Momentum Fluctuations Research Articles

High-bandwidth pressure field imaging of fin-generated shock wave–boundary layer interactions

The dynamics of a shock-induced separation unit generated by a 20 $^\circ$ sharp fin placed on a cylindrical surface in a Mach 2.5 flow was investigated. Specifically, the present work investigated the mechanisms that govern the mid-frequency range of separation shock unsteadiness in the fin shock wave–boundary layer interaction (SBLI) unit. Two-dimensional pressure fields were obtained over the cylinder surface spanning the entire fin SBLI unit using high-bandwidth pressure-sensitive paint at 40 kHz imaging rate that allowed probing the low- through mid-frequency ranges of the separation shock unsteadiness. The mean pressure field showed a progressive weakening of the separation shock with downstream distance, which is an artifact of the three-dimensional relief offered by the curved mounting surface. The root-mean-square (r.m.s.) pressure field exhibited a banded structure with elevated $p_{r.m.s.}$ levels beneath the intermittent region, separation vortex and adjacent to the fin root. The power spectral density (PSD) of the surface pressure fluctuations obtained beneath the intermittent region revealed that the separation shock oscillations exhibited the mid-frequency content over the majority of its length. Interestingly, neither the PSD nor the length of the intermittent region varied noticeably with downstream distance, revealing a constant separation shock foot velocity along the entire SBLI. The pressure fluctuation PSD beneath the separation vortex also exhibited the broadband peak at the mid-frequency range of the separation shock motions over the majority of its length within the measurement domain. By contrast, the region adjacent to the fin root exhibited pressure oscillations at a substantially lower frequency compared with the separation shock and the separation vortex. Two-point coherence and cross-correlation analysis provided unique insights into the critical sources and mechanisms that drive the separation shock unsteadiness. The separation vortex and separation shock dynamics were found to be driven by a combination of convecting perturbations that originated from the vicinity of the fin leading edge and the local interactions of the separated flow with the incoming boundary layer. The boundary layer locally strengthened or weakened the convecting pressure perturbations depending on the local momentum fluctuations within the boundary layer.

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.

Probing collectivity in heavy-ion collisions with fluctuations of the pT spectrum

Event-by-event fluctuations in the initial stages of ultrarelativistic nucleus-nucleus collisions depend little on rapidity. The hydrodynamic expansion which occurs in later stages then gives rise to correlations among outgoing particles which depend weakly on their relative rapidity. Azimuthal correlations, through which anisotropic flow (vn(pT)) is defined, have been the most studied. Here we study a new observable introduced in 2020 by Schenke, Shen and Teaney and dubbed v0(pT), which quantifies the relative change in the pT spectrum induced by a fluctuation. We describe how it can be measured. Using hydrodynamic simulations, we make quantitative predictions for v0(pT) of charged and identified hadrons. We then discuss how v0(pT) relates to two phenomena which have been measured: The increase of the mean transverse momentum in ultracentral collisions, and the event-by-event fluctuations of the transverse momentum per particle [pT]. We show that v0(pT) determines the dependence of these quantities on the pT cuts implemented in the analysis. We quantitatively explain the rise of σpT observed by ATLAS as the upper pT-cut is increased from 2 to 5 GeV/c.

Towards a momentum potential theory for reacting flows

Mutual coupling of (thermofluiddynamic) modes of perturbations can affect the thermo-acoustic stability of combustors and contribute to combustion noise. For example, vortical or entropic perturbations can be transferred to acoustic perturbations if accelerated by the mean flow. The decomposition of perturbation fields into the respective modes and a linear description of their interactions in terms of fluctuating primitive variables is challenging. In contrast, Doak’s momentum potential theory promises an unambiguous decomposition in terms of momentum fluctuations, which is not limited to the linear regime. Whereas classical momentum potential theory takes into account hydrodynamic, acoustic and entropic modes in unconfined flows, the investigation of noise generation in combustion chambers requires the extension of the momentum potential theory to capture modes linked to the fluctuation of species mass fractions (“species mode”) arising from the change in chemical composition due to the reaction. Furthermore, a rigorous treatment of boundary conditions due to the confinement of the flow inside the combustor is required. The herein presented extension to reactive flows consists of two steps, (i) the formulation of a potential for momentum fluctuations related to species modes and (ii) identification of the total fluctuating enthalpy related to species modes. The extended theory is applied to post-process computational fluid dynamic simulation data of the propagation of entropy and species perturbations through one-dimensional ducts, nozzles and premixed flames. We find that although momentum potential theory offers a complete decomposition of momentum perturbations for reactive flows, the meaningful interpretation of this decomposition is rather challenging, even for non-reactive flows.

Instability and transition control by steady local blowing/suction in a hypersonic boundary layer

The efficacy of steady large-amplitude blowing/suction on instability and transition control for a hypersonic flat plate boundary layer with Mach number 5.86 is investigated systematically. The influence of the blowing/suction flux and amplitude on instability is examined through direct numerical simulation and resolvent analysis. When a relatively small flux is used, the two-dimensional instability critical frequency that distinguishes the promotion/suppression mode effect closely aligns with the synchronisation frequency. For the oblique wave, as the spanwise wavenumber increases, the suppression effects would become weaker and the mode suppression bandwidth diminishes/increases in general in the blowing/suction control. Increasing the blowing/suction flux can effectively broaden the frequency bandwidth of disturbance suppression. The influence of amplitude on disturbance suppression is weak in a scenario of constant flux. To gain a deeper insight into disturbance suppression mechanism, momentum potential theory (MPT) and kinetic energy budget analysis are further employed in analysing disturbance evolution with and without control. When the disturbance is suppressed, the blowing induces the transport of certain acoustic components along the compression wave out of the boundary layer, whereas the suction does not. The velocity fluctuations are derived from the momentum fluctuations of the MPT. Compared with the momentum fluctuations, the evolutions indicated by each component's velocity fluctuations greatly facilitate the investigations of the acoustic nature of the second mode. The rapid variation of disturbance amplitude near the blowing is caused by the oscillations of the acoustic component and phase speed differences between vortical and thermal components. Kinetic energy budget analysis is performed to address the non-parallel effect of the boundary layer introduced by blowing/suction, which tends to suppress disturbances near the blowing. Moreover, viscous effects leading to energy dissipation are identified to be stronger in regions where the boundary layer is rapidly thickening. Finally, it is demonstrated that a flat plate boundary layer transition triggered by a random disturbance can be delayed by a blowing/suction combination control. The resolvent analysis further demonstrates that disturbances with frequencies that dominate the early transition stage are dampened in the controlled base flow.

The Jittering Jets Explosion Mechanism in Electron Capture Supernovae

We conduct one-dimensional stellar-evolution simulations of stars with zero-age main-sequence (ZAMS) masses of M ZAMS = 8.8 − 9.45 M ⊙ toward core collapse by electron capture and find that the convective zone of the precollapse core can supply the required stochastic angular momentum fluctuations to set a jet-driven electron capture supernova explosion in the frame of the jittering jets explosion mechanism. By our assumed criteria of a minimum convective specific angular momentum and an accreted mass during jet launching of M acc ≃ 0.001−0.01 M ⊙, the layer in the convective zone that when accreted launches the exploding jittering jets resides in the helium-rich zone. Depending on the model, this exploding layer is accreted at about a minute to a few hours after core collapse occurs, much shorter than the time the exploding shock crosses the star. The final (gravitational) mass of the neutron star (NS) remnant is in the range of M NS = 1.25−1.43 M ⊙.

Exploration and Prediction of Factors Influencing Athlete Momentum in Tennis Matches

In the field of sports competition, the momentum fluctuation of athletes in a match has an important impact on the final performance, especially in a high-intensity confrontational sport such as tennis. In this paper, based on the men's singles data of the 2023 Wimbledon Tennis Championships, a prediction model based on a decision tree and a BP neural network was established to analyze the momentum and fluctuation of athletes in a match. This study contributes to an in-depth understanding of athletes' performance during matches and provides a scientific basis for their training and tactical adjustments.

Research On the Role and Influencing Factors of Momentum in Tennis Matches Based on Linear Conditional Probability Model and Support Vector Machine

This research investigates the role and influencing factors of momentum in tennis matches using a Linear Conditional Probability Model (LCPM) and Support Vector Machine (SVM). The study begins with data preprocessing to address outliers and standardize scoring notations, followed by an analysis of the momentum's role in tennis, which is defined in relation to consecutive points, games won, and service breaks. The principal component analysis (PCA) is employed to synthesize key factors reflecting momentum, including consecutive scores, untouchable shots, aces, and net points, with a focus on their Markovian properties. A momentum formula is constructed, accounting for the sliding average of scoring differentials and the mutual cancellation of momentum between players. The study further examines the stochasticity of swings in play and runs of success, challenging the notion that these elements are random. The results of the Wald Wolfowitz Run Test and Granger Causality Test indicate that momentum significantly influences the probability of winning points and is not a random phenomenon. A PCA-SVM-SHAP model is developed to predict momentum fluctuations, achieving an 81.26% accuracy rate in the validation set. The model identifies net skills, serving skills, and untouchable shots as the most influential factors on momentum changes. The research extends the model's application to unknown tennis matches and other sports events, demonstrating its generalization ability with varying degrees of accuracy.

Misperceiving Momentum: Computational Mechanisms of Biased Striatal Reward Prediction Errors in Bipolar Disorder

BackgroundDysregulated reward processing and mood instability are core features of bipolar disorder that have largely been considered separately, with contradictory findings. We sought to test a mechanistic account that emphasizes an excessive tendency in bipolar disorder to enter recursive cycles in which reward perception is biased by signals that the environment may be changing for the better or worse. MethodsParticipants completed a probabilistic reward task with functional magnetic resonance imaging. Using an influential computational model, we ascertained whether participants with bipolar disorder (n = 21) showed greater striatal tracking of momentum-biased reward prediction errors (RPEs) than matched control participants (n = 21). We conducted psychophysiological interaction analyses to quantify the degree to which each group modulated functional connectivity between the ventral striatum and left anterior insula in response to fluctuations in momentum. ResultsIn participants with bipolar disorder, but not control participants, the momentum-biased RPE model accounted for significant additional variance in striatal activity beyond a standard model of veridical RPEs. Compared with control participants, participants with bipolar disorder exhibited lower insular-striatal functional connectivity modulated by momentum-biased RPEs, an effect that was more pronounced as a function of current manic symptoms. ConclusionsConsistent with existing theory, we found evidence that bipolar disorder is associated with a tendency for momentum to excessively bias striatal tracking of RPEs. We identified impaired insular-striatal connectivity as a possible locus for this propensity. We argue that computational psychiatric approaches that examine momentary shifts in reward and mood dynamics have strong potential for yielding new mechanistic insights and intervention targets.

Multiparticle integral and differential correlation functions

This paper formalizes the use of integral and differential cumulants for measurements of multiparticle event-by-event transverse momentum fluctuations, rapidity fluctuations, as well as net-charge fluctuations. This enables the introduction of multiparticle balance functions, defined based on differential correlation functions (factorial cumulants), that suppress two- and three-prong resonance decays effects and enable measurements of underlying long-range correlations obeying quantum number conservation constraints. These multiparticle balance functions satisfy simple sum rules determined by quantum number conservation. It is additionally shown that these multiparticle balance functions arise as an intrinsic component of high-order net-charge cumulants. This implies that the magnitude of these cumulants, measured in a specific experimental acceptance, is strictly constrained by charge conservation and primarily determined by the rapidity and momentum width of these balance functions. The paper also presents techniques to reduce the computation time of differential correlation functions up to order n=10 based on the methods of moments. Published by the American Physical Society 2024

Momentum Study Based on Logistic Regression Models and BP Neural Networks

In the context of a game, "momentum" usually refers to a set of events (e.g., consecutive points scored) that create momentum or a trend in a game, which may have a significant impact on the outcome of the game. The purpose of this paper is to investigate how momentum affects the outcome of a game through mathematical modeling. First, an AHP-TOPSIS model is built to calculate the score of each athlete at each moment to quantify and visualize momentum. Second, based on real game data, a Kruskal-Wallis H model test is established to assess the correlation between momentum and score. To predict the fluctuation of players' momentum, logistic regression model was used to predict the momentum fluctuation. Finally, GABP neural network and genetic algorithm are established to visualize the performance data of the players and predict the inflection points during the game. The model proposed in this paper effectively solves the problem of momentum during the game and improves the ability to predict and analyze the game results.

Scalar QED Model for Polarizable Particles in Thermal Equilibrium or in Hyperbolic Motion in Vacuum

We consider a scalar QED (quantum electrodynamics) model for the frictional force and the momentum fluctuations of a polarizable particle in thermal equilibrium with radiation or in hyperbolic motion in a vacuum. In the former case the loss of particle kinetic energy due to the frictional force is compensated by the increase in kinetic energy associated with the momentum diffusion, resulting in the Planck distribution when it is assumed that the average kinetic energy satisfies the equipartition theorem. For hyperbolic motion in vacuum the frictional force and the momentum diffusion are similarly consistent with an equilibrium with a Planckian distribution at the temperature T=ℏa/2πkBc. The quantum fluctuations of the momentum imply that it is only the average acceleration a that is constant when the particle is subject to a constant applied force.

Improving Stratocumulus Cloud Amounts in a 200‐m Resolution Multi‐Scale Modeling Framework Through Tuning of Its Interior Physics

AbstractHigh‐Resolution Multi‐scale Modeling Frameworks (HR)—global climate models that embed separate, convection‐resolving models with high enough resolution to resolve boundary layer eddies—have exciting potential for investigating low cloud feedback dynamics due to reduced parameterization and ability for multidecadal throughput on modern computing hardware. However low clouds in past HR have suffered a stubborn problem of over‐entrainment due to an uncontrolled source of mixing across the marine subtropical inversion manifesting as stratocumulus dim biases in present‐day climate, limiting their scientific utility. We report new results showing that this over‐entrainment can be partly offset by using hyperviscosity and cloud droplet sedimentation. Hyperviscosity damps small‐scale momentum fluctuations associated with the formulation of the momentum solver of the embedded large eddy simulation. By considering the sedimentation process adjacent to default one‐moment microphysics in HR, condensed phase particles can be removed from the entrainment zone, which further reduces entrainment efficiency. The result is an HR that can produce more low clouds with a higher liquid water path and a reduced stratocumulus dim bias. Associated improvements in the explicitly simulated sub‐cloud eddy spectrum are observed. We report these sensitivities in multi‐week tests and then explore their operational potential alongside microphysical retuning in decadal simulations at operational 1.5° exterior resolution. The result is a new HR having desired improvements in the baseline present‐day low cloud climatology, and a reduced global mean bias and root mean squared error of absorbed shortwave radiation. We suggest it should be promising for examining low cloud feedbacks with minimal approximation.

Skewness and kurtosis of mean transverse momentum fluctuations at the LHC energies

The first measurements of skewness and kurtosis of mean transverse momentum (〈pT〉) fluctuations are reported in Pb–Pb collisions at sNN = 5.02 TeV, Xe–Xe collisions at sNN = 5.44 TeV and pp collisions at s=5.02 TeV using the ALICE detector. The measurements are carried out as a function of system size 〈dNch/dη〉|η|<0.51/3, using charged particles with transverse momentum (pT) and pseudorapidity (η), in the range 0.2<pT<3.0 GeV/c and |η|<0.8, respectively. In Pb–Pb and Xe–Xe collisions, positive skewness is observed in the fluctuations of 〈pT〉 for all centralities, which is significantly larger than what would be expected in the scenario of independent particle emission. This positive skewness is considered a crucial consequence of the hydrodynamic evolution of the hot and dense nuclear matter created in heavy-ion collisions. Furthermore, similar observations of positive skewness for minimum bias pp collisions are also reported here. Kurtosis of 〈pT〉 fluctuations is found to be in good agreement with the kurtosis of Gaussian distribution, for most central Pb–Pb collisions. Hydrodynamic model calculations with MUSIC using Monte Carlo Glauber initial conditions are able to explain the measurements of both skewness and kurtosis qualitatively from semicentral to central collisions in Pb–Pb system. Color reconnection mechanism in PYTHIA8 model seems to play a pivotal role in capturing the qualitative behavior of the same measurements in pp collisions.

BPS fivebrane stars. Part I. Expectation values of observables

We study ensembles of 1/2-BPS bound states of fundamental strings and NS-fivebranes (NS5-F1 states) in the AdS decoupling limit. We revisit a solution corresponding to an ensemble average of these bound states, and find that the appropriate duality frame for describing the near-source structure is the T-dual NS5-P frame, where the bound state is a collection of momentum waves on the fivebranes. We find that the fivebranes are generically well-separated; this property results in the applicability of perturbative string theory. The geometry sourced by the typical microstate is not close to that of an extremal non-rotating black hole; instead the fivebranes occupy a ball whose radius is parametrically much larger than the “stretched horizon” scale of the corresponding black hole. These microstates are thus better characterized as BPS fivebrane stars than as small black holes.When members of the ensemble spin with two fixed angular potentials about two orthogonal planes, we find that the spherical ball of the non-rotating ensemble average geometry deforms into an ellipsoid. This contrasts with ring structures obtained when fixing the angular momenta instead of the angular potentials; we trace this difference of ensembles to large fluctuations of the angular momentum in the ensemble of fixed angular potential.

Extension of Doak's momentum potential theory for multi-species and reacting flows.

This work extends Doak's momentum potential theory to multi-chemical-component and reactive, time-stationary fluctuating flows. Additional mixture-related components are found to be superimposed on the canonical vortical, acoustic, and thermal parts of momentum fluctuations and total fluctuating enthalpy. These extended relations are used to develop a time-averaged model that relates the acoustic power radiated to the far-field with clearly defined vortical, acoustic, thermal, and compositional near-field sources. The resulting model is designed to offer a more general and comprehensive way to describe the noise generated within combustion chambers.

ATLAS measurement of mean momentum fluctuations and correlations with the flow in Xe+Xe and Pb+Pb collisions

The thermal fluctuations in the QGP medium formed in heavy ion collisions present themselves as event-wise mean transverse momentum ([pT]) fluctuations in the final state. Recent studies have shown that the fluctuations are sensitive to radial flow, random thermal motion, and nuclear deformation. They can provide constraints on the extent of thermalization of the QGP droplet. Recently, correlations of [pT] with flow harmonic coefficients (vn) also gained interest, as they were found to be sensitive primarily to the initial state fluctuations. This talk presents precise measurements of up to 3rd order [pT] cumulants as a function of multiplicity and centrality with an emphasis on ultra-central collisions. These results have strong implications for understanding the impacts of the initial condition, medium thermalization, and medium properties on final state [pT] fluctuations.

Transverse momentum fluctuation in ultra-central Pb+Pb collision at the LHC

The ATLAS collaboration has recently observed that the variance of the transverse momentum per particle ([pt]), when measured as a function of the collision multiplicity (Nch) in Pb+Pb collisions, decreases by a factor 2 for the largest values of Nch, corresponding to ultra-central collisions. We show that this phenomenon is naturally explained by invoking impact parameter (b) fluctuations, which contribute to the variance, and gradually disappear in ultracentral collisions. It implies that Nch and [pt] are strongly correlated at fixed b, which is explained by the local thermalization of the QGP medium.

Energy and system size dependence of strongly intensive fluctuation measures in heavy-ion collisions at FAIR energies

Event-by-event fluctuations of multiplicity and transverse momentum of charged hadrons produced in heavy-ion collisions at FAIR energies, 10A, 20A, 30A, and 40A GeV are studied in the framework of relativistic transport model, URQMD. Dependence of two families of strongly intensive measures of multiplicity(N) and transverse momentum (p T) fluctuations, Δ[p T, N] and Σ[p T, N], on collision centrality, centrality bin-widths and pseudorapidity windows are examined. Attempts are also made to study NN, N p T, and p T p T fluctuations using two window analysis method. The findings suggest that the measure, Δ[p T, N] be dealt with proper selection of centrality intervals. This measure also exhibits a strong dependence on the widths of η windows. The variable Σ[p T, N], however, is observed to be insensitive to the centrality bin-widths and shows a variation of <5% with the widths of η windows. The analysis of data after event mixing gives Δ[p T, N] and Σ[p T, N] values as ∼1 irrespective of the widths of η windows and collision centrality, as predicted by a model of independent particle emission, IPM. The study of joint fluctuations of the two quantities on two η windows separated in η space, reveals that Σ[N F, N B] values are ∼1 irrespective of the position of η windows whereas, the values of and firstly increase with η sep and later acquire saturations. The observed trend of centrality dependence of and agrees fairly well with those observed in MC simulated studies carried out for AA collisions at LHC energies in the framework model of string fusion.

Uncertainty relation in viscous hydrodynamics and its effects in collective flow observables

AbstractThe uncertainty relation is considered to be one of key features of quantum mechanics which distinguishes quantum and classical systems. Recently, we developed a new formulation of the uncertainty relation based on the generalized scheme of variational principle, the stochastic variational method (SVM). In this method, the uncertainty relation is related to the nondifferentiability of observables and thus can be obtained even in classical stochastic systems. This new formulation resolves the famous paradox in quantum mechanics, the angular uncertainty relation without introducing artificial assumptions. In this paper, we show that the fluctuations of position and momentum for a nonrelativistic viscous fluid element satisfies the uncertainty relation analogous to the corresponding quantum mechanical one. Such a fluctuation is sensitive to the temperature gradient at the freezeout surface and can affect the collective flow anisotropy in relativistic heavy‐ion collisions.