Momentum Change Research Articles

Understanding the puzzle of angular momentum conservation in beta decay and related processes

We ask the question of how angular momentum is conserved in electroweak interaction processes. To introduce the problem with a minimum of mathematics, we first raise the same issue in elastic scattering of a circularly polarized photon by an atom, where the scattered photon has a different spin direction than the original photon, and note its presence in scattering of a fully relativistic spin-1/2 particle by a central potential. We then consider inverse beta decay in which an electron is emitted following the capture of a neutrino on a nucleus. While both the incident neutrino and final electron spins are antiparallel to their momenta, the final spin is in a different direction than that of the neutrino-an apparent change of angular momentum. However, prior to measurement of the final particle, in all these cases angular momentum is indeed conserved. The apparent nonconservation of angular momentum arises in the quantum measurement process in which the measuring apparatus does not have an initially well-defined angular momentum, but is localized in the outside world. We generalize the discussion to massive neutrinos and electrons, and examine nuclear beta decay and electron-positron annihilation processes through the same lens, enabling physically transparent derivations of angular and helicity distributions in these reactions.

Design of optimum spacecraft reorientation control with a combined criteria of quality based on the quaternions

Specifical original problem of attitude controlling for spacecraft was proposed in this paper. Problem of optimal rotation from a known initial state in a prescribed spatial orientation was studied in detail (turnaround time is not fixed). Design of optimal program of reorientation is based on new indicator of quality that combines energy costs including the contribution of controlling torques and integral of rotary energy (in a known proportion) and reorientation time; presence of duration factor bounds time of rotation finish. To construct an optimal control of angular momentum changing, quaternionic method and the maximum principle were applied. Differential equation that relates spacecraft angular momentum and quaternion of spacecraft orientation is a base to obtain analytic solution to a problem. We reveal the properties of optimum control program analytically, and study key features of optimum motion in details. Also, we write the formalized equations, mathematical formulas to design optimal law for change of spacecraft’s angular momentum. Analytic relations and equations are given for finding the optimal solution. Control law (in as explicit dependence between phase variables and con-trolling variables has been formulated. Main relations determining optimum values of parameters for rotation control algorithm were given. The closed-form law for rotation was obtained for dynamically symmetric solids. Numerical example as well as results of mathematical modeling of spacecraft motion that formed using optimum control are presented. This data as addition to the made theoretic descriptions shows reorientation process (in virtual form) and demonstrates practical feasibility of the developed control method. A designed algorithm for optimal control of rotation improves an efficiency of attitude system, and originates more economical performing of space vehicle during its flight along orbit.

Design of optimum spacecraft reorientation control with a combined criteria of quality based on the quaternions

Specifical original problem of attitude controlling for spacecraft was proposed in this paper. Problem of optimal rotation from a known initial state in a prescribed spatial orientation was studied in detail (turnaround time is not fixed). Design of optimal program of reorientation is based on new indicator of quality that combines energy costs including the contribution of controlling torques and integral of rotary energy (in a known proportion) and reorientation time; presence of duration factor bounds time of rotation finish. To construct an optimal control of angular momentum changing, quaternionic method and the maximum principle were applied. Differential equation that relates spacecraft angular momentum and quaternion of spacecraft orientation is a base to obtain analytic solution to a problem. We reveal the properties of optimum control program analytically, and study key features of optimum motion in details. Also, we write the formalized equations, mathematical formulas to design optimal law for change of spacecraft’s angular momentum. Analytic relations and equations are given for finding the optimal solution. Control law (in as explicit dependence between phase variables and con-trolling variables has been formulated. Main relations determining optimum values of parameters for rotation control algorithm were given. The closed-form law for rotation was obtained for dynamically symmetric solids. Numerical example as well as results of mathematical modeling of spacecraft motion that formed using optimum control are presented. This data as addition to the made theoretic descriptions shows reorientation process (in virtual form) and demonstrates practical feasibility of the developed control method. A designed algorithm for optimal control of rotation improves an efficiency of attitude system, and originates more economical performing of space vehicle during its flight along orbit.

Self-similar Buildup and Inside-out Growth: Tracing the Evolution of Intermediate-to-high-mass Star-forming Galaxies since z = 2

We aim to discern scenarios of structural evolution of intermediate-to-high-mass star-forming galaxies (SFGs) since cosmic noon by comparing their stellar mass profiles with present-day stellar masses of log(M*,0/M⊙)=10.3−11 . We addressed discrepancies in the size evolution rates of SFGs, which may be caused by variations in sample selection and methods for size measurements. To check these factors, we traced the evolution of individual galaxies by identifying their progenitors using stellar mass growth histories (SMGHs), integrating along the star-forming main sequence and from the IllustrisTNG simulations. Comparison between the structural parameters estimated from the mass- and light-based profiles shows that mass-weighted size evolves at a slower pace compared to light-based ones, highlighting the need to consider the mass-to-light ratio (M/L) gradients. Additionally, we observed mass-dependent growth in stellar mass profiles: massive galaxies ( log(M*,0/M⊙)≳10.8 ) formed central regions at z ≳ 1.5 and grew faster in outer regions, suggesting inside-out growth, while intermediate-mass and less massive SFGs followed a relatively self-similar mass buildup since z ∼ 2. Moreover, slopes of observed size evolution conflict with the predictions of TNG50 for samples selected using the same SMGHs across our redshift range. To explore the origin of this deviation, we examined changes in angular momentum (AM) retention fraction using the half-mass size evolution and employing a simple disk formation model. Assuming similar dark matter halo parameters, our calculations indicate that the AM inferred from observations halved in the past 10 Gyr while it remained relatively constant in TNG50. This higher AM in simulations may be due to the accretion of high-AM gases into disks.

Core prominence as a signature of restarted jet activity in the LOFAR radio-galaxy population

Context. Recurrent phases of dormancy and activity occur in the supermassive black holes in active galactic nuclei. Characterizing the duty cycles of this process is crucial in understanding the impact of the energy released on the host galaxies, and their evolution. However, it is challenging to identify sources in the quiescent and restarted phases. Aims. Our goal is to identify and characterize a substantial sample of radio galaxies in a restarted phase and explore the idea of core prominence as a signature of restarted activity. We expand our prior study of identifying restarted sources from a 30 deg2 area in the Lockman Hole to a larger 424 deg2 region in the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) extragalactic field using a sample of core-dominated radio galaxies selected visually. Methods. We used the 144 MHz LOFAR survey images of the HETDEX field to identify galaxies with restarting jets. By assessing diverse selection criteria including radio core dominance along with low surface brightness extended emission, spectral index properties (e.g., steep or inverted spectra of a core and an ultra-steep spectrum of extended emission), and morphology, we found 69 candidate restarted radio galaxies in the HETDEX field. Results. The restarted candidates show a diverse intrinsic morphology, spanning from FRI, FRII, core-with-halo, to asymmetric forms, feasibly proposing different progenitors. Within these 69 restarted candidates, we identified a subset of nine galaxies characterized by ultra-steep spectrum extended emission combined with high radio core prominence, representing previous and current epochs of jet activity. We interpret our findings for this small subset as support for a model in which the switch-on and switch-off mechanism happens with a relatively fast duty cycle in these sources. We found a peculiar case, J131728.61+561544.8, which appears to have altered its jet orientation, possibly due to changes in the angular momentum or spin of its supermassive black hole, interactions with surrounding material, and/or variations in the magnetic flux threading its accretion disk. Conclusions. The restarted candidates span a range of radio luminosities from log10(L144 MHz/WHz−1) = 23.24 to log10(L144 MHz/WHz−1) = 26.80, and linear sizes between 88 and 1659 kpc at 144 MHz, with 16 sources identified as giant radio galaxies with sizes exceeding 0.7 Mpc. The total stellar content of restarted sources is consistent with massive elliptical galaxies, with at least 17% inhabiting cluster environments. Our findings at z < 0.4 suggest that many restarting radio galaxies are not found in rich cluster environments, aligning with the environmental properties of the broader radio-galaxy population. The present study confirms the core prominence as an effective parameter for selecting candidate restarted radio sources.

Quantification Analysis of Sports Momentum Based on a Multi-Index Approach and TOPSIS

This study quantifies the concept of momentum in sports, inspired by Novak Djokovic's unexpected loss in 2023, and evaluates its impact on game outcomes. Utilizing a structured multi-index approach, we categorized performance into fourteen primary and three secondary indexes. The TOPSIS model enhanced by entropy weighting, along with the Delphi model, was applied for weight assessments of these indexes. Our analysis, incorporating the Mann-Kendall trend test and Spearman correlation coefficient, revealed a significant correlation of 0.51 between momentum and match results, underscoring its pivotal role. The results contribute to a deeper understanding of momentum, enabling coaches to refine strategies and optimize performance based on dynamic changes in momentum. This study provides a comprehensive framework for quantifying momentum, with potential applications extending beyond tennis to other sports where strategic momentum management could influence outcomes.

Prediction of potential energy on player scoring trend in tennis match based on Hopfield neural network model

In tennis, it is very important to catch the direction and trend of the match when the score happens. This paper aims to establish a mathematical model to predict the dynamic change of match progress and the appearance of match points, and explain the role of "momentum" in the match. By mining the real-time match data of 2023 Wimbledon Tennis Open, based on Hopfield neural network and entropy weight method, the technical level, psychological pressure and fatigue level of players in the match are selected as the influencing factors, and the mathematical model between the "momentum" of players and the change of the match flow is established, and the change of the match schedule can be predicted more accurately. The change of momentum may affect the motivation of players, and the choice of a reasonable strategy may be a magic weapon to win the match. It is hoped that this can help the pre-competition training of tennis players and promote the vigorous development of tennis events.

Quantifying Tennis Players’ Performance and Analyzing Momentum Fluctuations Based on Weighted Logistic Regression Model

This paper proposes a dual-model approach to analyze tennis players’ performance and predict match outcomes, which combines a weighted logistic regression model and a decision tree model. By examining key factors such as scoring rate and serving status, the models calculate the scoring probabilities at different time points, quantifying the performance of players throughout the match. Furthermore, the paper constructs a decision tree model to predict shifts in the match situation based on momentum fluctuations. The research findings underscore the importance of momentum in determining match outcomes and provide valuable insights for training and match strategies. This dual-model approach offers a fresh perspective on the impact of momentum in tennis matches, allowing players to better understand and adapt to the dynamics of momentum fluctuations throughout a match. Additionally, the study suggests targeted training, simulated match conditions, psychological training, real-time data tracking, and physical preparation as strategies to enhance performance and adapt to momentum changes. This comprehensive approach provides players with valuable insights to optimize their performance and strategies in tennis matches.

Relativistic beam loading, recoil-reduction, and residual-wake acceleration with a covariant retarded-potential integrator

An algorithm is demonstrated that performs first-principles tracking of relativistic charged-particles. A covariant approach is used which relies on retarded vector potentials for trajectory integration instead of performing electromagnetic field calculations. When accounting for retardation effects, the peak vector potential and corresponding Lorentz force in the direction of travel increase asymptotically for high-β particles. This produces a very strong field distribution at small angles from the particle’s direction of travel, which can result in considerable change in momentum when approaching a conducting or charged object. We study these dynamics using protons and electrons at relativistic energies passing through apertures in conducting surfaces, where substantial energy shifts are observed for particles passing within roughly 10μm of the aperture boundary.We also simulate breaking a test particle’s line of sight with a conductor or other charged body. After this instant, the test particle continues to accelerate due to residual fields, but no longer produces an opposing force on any charged or conducting object; thus any recoil on the enclosing structure is effectively reduced. In this test, a 1% energy gain is observed for an 85 MeV electron traversing its reflected wake after having conducting plate in its path screened by a dielectric object.We then incorporate a micro-scale dielectric laser acceleration (DLA) device into our simulations. Compared with a 2 mm DLA on its own, we find a factor of two increase in energy gain when adding a series of conducting-surface choppers.

Research on Momentum Prediction of Tennis Match Based on Scoring Model and Multilayer Perceptron

During a tennis match, players may encounter various circumstances that can significantly influence their performance. This force, known as "momentum," can drastically alter the game's flow and ultimately determine the winner. Addressing the challenge of analyzing and predicting momentum shifts, this study applied the Entropy Weight TOPSIS method combined with fuzzy comprehensive evaluation to assess player performance across technical, physical, and psychological factors. These methods provided a comprehensive analysis of the players' performance metrics, revealing patterns linked to momentum changes. Following this, Pearson correlation analysis was conducted to identify key performance indicators strongly associated with match outcomes. These indicators were then integrated into a Multilayer Perceptron (MLP) model, which demonstrated high predictive accuracy, with an R-value of 0.868, effectively capturing momentum shifts in real-time. The study's findings offer valuable insights for improving strategic decision-making during matches and hold potential applications in other fields that require real-time predictive analysis.

Horizon fluxes of binary black holes in eccentric orbits

We compute the rate of change of mass and angular momentum of a black hole, namely tidal heating, in an eccentric orbit. The change is caused due to the tidal field of the orbiting companion. We compute the result for both the spinning and non-spinning black holes in the leading order of the mean motion, namely ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. We demonstrate that the rates get enhanced significantly for nonzero eccentricity. Since eccentricity in a binary evolves with time we also express the results in terms of an initial eccentricity and azimuthal frequency ξϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi _{\\phi }$$\\end{document}. In the process, we developed a prescription that can be used to compute all physical quantities in a series expansion of initial eccentricity, e0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_0$$\\end{document}. These results are computed taking account of the spin of the binary components. The prescription can be used to compute very high-order corrections of initial eccentricity. We use it to find the contribution to eccentricity up to O(e05)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(e_0^5)$$\\end{document} in the spinning binary. Using the computed expression of eccentricity, we derived the rate of change of mass and angular momentum of a black hole, both rotating and non-rotating, in terms of initial eccentricity and azimuthal frequency up to O(e06)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(e_0^6)$$\\end{document}. With the computed fluxes we also compute for the first time the leading order dephasing in both cases analytically up to O(e06)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(e_0^6)$$\\end{document} and study its impact. We argue that for high signal-to-noise ratio sources, these contributions require inclusion in the waveform modeling.

Corrected mathematical models for inertial torques generated by a spinning sphere

The recent publications about inertial torques acting on spinning objects describe their physics by mathematical models. The several inertial torques are generated by the rotating mass which produces centrifugal, Coriolis forces, and the change in the angular momentum. The values of the inertial torques depend on the geometries of the spinning objects. The volumetric geometries of the objects request complex analytical processing of the expressions for the inertial torques. The analysis of the known publication related to the spinning sphere shows the expressions of inertial torques derived from errors in the mathematical processing of integral equations. The wrong limits of the integral equations that give incorrect values for the inertial torques of the spinning sphere present these errors. This manuscript presents the corrected mathematical model for the inertial torques generated by the rotating mass of the spinning solid and hollow sphere.

INVESTIGATION OF PLASMA VISCOSITY AND MAGNETIC FORCES IN COAXIAL PLASMA DISCHARGE DEVICE

This paper investigates the axial plasma current sheath, PCS viscosity force, and its correlation with other magnetic forces acting on it at three different radial positions (2.625, 3.625, and 4.125 cm) within the annular space between the coaxial electrodes system of plasma discharge device (12 kV-56 kA) with positive central electrode. The rate of change of PCS momentum was also investigated at these axial and radial positions. The discharge processes are carried out with an argon gas pressure of 0.8 Torr. Experimental results of azimuthal magnetic induction as a function of axial and radial positions and Navier Stokes equation were employed to compute exactly, the rate of change of PCS momentum, axial magnetic force, magnetic pressure gradient force, and viscosity force.

Exploring waveforms with non-GR deviations for extreme mass-ratio inspirals

The fundamental process of detecting and examining the polarization modes of gravitational waves plays a pivotal role in enhancing our grasp on the precise mechanisms behind their generation. A thorough investigation is essential for delving deeper into the essence of gravitational waves and rigorously evaluating and validating the range of modified gravity theories. In this line of interest, a general description of black holes in theories beyond general relativity can serve a meaningful purpose where distinct deviation parameters can be mapped to solutions representing distinct theories. Employing a refined version of the deformed Kerr geometry, which is free from pathological behaviours such as unphysical divergences in the metric, we explore an extreme mass-ratio inspiral system, wherein a stellar-mass object perturbs a supermassive black hole. We compute the effects of deformation parameters on the rate of change of orbital energy and angular momentum, orbital evolution and phase dynamics with leading order post-Newtonian corrections. With the waveform analysis, we assess the plausibility of detecting deviations from general relativity through observations facilitated by the Laser Interferometer Space Antenna (LISA), simultaneously constraining the extent of these deviations. Therefore, this analysis provides an understanding while highlighting the essential role of observations in advancing gravitational phenomena beyond general relativity.

Exploring the control of whole-body angular momentum in young and elderly based on the virtual pivot point concept.

While walking, ground reaction forces point from the centre of pressure to the neighbourhood of a focal point, namely the virtual pivot point (VPP), that adjusts angular momentum around the centre of mass (CoM). This study explores how age and speed affect the VPP quality and position during walking. Analysing an experimental dataset reveals high quality of the VPP in the sagittal plane for both young and elderly groups, regardless of speed. However, in the frontal plane, the VPP quality decreases with increasing speed, with elderly participants exhibiting significantly lower quality. Although not a direct measure of balance, VPP quality reflects changes in whole-body angular momentum owing to ageing and speed. Additionally, a template model is used to reproduce the VPP quality and position trends observed in the experiment. Simulation results highlight the sensitivity of VPP quality to leg force feedback and show that changing VPP height has minimal effect on gait speed. Furthermore, energy redistribution occurs through increased hip extension and leg damping, associated with a greater horizontal VPP distance from the CoM, observed in elderly walking. This study shows promise for analysing gait based on VPP, potentially aiding clinical interventions and supporting locomotion in the elderly.

Determining the aerodynamic performance of a high-speed unmanned marine wig craft

The study object of this paper is the aerodynamic processes during the movement of an unmanned aerial vehicle flying low over the underlying surface. The ground effect is known to enhance the aerodynamic performance of low-flying aircraft, particularly larger ones. However, this effect is most noticeable for large objects. Unmanned vehicles are typically characterized by their relatively compact geometry. This study explores the aerodynamic processes involved in the flight of a small-sized vehicle using the principle of dynamic support over a surface. The particular prototype of the unmanned aerial vehicle suggested by the authors has been examined herein. The aim of the study is to evaluate the aerodynamic forces affecting a small-sized unmanned high-speed vehicle that employs the dynamic principle of support over the surface (WIG craft) by using CFD modeling. In contrast to most available studies on the ground effect, a 3D problem statement was used in this work. Computational experiments have visualized the physical fields surrounding an aircraft in flight over the ground. This study determines how the distance from the surface affects the aerodynamic properties of a small-sized aircraft, as well as the height of the effective zone where ground effect influences the small-sized WIG craft within . It has been shown that approaching the surface leads to a shift in the center of pressure of the vehicle, which leads to a change in aerodynamic momentum. This phenomenon must be taken into account when designing a control system to provide a stable flight. The study's findings are directly relevant for the development of a type of unmanned vehicles that use the dynamic principle of support over the surface.

Magnetic field induced spin wave reflection by a domain wall in synthetic antiferromagnets

Micromagnetic simulations are used to investigate the effect of an external magnetic field on the interaction between domain walls and linearly polarized propagating spin waves in synthetic antiferromagnets. Two regimes with a sharp transition between them are found. At large fields, spin waves are strongly reflected by the domain wall and, consequently, the latter is propelled forward. At low fields, however, there is no reflection and yet the domain wall undergoes a small forward displacement, which is attributed to the change in linear momentum of the magnons as they pass through the domain wall and to the imbalance in the population of the two oscillation modes present in the linearly polarized excitation. The transition between the two regimes occurs at the field value for which the excitation frequency falls below the threshold of the high-frequency mode.

Healthy older adults generate transverse-plane momenta required for 90° turns while walking during the same phases of gait as used in straight-line gait

BackgroundGeneration and regulation (control) of linear and angular momentum is a challenge during turning while walking which may be exacerbated by age-related changes. In healthy older adults, little is known about how momentum is controlled during turns, especially within each phase of gait. Each phase of gait affords unique mechanical contexts to control momenta and regulate balance. In healthy young adults, we found that the transverse-plane linear and angular momenta generation strategies observed within specific phases of gait during straight-line gait were also used during turns. Therefore, in this study, we investigated whether healthy older adults shared similar momentum control strategies specific to each gait phase during straight-line gait and turns.MethodsNine healthy older adults completed straight-line gait and 90° leftward walking turns. We compared the change in transverse-plane whole-body linear and angular momentum across gait phases (left and right single and double support). We also compared the average leftward force and transverse-plane moment across gait phases.ResultsWe found that leftward linear momentum was generated most during right single support in straight-line gait and leftward turns. However, in contrast to straight-line gait, during leftward turns, average leftward force was applied across gait phases, with left single support generating significantly less leftward average force than other gait phases. Leftward angular momentum generation and average moment were greatest during left double support in both tasks. We observed some within-participant results that diverged from the group statistical findings, illustrating that although they are common, these momenta control strategies are not necessary.ConclusionsOlder adults generated transverse-plane linear and angular momentum during consistent phases of gait during straight-line gait and 90° turns, potentially indicating a shared control strategy. Understanding momentum control within each phase of gait can help design more specific targets in gait and balance training interventions.

An Exploration of Momentum Changes in Tennis Players Based on CART Decision Regression Trees

An Exploration of Momentum Changes in Tennis Players Based on CART Decision Regression Trees

Research on Momentum Evaluation and Turning Point Prediction in Tennis Matches Based on RSR and GSRF

In the men's singles final of the 2023 Wimbledon Open, rising star Carlos Alcaraz defeated veteran Novak Djokovic, an astonishing turnaround and result that sparked an in-depth exploration of the sports phenomenon of "momentum". When one side of a match gains momentum, its technical level and adaptability will be greatly utilized, which will directly affect the victory or defeat of the match. Most of the past researches focus on verifying the authenticity of momentum in sports games and the factors affecting the change of momentum. In this paper, taking the above match as the research object, we use the rank and ratio comprehensive evaluation method (RSR) to mine the match data, and propose a new prediction model GSRF by combining the random forest model and the lattice search algorithm, and based on the independently established momentum model and the momentum difference model, we predicted the turning point of the momentum in the match and the result of the match. The difference effect size of Cohen's d-value of 0.035 and accuracy R² of 0.826 was obtained, which verified the higher accuracy and generalizability of the model. The study helps coaches and instructors optimize training programs, develop game strategies, and provide new ideas and approaches for coaches and instructors.