optimization, using novel constraints that can be selectively applied to shape the trajectory such that it generates the desired social perception. We demonstrate the ability of the proposed algorithm to accurately change each of the features of the generated trajectories based on the selected constraints, enabling subtle variations in the robot's motion to be consistently applied. By controlling the trajectories to induce different social perceptions, we provide a tool to better tailor the robot's actions to its role and deployment context to enhance acceptability. [ABSTRACT FROM AUTHOR]

Objectives: Infant growth is recognized to vary over the short term, with periods of greater and lesser linear growth velocity. Our objectives were to (1) examine the potential differences in overall growth profiles between children who experienced cumulative growth faltering in the first year of life consistent with that seen by many children living in poverty in low‐ and middle‐income countries, versus children without growth faltering and (2) test whether biological factors were associated with the timing of magnitude of growth saltations. Methods: Thrice‐weekly measurements of length were recorded for n = 61 Peruvian infants (28 boys and 33 girls) enrolled from birth to 1 year. A total of 6040 measurements were analyzed. We tested for the evidence of saltatory growth and used hurdle models to test whether the timing and magnitude of saltations varied between children with greater or lesser growth faltering. Results: There were no differences in the duration of stasis periods or magnitude of growth saltations between children who were stunted at 1 year old (N = 18) versus those who were not stunted (N = 43). Children who experienced greater declines in LAZ in the first year of life trended toward longer periods between saltations than those with less of a decline (14.5 days vs. 13.4 days, p =.0512). A 1‐unit increase in mid upper arm circumference for age Z‐score in the 21 days prior was associated with 35% greater odds of a saltation occurring (p <.001), and a 0.128 cm greater saltation (p <.001). Conclusions: After characterizing infant growth into periods of saltation and stasis, our results suggest that increases in weight preceded increases in length. [ABSTRACT FROM AUTHOR]

An exact similarity solution is worked out for fluid motion in the vicinity of a cylindrical surface in an electrically conducting viscoelastic fluid obeying the Jeffrey model. Cylindrical surface expands axially with linear velocity and has a prescribed surface temperature. The present analysis focuses on the partial slip assumption which gives rise to a nonlinear case Robin-type (mixed) boundary condition in axial velocity. In contrast to a previously published study (J. Mech., vol 31, pp. 69–78, 2015) which only reported local similarity solutions in no-slip case, the present work provides an exact similarity analysis by defining a quadratic surface temperature. The effects of the magnetic field and Joule heating on the momentum and thermal transport phenomena are also scrutinized. A numerical routine is used to solve the equation accurately for a wide range of fluid parameters, including ranges that could not be handled by previous approximate analytical methods that were limited to the no-slip limit. The influences of viscoelasticity and partial slip on the flow behavior are investigated, and the coefficient of skin friction for a Jeffrey fluid is calculated. Obtained results are consistent with the previously published works under special situations. The case of flat surface, which can be obtained as a limiting case of the model, is not even explored in the past. [ABSTRACT FROM AUTHOR]

• A set of multiplicative extended Kalman filters for uncooperative relative navigation is developed. • Unit quaternions are used to represent the coupled roto-translational relative dynamics. • The filters estimate the 6 DoF state and – in some options - the main parameters of the Target object. • These filters can serve several architectures of the relative navigation system. • Numerical simulations representative of close-range Target inspection are performed. This work presents a set of dynamic filters for estimating the relative roto-translational state and the main parameters of a noncooperative target from an observing chaser satellite during close proximity operations. The proposed different options address a wide range of design possibilities for the architecture of the relative navigation system. All filters are derived from a common, general, core shaped as a dynamic multiplicative extended Kalman filter using dual quaternions. This allows exploiting the advantages of handling the pose (i.e. , attitude and position) in a multiplicative fashion, while improving the accuracy in the estimation of the angular and linear relative velocities, as well as enabling the estimation of some meaningful parameters of the target spacecraft (e.g. , the ratios of the moments of inertia, position and orientation of the principal axes frame). Moreover, by adopting relative kinematics and dynamics equations in dual quaternions, the inherent coupling of the six degrees-of-freedom motion is addressed with no approximations. All filters take as observations only the noisy pose measurements from an electro-optical device. For each proposed formulation, numerical simulations are carried out to show the behavior of the filter within a scenario representative of close-range target inspection at conclusion of the mid-range rendezvous. [ABSTRACT FROM AUTHOR]

The oil film lubrication performance of a large hydrostatic turntable operating at the model of constant surface cutting speed is studied. Firstly, the rotary speed equation which is bound by the constant surface cutting speed is established. According to the fluid lubrication theory, the gap flow equation, the oil film temperature rise equation and the double‐rectangular‐cavity oil pad bearing capacity equation are derived. Further, a prediction model of oil film lubrication performance in the operating mode is established. The change rules of temperature, pressure and other performance indexes of the film with time are obtained by numerical simulation. And, the above laws are verified by design experiments. It is found that the cutting speed, feed rate leaves a significant impact on the law of variations of oil film performance with time. According to the conclusions, it will be beneficial to improve the bearing capacity of the hydrostatic turntable and further improve the machining accuracy by using cutting parameters reasonably to control the speed within a certain range. [ABSTRACT FROM AUTHOR]

Autonomous mobile robots are essential to the industry, and human–robot interactions are becoming more common nowadays. These interactions require that the robots navigate scenarios with static and dynamic obstacles in a safely manner, avoiding collisions. This paper presents a physical implementation of a method for dynamic obstacle avoidance using a long short-term memory (LSTM) neural network that obtains information from the mobile robot's LiDAR for it to be capable of navigating through scenarios with static and dynamic obstacles while avoiding collisions and reaching its goal. The model is implemented using a TurtleBot3 mobile robot within an OptiTrack motion capture (MoCap) system for obtaining its position at any given time. The user operates the robot through these scenarios, recording its LiDAR readings, target point, position inside the MoCap system, and its linear and angular velocities, all of which serve as the input for the LSTM network. The model is trained on data from multiple user-operated trajectories across five different scenarios, outputting the linear and angular velocities for the mobile robot. Physical experiments prove that the model is successful in allowing the mobile robot to reach the target point in each scenario while avoiding the dynamic obstacle, with a validation accuracy of 98.02%. [ABSTRACT FROM AUTHOR]

This paper focuses on the 2D incompressible anisotropic magneto-micropolar fluid equations with vertical dissipation, horizontal magnetic diffusion, and horizontal vortex viscosity. The goal is to investigate the stability of perturbations near a background magnetic field in the 2D magneto-micropolar fluid equations. Two main results are obtained. The first result is based on the linear system. Global existence for any large initial data and asymptotic linear stability are established. The second result explores stability for the nonlinear system. It is proven that if the initial data are sufficiently small, then the solution for some perturbations near a background magnetic field remains small. Additionally, the long-time behaviour of the solution is presented. The most challenging terms in the proof are the linear terms in the velocity equation and the micro-rotation equation that will grow with respect to time t. We are able to find some background fields to control the growth of the linear terms. Our results reveal that some background fields can stabilise electrically conducting fluids. [ABSTRACT FROM AUTHOR]

When the airlift bioreactor is applied to the field of industrial fermentation, there is a common problem of low mixing and flow efficiency due to its simple structure. In order to expand the application of airlift bioreactor in the field of industrial fermentation, a new type of airlift bioreactor with three-dimensional bumps in the draft tube has been designed to enhance the mixing and flow of gas-liquid two-phase in the reactor. In order to determine the specific influence of the three-dimensional bumps on the internal flow field of the reactor, and to provide technical reference for the improvement of the structure of the airlift bioreactor, in this paper, the CFD simulation of this type of bioreactor is carried out. Based on the Euler multiphase flow, the Realizable k-ε model was used to analyze the flow field of the reactor with average gas-liquid flow linear velocity and temperature as parameters. The results show that under certain conditions, the three-dimensional bumps inside the draft tube can effectively accelerate the gas-liquid two-phase flow and better promotes the mixing of pig manure fermentation broth and air. [ABSTRACT FROM AUTHOR]

Autonomous navigation and information gathering in challenging environments are demanding since the robot's sensors may be susceptible to non-negligible noise, its localization and mapping may be subject to significant uncertainty and drift, and performing collision-checking or evaluating utility functions using a map often requires high computational costs. We propose a learning-based method to efficiently tackle this problem without relying on a map of the environment or the robot's position. Our method utilizes a Collision Prediction Network (CPN) for predicting the collision scores of a set of action sequences, and an Information gain Prediction Network (IPN) for estimating their associated information gain. Both networks assume access to a) the depth image (CPN) or the depth image and the detection mask from any visual method (IPN), b) the robot's partial state (including its linear velocities, z -axis angular velocity, and roll/pitch angles), and c) a library of action sequences. Specifically, the CPN accounts for the estimation uncertainty of the robot's partial state and the neural network's epistemic uncertainty by using the Unscented Transform and an ensemble of neural networks. The outputs of the networks are combined with a goal vector to identify the next-best-action sequence. Simulation studies demonstrate the method's robustness against noisy robot velocity estimates and depth images, alongside its advantages compared to state-of-the-art methods and baselines in (visually-attentive) navigation tasks. Lastly, multiple real-world experiments are presented, including safe flights at 2.5 m/s in a cluttered corridor, and missions inside a dense forest alongside visually-attentive navigation in industrial and university buildings. [ABSTRACT FROM AUTHOR]

The two-point statistics of the cosmic velocity field, measured from galaxy peculiar velocity (PV) surveys, can be used as a dynamical probe to constrain the growth rate of large-scale structures in the Universe. Most works use the statistics on scales down to a few tens of Megaparsecs, while using a theoretical template based on the linear theory. In addition, while the cosmic velocity is volume-weighted, the observable line-of-sight velocity two-point correlation is density-weighted, as sampled by galaxies, and therefore the density–velocity correlation term also contributes, which has often been neglected. These effects are fourth order in powers of the linear density fluctuation |$\delta _{\rm L}^4$|⁠ , compared to |$\delta _{\rm L}^2$| of the linear velocity correlation function, and have the opposite sign. We present these terms up to |$\delta _{\rm L}^4$| in real space based on the standard perturbation theory, and investigate the effect of non-linearity and the density–velocity contribution on the inferred growth rate f σ8, using N -body simulations. We find that for a next-generation PV survey of volume |$\sim {\cal O}(500 \, h^{-1} \, {\rm Mpc})^3$|⁠ , these effects amount to a shift of f σ8 by ∼10 per cent and is comparable to the forecasted statistical error when the minimum scale used for parameter estimation is |$r_{\rm min} = 20 \, h^{-1} \, {\rm Mpc}$|⁠. [ABSTRACT FROM AUTHOR]

The default mode network (DMN) is a large-scale brain network known to be suppressed during a wide range of cognitive tasks. However, our comprehension of its role in naturalistic and unconstrained behaviors has remained elusive because most research on the DMN has been conducted within the restrictive confines of MRI scanners. Here, we use multisite GCaMP (a genetically encoded calcium indicator) fiber photometry with simultaneous videography to probe DMN function in awake, freely exploring rats. We examined neural dynamics in three core DMN nodes--the retrosplenial cortex, cingulate cortex, and prelimbic cortex--as well as the anterior insula node of the salience network, and their association with the rats' spatial exploration behaviors. We found that DMN nodes displayed a hierarchical functional organization during spatial exploration, characterized by stronger coupling with each other than with the anterior insula. Crucially, these DMN nodes encoded the kinematics of spatial exploration, including linear and angular velocity. Additionally, we identified latent brain states that encoded distinct patterns of time-varying exploration behaviors and found that higher linear velocity was associated with enhanced DMN activity, heightened synchronization among DMN nodes, and increased anticorrelation between the DMN and anterior insula. Our findings highlight the involvement of the DMN in collectively and dynamically encoding spatial exploration in a real-world setting. Our findings challenge the notion that the DMN is primarily a "task-negative" network disengaged from the external world. By illuminating the DMN's role in naturalistic behaviors, our study underscores the importance of investigating brain network function in ecologically valid contexts. [ABSTRACT FROM AUTHOR]

We study the dynamics of a class of mechanical systems subjected to non-holonomic constraints by employing a method termed "modified vakonomic method" (MVM), and developed by Llibre, Ramírez and Sadovskaia in 2014. In particular, we test the MVM for the "rolling coin" problem and a variant of the "non-holonomic skate" problem. For our purposes, we divide our work in two parts. For the first one, our point of departure is a paper published in this journal by Lemos in 2022, in which, for the "rolling coin" problem, Kozlov's vakonomic method is shown to lead to inconsistencies with the so-called Lagrange–D'Alembert traditional non-holonomic method (TNHM). In this case, we prove that, if the MVM is used, the equivalence with the TNHM can be restored, and the two methods can be reconciled. In the second part, we formulate a thought experiment consisting of an electrically charged "non-holonomic skate" interacting with a magnetic field, and we examine its dynamics by means of the MVM. In this case, we point out the differences with the predictions of the TNHM, and we propose a reformulation of the MVM capable of retrieving the results obtained with the TNHM. Moreover, we give some insight into the main computational aspects related to the MVM for non-holonomic constraints linear in the generalized velocities. [ABSTRACT FROM AUTHOR]

The flow of viscous fluids is considered as the aggregation of the motion of fluid particles when the fluid is conceived to be made up by an infinite number of particles. As an alternative of this conventional model, fluid motion could be understood as the slip of fluid layers with a molecular scale over each other, where the slip structures of fluid and their associated small-scale motion are characterized by an axial-vector-valued differential 1-form, called the vortex field. In this paper, in the case of steady flows we define the swirling degree of the velocity field at a point, and further the swirl field of the steady flow, to study the slip topology of fluid or the local streamline pattern around the critical point. The linear velocity field in the right real Schur form is used to carry out detailed analyses around the isolated critical point. Theoretical deduction and numerical test unveil the connection between the swirling degree and the swirl field, greatly make clear the topological property of slip structures of fluid in steady flows, especially in three-dimensional space. [ABSTRACT FROM AUTHOR]

The standard Permanent Scatterer Interferometric Synthetic Aperture Radar (PSInSAR) technique, which is commonly used for surface motion analysis, assumes linear deformation velocities. While effective for monitoring urban subsidence over short periods, it falls short when dealing with non-linear, earthquake-related deformations over extended timeframes. To address this limitation, we use a non-linear PSInSAR technique, which is an enhancement of PSInSAR, to identify non-linear deformation patterns. We processed Sentinel-1A images from ascending and descending orbits in the Islamabad/Rawalpindi region from December 2015 to January 2023 using non-linear PSInSAR. By calculating the differences in deformation, we analyzed surface movements and assessed the impact of the 2017 earthquake on urban areas. Our findings reveal that the earthquake significantly increased the deformation in ascending and descending orbit tracks, with an average deformation of up to 70 mm/yr and a line-of-sight movement of up to 30 mm/yr. Our observations indicate that the deformation is directed towards the line of sight in the north and south of the deformed area, suggesting subsidence between the two uplifting faults, potentially linked to a concealed fault line along the deformation zone boundary. This contradicts previous arguments, suggesting that water extraction is the leading cause of deformation. Our analysis with non-linear PSInSAR demonstrates that tectonics play a significant role in deformation, providing valuable insights into tectonic-activity-induced deformations in urban areas over the long term. [ABSTRACT FROM AUTHOR]

A stochastic model for a superposition of uncorrelated pulses with a random distribution of amplitudes, sizes, and velocities is analyzed. The pulses are assumed to move radially with fixed shape and amplitudes decreasing exponentially in time due to linear damping. The pulse velocities are taken to be time-independent but randomly distributed. The implications of a broad distribution of pulse amplitudes and velocities, as well as correlations between these, are investigated. Fast and large-amplitude pulses lead to flattened average radial profiles with order unity relative fluctuations in the scrape-off layer. For theoretically predicted blob velocity scaling relations, the stochastic model reveals average radial profiles similar to the case of a degenerate distribution of pulse velocities but with more intermittent fluctuations. The profile e-folding length is given by the product of the average pulse velocity and the linear damping time due to losses along magnetic field lines. The model describes numerous common features from experimental measurements and underlines the role of large-amplitude fluctuations for plasma–wall interactions in magnetically confined fusion plasmas. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) network analysis benefits from precise point positioning with undifferenced (UD) or double differenced (DD) integer ambiguity resolution (IAR). Position time series with UD-IAR and a practical DD-IAR are compared for a mixture network consisting of 57 global and 82 regional stations with 4-year observations. The sparse global stations are more affected by different IAR methods than the regional stations of Crustal Movement Observation Network of China (CMONOC). The most significant differences between UD-IAR and the practical DD-IAR are observed in velocity estimations, with averages of 0.15 and 0.30 mm/yr for the horizontal and vertical components, respectively. UD-IAR can achieve smaller root mean square at 70–83 % of the daily solutions than the practical DD-IAR for global stations. Nevertheless, moderate differences of frame parameters and annual variations are introduced by different IAR methods. The IAR is also proved to be one of the potential origins for Global Positioning System (GPS) draconitic signals and white noise at high frequency. [ABSTRACT FROM AUTHOR]

The problem of wave interaction with multiple adjacent floating solar panels with arbitrary types and numbers of constraints is considered. All the solar panels are assumed to be homogeneous, with the same physical properties, as well as modeled by using the Kirchhoff-Love plate theory. The motion of the fluid is described by the linear velocity potential theory. The domain decomposition method is employed to obtain the solutions. In particular, the entire fluid domain is divided into two types, the one below the free surface, and the other below elastic plates. The velocity potential in the free surface domain is expressed into a series of eigenfunctions. By contrast, the boundary integral equation and the Green function are employed to construct the velocity potential of fluid beneath the entire elastic cover, with unknowns distributed along two interfaces and jumps of physical parameters of the plates. All these unknowns are solved from the system of linear equations, which is established from the matching conditions of velocity potentials and edge conditions. This approach is confirmed with much higher computational efficiency compared with the one only involving eigenfunction expansion for the fluid beneath each plate. Extensive results and discussions are provided for the reflection and transmission coefficients of water waves, maximum deflection, and principal strain of the elastic plates; especially, the influence of different types and numbers of edge constraints are investigated in detail. [ABSTRACT FROM AUTHOR]

Elastic full-waveform inversion (FWI) is powerful in resolving fine-scale structures in complex models, but suffering from strong nonlinearity and slow convergence rate, especially in the presence of cycle-skipping issues when the initial model is not well constrained. We present a progressive data assimilation (PDA) strategy to mitigate the cycle-skipping issue and boost the convergence rate. Specifically, we split each seismogram into several time windows with a constant length after the first arrival. At each iteration, the PDA strategy automatically screens the windows that are not cycle skipped for inversion according to the criteria of similarity measured between the observed and predicted waveform within a given window. Through the iterations, the model improves and more data will automatically be assimilated into the inversion, forming a positive feedback of model update, and speed up the convergence rate. To provide additional constraints and also stabilise the inversion at the beginning, we include low-frequency surface waves and examine their contribution to the inversion. We validate the effectiveness of the PDA strategy in FWI through numerical experiments using the 1D linear gradient velocity model and the Foothill model. Compared with the conventional FWI strategy, the proposed PDA strategy in an elastic FWI can effectively mitigate the cycle-skipping problem and significantly accelerate the convergence rate. We further apply this method to the field data, and it improves the shallow part of the model with only a fraction of the entire dataset, demonstrating the great potential for practical usage. [ABSTRACT FROM AUTHOR]

Dual‐porosity models are often used to describe solute transport in heterogeneous media, but the parameters within these models (e.g., immobile porosity and mobile/immobile exchange rate coefficients) are difficult to identify experimentally or relate to measurable quantities. Here, we performed synthetic, pore‐scale millifluidics simulations that coupled fluid flow, solute transport, and electrical resistivity (ER). A conductive‐tracer test and the associated geoelectrical signatures were simulated for four flow rates in two distinct pore‐scale model scenarios: one with intergranular porosity, and a second with an intragranular porosity also defined. With these models, we explore how the effective characteristic‐length scale estimated from a best‐fit dual‐domain mass transfer (DDMT) model compares to geometric aspects of the flow field. In both model scenarios we find that: (1) mobile domains and immobile domains develop even in a system that is explicitly defined with one domain; (2) the ratio of immobile to mobile porosity is larger at faster flow rates as is the mass‐transfer rate; and (3) a comparison of length scales associated with the mass‐transfer rate (Lα) and those associated with calculation of the Peclet number (LPe) show LPe is commonly larger than Lα. These results suggest that estimated immobile porosities from a DDMT model are not only a function of physically mobile or immobile pore space, but also are a function of the average linear pore‐water velocity and physical obstructions to flow, which can drive the development of immobile porosity even in single‐porosity domains. [ABSTRACT FROM AUTHOR]

Fast‐start predator‐escape performance and its sensitivity to temperature (24, 30, and 36°C) were evaluated in mummichog Fundulus heteroclitus across a range of body sizes spanning YOY to adult (35–68 mm standard length). Mummichogs exhibit isometry of body dimensions and areas of the dorsal and anal fins but negative allometry of the caudal fin area. These scaling relationships are consistent with observed decreases in fast‐start angular velocities with increasing body size. Linear velocity, on the contrary, does not vary with size, and both large and small mummichogs are capable of traversing similar distances in a given amount of time. In addition, temperature influences fast‐start performance in similar ways over the size range, though the magnitude of the effect varies with size for some performance measures. In general, fast‐start performance increases with test temperature, but mummichogs acclimated to warmer temperatures exhibit lower performance at each test temperature. Altogether, our results suggest that mummichogs across the adult size range may suffer decreases in their predator‐escape performance as increasing sea temperatures combine with short‐term temperature fluctuations in the estuaries these fish occupy. [ABSTRACT FROM AUTHOR]

Aluminum (Al) fluoropolymer composites are widely used in the field of energetic materials. At present, it is a research hotspot to improve the agglomeration of nano-aluminum powder in fluoropolymer and make micro-nano-Al/fluorine rubber (F2601) composites. In this study, it was the first step to modify the surface of nano-aluminum (n-Al) powders, and then Al/F2601 composite microspheres were prepared by Pickering emulsion. The effects of oil–water ratio, solid content and fluorine–aluminum ratio on the stability of the emulsion were investigated. Al/F2601 microspheres with particle sizes of about ≤ 50 μm and different surface pores were prepared by controlling various conditions, which appeared the thermal decomposition peak between 485.5 °C and 524.9 °C. The combustion process of samples in the air was recorded by a high-speed camera, the composites with different F2601 contents burn stably and show a clear pattern of combustion velocity, and the maximum linear combustion velocity is up to 30.7 cm s−1. [ABSTRACT FROM AUTHOR]

To clarify the effect of different radial cooling intensities on the formation of central cracks in large round bloom continuous casting, it is necessary to study the solidification characteristics and dynamics of P91 high‐alloy steel at different cooling rates (CRs) to improve the central defects. In this article, the solidification characteristics of P91 high‐alloy steel at different CRs are studied by using the Thermo‐Calc software, high‐temperature laser confocal microscopy, scanning electron microscopy, and optical microscopy. Meanwhile, the growth kinetics of δ‐Fe and γ‐Fe phases under different CRs are determined. The results show that the solidification path of P91 high‐alloy steel is L(L + δ‐Fe) → (L + γ‐Fe + δ‐Fe) → (δ‐Fe + γ‐Fe). The δ‐Fe and γ‐Fe phase precipitation process is divided into two stages. Stage I is the nucleation and rapid growth phase, in which a high undercooling is required. Stage II is the slow growth stage, where the undercooling decreases and remains constant. The initial growth linear velocities of the δ‐Fe phase are 0.51, 2.72, and 2.09 μm s−1 at CRs of 10, 50, and 100 °C min−1, respectively, while those of the γ‐Fe phase are 0.10, 1.42, and 1.41 μm s−1. [ABSTRACT FROM AUTHOR]

The present study offers a thorough evaluation of the influence of partial slip conditions and viscoelastic behavior on axial fluid flow driven by a cylinder or plate experiencing axial deformation with linear velocity. The momentum transport features a partial velocity slip which generates a nonlinear Robin-type boundary condition, while the energy transport employs a linear thermal slip boundary condition, as opposed to the previous studies that were limited to the no-slip conditions. The adoption of a quadratic surface temperature led to a novel and precise similarity solution. Furthermore, the study investigates the impact of an electrically conducting fluid assumption on momentum transport and viscous heating mechanism on thermal transport. The study utilizes a powerful routine that produces numerical results for a full range of parameters. Numerically evaluated coefficient of skin friction for the viscoelastic fluid flow is analyzed over a range of second-grade fluid parameters. In addition, heat transfer rates are determined for a variety of controlling parameters. A comparison of the present numerical approach with the homotopy scheme used by a previous study is presented and deliberated. [ABSTRACT FROM AUTHOR]

This study introduces a framework to improve upper extremity motion-based telemanipulation by component-wise rescaling (CWR) of spatial twist. This method allows for separate adjustments of linear and angular scaling parameters, significantly improving precision and dexterity even when the operator's heading direction changes. By finely controlling both the linear and angular velocities independently, the CWR method enables more accurate telemanipulation in tasks requiring diverse speed and accuracy based on personal preferences or task-specific demands. The study conducted experiments confirming that operators could precisely control the robot gripper with a steady, controlled motion even in confined spaces, irrespective of changes in the subject's body-heading direction. The performance evaluation of the proposed motion-scaling-based telemanipulation leveraged Optitrack's motion-capture system, comparing the trajectories of the operator's hand and the manipulator's end effector (EEF). This verification process solidified the efficacy of the developed framework in enhancing telemanipulation performance. [ABSTRACT FROM AUTHOR]

Robot workpiece machining is interesting in industry as it offers some advantages, such as higher flexibility in comparison with the conventional approach based on CNC technology. However, in recent years, we have been facing a strong progressive shift to custom-based manufacturing and low-volume/high-mix production, which require a novel approach to automation via the employment of collaborative robotics. However, collaborative robots feature only limited motion capability to provide safety in cooperation with human workers. Thus, it is highly necessary to perform more detailed robot task planning to ensure its feasibility and optimal performance. In this paper, we deal with the problem of studying kinematic robot performance in the case of such manufacturing tasks, where the robot tool is constrained to follow the machining path embedded on the workpiece surface at a prescribed orientation. The presented approach is based on the well-known concept of manipulability, although the latter suffers from physical inconsistency due to mixing different units of linear and angular velocity in a general 6 DOF task case. Therefore, we introduce the workpiece surface constraint in the robot kinematic analysis, which enables an evaluation of its available velocity capability in a reduced dimension space. Such constrained robot kinematics transform the robot's task space to a two-dimensional surface tangent plane, and the manipulability analysis may be limited to the space of linear velocity only. Thus, the problem of physical inconsistency is avoided effectively. We show the theoretical derivation of the proposed method, which was verified by numerical experiments. [ABSTRACT FROM AUTHOR]

Manual therapy (MT) is commonly used in rehabilitation to deal with motor impairments in Parkinson's disease (PD). However, is MT an efficient method to improve gait in PD? To answer the question, a systematic review of clinical controlled trials was conducted. Estimates of effect sizes (reported as standard mean difference (SMD)) with their respective 95% confidence interval (95% CI) were reported for each outcome when sufficient data were available. If data were lacking, p values were reported. The PEDro scale was used for the quality assessment. Three studies were included in the review. MT improved Dynamic Gait Index (SMD = 1.47; 95% CI: 0.62, 2.32; PEDro score: 5/10, moderate level of evidence). MT also improved gait performances in terms of stride length, velocity of arm movements, linear velocities of the shoulder and the hip (p < 0.05; PEDro score: 2/10, limited level of evidence). There was no significant difference between groups after MT for any joint's range of motion during gait (p > 0.05; PEDro score: 6/10, moderate level of evidence). There is no strong level of evidence supporting the beneficial effect of MT to improve gait in PD. Further randomized controlled trials are needed to understand the impact of MT on gait in PD. [ABSTRACT FROM AUTHOR]

The current paper concerned with a non-linear convection flow of the Oldroyd-B nanofluid at a point of stagnation across a rotating sphere under the influence of convective heat and passive control conditions. The analysis of energy and concentration transition has been scrutinized based on the Cattaneo–Christov diffusion model. The formulated coupled mathematical problem involving boundary requirements can be alerted to a set of highly nonlinear ordinary differential equations by employing similarity analysis. The numerical solution for the governing problem was computed by utilizing bvp4c solver method. The performance of velocity fields, skin friction drag, energy, heat transfer rate, and concentration for various control parameters has been analyzed using diagrams and tables. The findings stipulated that velocity, temperature, and nanoparticle are enhanced for the relaxation time constant while they decay for the retardation time parameter. The upshots also confirmed that enlarging magnetic parameters leads to improve both linear velocity and coefficient of skin friction. The velocity profiles are enhanced as a function of the rotation constant. But, normal velocity declines for buoyancy force ratio, and the same trend is being noted for magnetic and relaxation time parameters on angular velocity. The fluid temperature declines for the Prandtl number and augments for thermal convective parameter. The coefficient of skin friction decreases for larger thermal relaxation and rotation parameters, whereas an analogous effect is being noticed for Brownian parameter on the concentration field. Further, the thermophoresis parameter displays an enhancing tendency on temperature as well as concentration profile while bringing down the Nusselt number. The Lewis number and solutal relaxation parameter filter the concentration field. The graph of the streamline is sketched for identical values of the magnetic parameter and noticed that the contour lines increased as magnified. Confirmation of the current outcomes with former studies is presented. [ABSTRACT FROM AUTHOR]

The interaction between surface waves and a finite rectangular floating plate in a channel is considered analytically, while the location of the plate is not restricted. The mathematical model is based on the linear velocity potential flow theory for the fluid and the Kirchhoff–Love plate theory for the plate. The problem is converted into an integral equation through using the Green function. The second-order singularity associated with a body with no thickness is treated with the Dirac delta function. The developed scheme is used for case studies of various edge constraints. Extensive results are provided for the hydrodynamic forces acting on the plate and the wave reflection and transmission coefficients. The effects of wave frequency, channel width, plate length, and edge conditions are analyzed, and their physical implications are highlighted. Significant findings comprise the highly oscillatory nature of force curves, influenced by the natural frequencies of the channels and the length of the plate, and substantial effects of edge conditions and the plate position on the results. [ABSTRACT FROM AUTHOR]

The linear instability analysis of liquid jets with periodic velocity modulation in the ambient gas is carried out. Utilizing the viscous potential theory and the Floquet theory, an analytical dispersion relation for the perturbation growth can be obtained. Due to the parametric resonance caused by velocity modulation, the oscillatory Kelvin–Helmholtz instability (OKHI) can be triggered in the short-wavelength region, leading to the competition between the OKHI and the intrinsic Rayleigh–Plateau and Kelvin–Helmholtz instability (RP-KHI). The parametric study shows that the increase in the velocity oscillation amplitude can enhance the jet instability and lead to the transition of the instability mechanism from the RP-KHI to the OKHI. The velocity oscillation frequency mainly affects the growth of the OKHI. Specifically, the maximum growth rates of perturbation vary with the oscillation frequency at moderate frequencies due to the competition between the RP-KHI and the OKHI, whereas they converge to constant values as the frequency either increases or decreases continuously. The increase in the Weber number promotes the RP-KHI and the OKHI simultaneously, and the jet breakup is dominated by the axisymmetric perturbation of the RP-KHI consistently. The increase in the Reynolds number enhances the jet instability, but hardly affects unstable wavenumber regions. By comparing the maximum growth rates of axisymmetric and non-axisymmetric perturbations, the predominant mode of the jet instability can be identified. Considering variations in the velocity oscillation amplitude and frequency, the transition between the RP-KHI and the OKHI can be predicted by a phase diagram. [ABSTRACT FROM AUTHOR]

In the present study, the impact of a water droplet onto a rotational surface was experimentally studied. The effects of the impact velocity, the rotational speed, and the impact radial position on the impact phenomena were carefully investigated. The phenomena of asymmetric spreading, finger formation, and secondary droplets were observed. Moreover, experiments of a water droplet impacting onto a stationary surface with different impact velocities were also conducted for comparisons. The results showed that, at the same impact velocity, the increase in the rotational speed or the impact radial position could result in the increase in the wetting length in the angular direction and the wetting area. In addition, at the same impact velocity, the dimensionless wetting length in the radial direction on the rotational surface was generally lower than the spreading factor on the stationary surface. In addition, new correlations for the spreading ratio, the dimensionless excess spread area, the dimensionless maximum wetting area, and the number of fingers appearing at the angle of 50° after impact were proposed. The increase in the impact velocity and the surface linear velocity could both promote the formation of the fingers at the angle of 50° after impact. In addition, the dimensionless horizontal displacement of the secondary droplet was found to be mainly influenced by the impact velocity, while the surface linear velocity only had a minor influence. [ABSTRACT FROM AUTHOR]

We analysed the excitation of a surface magnetoplasmon wave by the mode conversion of a p-polarized laser beam over a rippled semiconductor (n-type)-free space interface. The pump surface magnetoplasmon wave exerts a ponderomotive force on the free electrons in the semiconductor, imparting a linear oscillatory velocity at the laser modulation frequency to them. This linear oscillatory velocity couples with the modulated electron density to produce a current density, which develops a resonant surface magnetoplasmon wave in the terahertz region. The amplitude of the terahertz surface magnetoplasmon wave can be tuneable with an external magnetic field and the semiconductor's temperature. [ABSTRACT FROM AUTHOR]

Sea ice profoundly influences the polar environment and the global climate. Traditionally, sea ice has been modeled as a continuum under Eulerian coordinates to describe its largescale features, using, for instance, viscous-plastic rheology. Recently, Lagrangian particle models, also known as the discrete element method models, have been utilized for characterizing the motion of individual sea ice fragments (called floes) at scales of 10 km and smaller, especially in marginal ice zones. This paper develops a multiscale model that couples the particle and the continuum systems to facilitate an effective representation of the dynamical and statistical features of sea ice across different scales. The multiscale model exploits a Boltzmann-type system that links the particle movement with the continuum equations. For the small-scale dynamics, it describes the motion of each sea ice floe. Then, as the large-scale continuum component, it treats the statistical moments of mass density and linear and angular velocities. The evolution of these statistics affects the motion of individual floes, which in turn provides bulk feedback that adjusts the large-scale dynamics. Notably, the particle model characterizing the sea ice floes is localized and fully parallelized in a framework that is sometimes called superparameterization, which significantly improves computational efficiency. Numerical examples demonstrate the effective performance of the multiscale model. Additionally, the study demonstrates that the multiscale model has a linear-order approximation to the truth model. [ABSTRACT FROM AUTHOR]

The detection and feedback of displacement and velocity significantly impact the control accuracy of the linear feed system. In this study, we propose a flexible and self-powered displacement sensor based on the triboelectric effect, designed for seamless integration into linear feed systems. The displacement sensor comprises two parts, the mover and stator, operating in a sliding mode. This sensor can precisely detect the displacement of the linear feed system with a large detection range. Additionally, the sensor is capable of real-time velocity detection of linear feed systems, with an error rate below 0.5%. It also offers advantages, such as excellent flexibility, compact size, stability, easy fabrication, and seamless integration, with linear feed systems. These results highlight the potential of the self-powered displacement sensor for various applications in linear feed systems. [ABSTRACT FROM AUTHOR]

The sense of orientation of an animal is derived from the head direction (HD) system found in several limbic structures and depends on an intact vestibular labyrinth. However, how the vestibular system influences the generation and updating of the HD signal remains poorly understood. Anatomical and lesion studies point toward three key brainstem nuclei as key components for generating the HD signal--nucleus prepositus hypoglossi, supragenual nucleus, and dorsal paragigantocellularis reticular nuclei. Collectively, these nuclei are situated between the vestibular nuclei and the dorsal tegmental and lateral mammillary nuclei, which are thought to serve as the origin of the HD signal. To determine the types of information these brain areas convey to the HD network, we recorded neurons from these regions while female rats actively foraged in a cylindrical enclosure or were restrained and rotated passively. During foraging, a large subset of cells in all three nuclei exhibited activity that correlated with the angular head velocity (AHV) of the rat. Two fundamental types of AHV cells were observed; (1) symmetrical AHV cells increased or decreased their firing with increases in AHV regardless of the direction of rotation, and (2) asymmetrical AHV cells responded differentially to clockwise and counterclockwise head rotations. When rats were passively rotated, some AHV cells remained sensitive to AHV, whereas firing was attenuated in other cells. In addition, a large number of AHV cells were modulated by linear head velocity. These results indicate the types of information conveyed from the vestibular nuclei that are responsible for generating the HD signal. [ABSTRACT FROM AUTHOR]

A three-dimensional reachable set for a nonlinear controlled object "Dubins car" is investigated. The control is the angular velocity of rotation of the linear velocity vector. An integral quadratic constraint is imposed on the control. Based on the Pontryagin maximum principle, a description of the motions generating the boundary of the reachable set is given. The motions leading to the boundary are optimal Euler elasticae. Simulation results are presented. [ABSTRACT FROM AUTHOR]

This paper presents an approach for designing angular and linear velocity observers for rigid bodies using two inertial vectors and one landmark measurements directly. Compared with the classical velocity estimation algorithms, the proposed observer does not need to reconstruct the pose information from measurements nor be coupled with velocity sensors. The linear‐time varying dynamics of the estimation error equation are analyzed, rigorously showing the uniform local exponential stability of the observer. Simulations are conducted to illustrate the significant performance of the proposed method. [ABSTRACT FROM AUTHOR]

Results of studying stabilization of a homogeneous hydrogen–air flame on an optical discharge plasma in a high-velocity flow are reported. The main aspect of experiments is providing stable combustion behind the region of laser beam focusing without any mechanical flame holders. The laser radiation parameters are sufficient for creating a quasi-steady plasma in the flow. It is shown that the optical discharge stabilizes the flame front in a wide range of equivalence ratios for flow velocities up to m/s. The laser radiation parameters within the range of their variation from one experiment to another exert a minor effect on the turbulent flame velocity. Flame stabilization behind the optical discharge region has some specific features. An important parameter is heat release due to hydrogen combustion. A dimensionless criterion is derived: the turbulent flame velocity is a linear function of this criterion. [ABSTRACT FROM AUTHOR]

In the process of collecting traffic information, traditional traffic flow control methods have some problems, such as high loss rate of sensing and detection information and long average queue length, which lead to the unsatisfactory effect of traffic control and evacuation in main roads. Therefore, based on multi-sensor information fusion technology, this study designs a new intelligent control method of traffic flow on main road. According to the multi-sensor information, the fusion algorithm and measurement equation are designed to obtain the main road traffic sensor position, vehicle linear velocity and other parameters, and update the fusion results in real time. Then, the short-term characteristics of traffic flow are used to control the appearance time of target section. Based on the ordinary differential equation, the main road traffic network is represented by intelligent directed graph, and the intelligent dredging model of urban main road traffic flow is constructed. The simulation results show that in five experimental roads, the average delay time of this method is less than 35 s, the maximum average number of stops is only 8.8, the average queue length is less than 30 m, the average travel speed is more than 25 km/h, the traffic flow per unit time is more than 250veh/10 min, and the traffic congestion index of main road is always more than 5.5. The above indexes of this method are better than those of traditional methods, which verifies that this method has better application performance. [ABSTRACT FROM AUTHOR]

The Orthoptera are a diverse insect order well known for their locomotive capabilities. To jump, the bush-cricket uses a muscle actuated (MA) system in which leg extension is actuated by contraction of the femoral muscles of the hind legs. In comparison, the locust uses a latch mediated spring actuated (LaMSA) system, in which leg extension is actuated by the recoil of spring-like structure in the femur. The aim of this study was to describe the jumping kinematics of Mecopoda elongata (Tettigoniidae) and compare this to existing data in Schistocerca gregaria (Acrididae), to determine differences in control of rotation during take-off between similarly sized MA and LaMSA jumpers. 269 jumps from 67 individuals of M. elongata with masses from 0.014 g to 3.01 g were recorded with a high-speed camera setup. In M. elongata, linear velocity increased with mass0.18 and the angular velocity (pitch) decreased with mass−0.13. In S. gregaria, linear velocity is constant and angular velocity decreases with mass−0.24. Despite these differences in velocity scaling, the ratio of translational kinetic energy to rotational kinetic energy was similar for both species. On average, the energy distribution of M. elongata was distributed 98.8% to translational kinetic energy and 1.2% to rotational kinetic energy, whilst in S. gregaria it is 98.7% and 1.3%, respectively. This energy distribution was independent of size for both species. Despite having two different jump actuation mechanisms, the ratio of translational and rotational kinetic energy formed during take-off is fixed across these distantly related orthopterans. [ABSTRACT FROM AUTHOR]

Objective: An annualised linear growth velocity (LGV) reference can identify groups of children at risk of growing poorly. As a single velocity reference for all preschool ages does not exist, we present an interim tool, derived from published, normative growth studies, for detecting growth faltering, illustrating its use in Nepali preschoolers. Design: The WHO Child Growth Velocity Standard was adapted to derive 12-month increments and conjoined to the Tanner-Whitehouse Height Velocity Reference data yielding contiguous preschool linear growth annualised velocities. Linear restricted cubic spline regressions were fit to generate sex-specific median and standard normal deviate velocities for ages 0 through 59 months. LGV Z -scores (LGVZ) were constructed, and growth faltering was defined as LGVZ < –2. Setting: Use of the reference was illustrated with data from Nepal's Tarai region. Participants: Children contributing the existing growth references and a cohort of 4276 Nepali children assessed from 2013 to 2016. Results: Fitted, smoothed LGV reference curves displayed monotonically decreasing 12-month LGV, exemplified by male/female annual medians of 26·4/25·3, 12·1/12·7, 9·1/9·4, 7·7/7·8 and 7/7 cm/years, starting at 0, 12, 24, 36 and 48 months, respectively. Applying the referent, 31·1 %, 28·6 % and 29·3 % of Nepali children <6, 6–11 and 12–23 months of age, and ∼6 % of children 24–59 months, exhibited growth faltering. Under 24 months, faltering velocities were more prevalent in girls (34·4 %) than boys (25·3 %) (P < 0·05) but comparable (∼6 %) in older preschoolers. Conclusions: A LGV reference, concatenated from extant data, can identify preschool groups at-risk of growth faltering. Application and limitations are discussed. [ABSTRACT FROM AUTHOR]

This article addresses the leader‐follower formation control problem for a group of quadrotors using only relative bearing measurements. Most existing methods require full position or velocity information, which cis challenging to obtain in harsh environments. In contrast, the proposed control scheme is based on a hierarchical system that does not rely on relative position or velocity measurements. The bearing‐only control law is designed to stabilize the desired formation, and each quadrotor maintains predetermined bearings with its neighbors. The control design relies on a non‐singular extraction algorithm for separate design of translation and rotation control. The outer loop of the control scheme utilizes a filter‐like approach to overcome the lack of bearing rate measurements in the bearing‐only formation controller. Moreover, employing differentiators following the separation principle with properties of asymptotic high accuracy, a uniform differentiator is provided for each following quadrotor to overcome the absence of linear velocity and acceleration feedback in the inner‐loop controller. Ultimately, the efficacy of the proposed control strategy is validated through a combination of Lyapunov stability theory and extensive numerical simulations. [ABSTRACT FROM AUTHOR]

Muscle fatigue is defined as a reduced ability to maintain maximal strength during voluntary contraction. It is associated with musculoskeletal disorders that affect workers performing repetitive activities, affecting their performance and well-being. Although electromyography remains the gold standard for measuring muscle fatigue, its limitations in long-term work motivate the use of wearable devices. This article proposes a computational model for estimating muscle fatigue using wearable and non-invasive devices, such as Optical Fiber Sensors (OFSs) and Inertial Measurement Units (IMUs) along the subjective Borg scale. Electromyography (EMG) sensors are used to observe their importance in estimating muscle fatigue and comparing performance in different sensor combinations. This study involves 30 subjects performing a repetitive lifting activity with their dominant arm until reaching muscle fatigue. Muscle activity, elbow angles, and angular and linear velocities, among others, are measured to extract multiple features. Different machine learning algorithms obtain a model that estimates three fatigue states (low, moderate and high). Results showed that between the machine learning classifiers, the LightGBM presented an accuracy of 96.2% in the classification task using all of the sensors with 33 features and 95.4% using only OFS and IMU sensors with 13 features. This demonstrates that elbow angles, wrist velocities, acceleration variations, and compensatory neck movements are essential for estimating muscle fatigue. In conclusion, the resulting model can be used to estimate fatigue during heavy lifting in work environments, having the potential to monitor and prevent muscle fatigue during long working shifts. [ABSTRACT FROM AUTHOR]

A Mössbauer spectrometer was built and evaluated using an amplified piezoelectric actuator under feedback control for the Doppler velocity drive. The actuator was driven with a quadratic displacement waveform, giving a linear velocity profile. The optimization of the piezoelectric Doppler drive under feedback control was performed with measurements from a laser Doppler vibrometer. 57Fe Mössbauer spectra of α-iron in transmission geometry show minimal peak distortions. The performance of this piezoelectric Doppler drive makes Mössbauer spectrometry possible in applications requiring small size, mass, and low cost. [ABSTRACT FROM AUTHOR]

The purpose of this report is to provide additional analysis and commentary on the men's 100 m world record of 9.58 s, set by Usain Bolt in the 2009 Berlin World Championships in Athletics. In addition, the entire race underwent a unique kinematic analysis, particularly emphasizing the maximum running velocity and its related factors. It was possible due the application of the new Stuhec software. The data were provided by LAVEG'S advanced laser measurement technology based on positional data with a high spatiotemporal resolution. The maximum velocity phase is the most critical determinant of the final race time. Bolt completed two phases in this world-record 100 m sprint: acceleration and top velocity. The borderline between these phases reached the highest velocity of 12.32 m/s on a 52 m run. He could keep the maximum velocity in five 10 m sections (50–100 m). The occurrence of functional asymmetry—the difference in step length between the left and right legs—was also noticed. Longer steps were taken with the left leg, almost over 80 m. From a practical point of view, new technologies (e.g., software) allow coaches and athletes to analyze the kinematic parameters of sprinting even more precisely and in detail. They must take into account precise changes in the course of maximum speed and the parameters determining it which are step length and frequency. Based on such an analysis, it is possible to modify the training process aimed at increasing the potential, both maximum speed and the supporting factors of strength and power. This must be conditioned by the appropriate selection of training measures shaping the abovementioned motor skills and parameters describing the optimal sprinting technique. [ABSTRACT FROM AUTHOR]

In this paper, the first‐order fractional step finite element method to solve the 2D/3D unstationary incompressible thermomicropolar fluid equations (ITME) is proposed. At each time step, the projection strategy about the linear velocity is adopted to get the linear velocity and pressure values in the first two sub‐steps, and then the angular velocity and temperature values are solved in the last two sub‐steps. Based on the proposed method, the variational problem is decomposed into four linear subproblems. By using the energy analysis technique, the unconditional stability and error estimates about the first‐order semi‐discrete method are derived, and the unconditional stability about the first‐order fully discrete method is analyzed. Finally, some numerical experiments are carried out to show the feasibility and effectiveness of the method. [ABSTRACT FROM AUTHOR]

Constraints on the linear growth rate, f σ8, using small-scale redshift space distortion measurements have a significant statistical advantage over those made on large scales. However, these measurements need to carefully disentangle the linear and non-linear information when interpreting redshift space distortions in terms of f σ8. It is particularly important to do this given that some previous measurements found a significant deviation from the expectation based on the Lambda cold dark matter (ΛCDM) model constrained by Planck cosmic microwave background data. We construct a new emulator-based model for small-scale galaxy clustering with scaling parameters for both the linear and non-linear velocities of galaxies, allowing us to isolate the linear growth rate. We train the emulator using simulations from the AbacusCosmos suite, and apply it to data from the extended Baryon Oscillation Spectroscopic Survey luminous red galaxy sample. We obtain a value of f σ8(z  = 0.737) = 0.368 ± 0.041, in 2.3σ tension with the Planck 2018 ΛCDM expectation, and find less dependence on the minimum measurement scale than previous analyses. [ABSTRACT FROM AUTHOR]