Body Simulations Research Articles

Prograde and retrograde stars in nuclear cluster merger. Evolution of the supermassive black hole binary and the host galactic nucleus

Nuclear star cluster (NSC) mergers, involving the fusion of dense stellar clusters near the centres of galaxies, play a pivotal role in shaping galactic structures. The distribution of stellar orbits has significant effects on the formation and characteristics of extreme mass ratio inspirals (EMRIs). In this study, we address the orbital distribution of stars in merging NSCs and the subsequent effects on supermassive black hole binary (SMBHB) evolution. We ran dedicated direct-summation $N$-body simulations with different initial conditions to do a detailed study of the resulting NSC after their progenitors had merged. Our findings reveal that prograde stars form a flattened structure, while retrograde stars have a more spherical distribution. The axial ratios of the prograde component vary based on the presence and mass ratio of the SMBHs. The fraction of prograde and retrograde stars depends on the merger orbital properties and the SMBH mass ratio. The interactions of retrograde stars with the SMBHB affect the eccentricity and separation evolution of the binary. Our analysis reveals a strong correlation between the angular momentum and eccentricity of the SMBH binary. This relationship could serve as a means to infer information about the stellar dynamics surrounding the binary. We find that prograde orbits are particularly close to the binary of SMBHs, a promising fact regarding EMRI production. Moreover, prograde and retrograde stars have different kinematic structures, with the prograde stars typically rotating faster than the retrograde ones. The line-of-sight velocity and velocity dispersion, as well as the velocity anisotropy of each NSC, depend on the initial merger orbital properties and SMBH mass ratios. The prograde and retrograde stars always show different behaviours. The distribution of stellar orbits and the dynamical properties of each kinematic population can potentially be used as a way to tell the properties of the parent nuclei apart, and has an important impact on expected rates of EMRIs, which will be detected by future gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA).

Stochastic dissipative Euler’s equations for a free body

Abstract Intrinsic thermal fluctuations within a real solid challenge the rigid body assumption that is central to Euler’s equations for the motion of a free body. Recently, we have introduced a dissipative and stochastic version of Euler’s equations in a thermodynamically consistent way (European Journal of Mechanics – A/Solids 103, 105,184 (2024)). This framework describes the evolution of both orientation and shape of a free body, incorporating internal thermal fluctuations and their concomitant dissipative mechanisms. In the present work, we demonstrate that, in the absence of angular momentum, the theory predicts that the principal axes unit vectors of a body undergo an anisotropic Brownian motion on the unit sphere, with the anisotropy arising from the body’s varying moments of inertia. The resulting equilibrium time correlation function of the principal eigenvectors decays exponentially. This theoretical prediction is confirmed in molecular dynamics simulations of small bodies. The comparison of theory and equilibrium MD simulations allow us to measure the orientational diffusion tensor. We then use this information in the Stochastic Dissipative Euler’s Equations, to describe a non-equilibrium situation of a body spinning around the unstable intermediate axis. The agreement between theory and simulations is excellent, offering a validation of the theoretical framework.

Self-consistent N-body simulation of planetesimal-driven migration. I. The trajectories of single planets in the uniform background

Abstract Recent exoplanet observations have revealed a diversity of exoplanetary systems, which suggests the ubiquity of radial planetary migration. One powerful known mechanism of planetary migration is planetesimal-driven migration (PDM), which can let planets undergo significant migration through gravitational scattering with planetesimals. In this series of papers, we present the results of our high-resolution, self-consistent N-body simulations of PDM, in which gravitational interactions among planetesimals, the gas drag, and Type I migration are all taken into account. In this first paper (Paper I), we investigate the migration of a single planet through PDM within the framework of the classical standard disk model (the minimum-mass solar nebula model). Paper I aims to improve our understanding of planetary migration through PDM, addressing previously unexplored aspects of both the gravitational interactions among planetesimals and the interactions with disk gas. Our results show that even small protoplanets can actively migrate through PDM. Such active migration can act as a rapid radial diffusion mechanism for protoplanets and significantly influence the early stages of planetary formation (i.e., during the runaway growth phase). Moreover, a fair fraction of planets migrate outward. This outward migration may offer a potential solution for the “planet migration problem” caused by Type I migration and gives a natural mechanism for outward migration assumed in many recent scenarios for the formation of outer planets.

Deep operator neural network applied to efficient computation of asteroid surface temperature and the Yarkovsky effect

Surface temperature distribution is crucial for thermal property-based studies about irregular asteroids in our Solar System. While direct numerical simulations could model surface temperatures with high fidelity, they often take a significant amount of computational time, especially for problems for which temperature distributions are required to be repeatedly calculated. To this end, the deep operator neural network (DeepONet) proves a powerful tool due to its high computational efficiency and generalization ability. In this work, we apply DeepONet to the modeling of asteroid surface temperatures. Results show that the trained network is able to predict temperature with an accuracy of ~1% on average, while the computational cost is five orders of magnitude lower, enabling thermal property analysis in a multidimensional parameter space. As a preliminary application, we analyzed the orbital evolution of asteroids through direct N- body simulations embedded with an instantaneous Yarkovsky effect inferred by DeepONet-based thermophysical modeling. Taking asteroids (3200) Phaethon and (89433) 2001 WM41 as examples, we show the efficacy and efficiency of our AI-based approach.

Dynamics and control of a high-altitude balloon with slung load

Abstract The high-altitude balloon proposed in this paper is a long-life balloon carrying a payload through a cable that flies at 20km altitude in near space. A dynamic model of the system, including the thermodynamics of the buoyancy body coupled with a hanging model of the pod, is developed using the Newton–Euler method. The buoyancy body consists of a helium balloon and a ballonet. A differential pressure difference-based altitude adjustment is achieved by tracking the pressure difference at the target altitude. A dynamic simulation of the buoyancy body with a slung pod in autonomous vertical takeoff and altitude regulation processes is presented. The internal thermodynamic variations and pressure differential of the buoyancy body are given. The air mass exchange and blower flow control of the ballonet are validated. The altitude holding error is analysed. The maximum pull force that the cable can withstand is calculated, and the maximum attitude angles of the pod during the ascending and descending processes are depicted. Simulation results provide basic knowledge for the structural design and payload installation of pods.

Double edged tech: navigating the public health and legal challenges of digital twin technology

Abstract This research addresses the legal challenges posed by the implementation of digital twin technology in public health. Digital twins are advanced computational models which aim to replicate human organ functions and biological processes. Their goal is to enable the simulation of the entire human body and to personalize the outputs with individual patient’s health data. Digital twin technology promises to bridge gap between personalized medicine and precision public health. This research is based on a comprehensive review of the current European and Swiss legal frameworks for medical devices and data protection that apply to digital twin technology. Within these frameworks, digital twins are in a grey area, as they are only considered as medical device software when applied to individuals. They also incorporate artificial intelligence, machine learning, and data analytics, which are already a source of legal concern in a healthcare setting, but their effective use in public health raises additional issues. Preliminary findings suggest significant shortcomings in the legal frameworks regarding data privacy, and the potential for increased surveillance by health insurance systems, which could lead to human rights violations. The public health application of digital twins would require global data analysis of sensitive personal information, raising further questions about the secure storage, transmission, and processing of this data. The study concludes that current legal frameworks must be future proofed to manage the complexities introduced by digital twins in public health. In particular, it suggests that regulatory oversight of medical devices needs to be significantly improved in order to safely harness the potential of digital twin technologies for public health. Finally, the new European Union health data space and the forthcoming EU AI act will also play important roles in the implementation of digital twin technologies. Key messages • Applying digital twin technology in public health faces considerable challenges, particularly the issues around data privacy, potential discrimination, and increased surveillance. • We need to adapt and strengthen existing legal frameworks to effectively manage the complexities introduced by digital twins, ensuring that these technologies can be safely used for public health.

The disc origin of the Milky Way bulg. The high velocity dispersion of metal-rich stars at low latitudes

Previous studies of the chemo-kinematic properties of stars in the Galactic bulge have revealed a puzzling trend. Along the bulge minor axis, and close to the Galactic plane, metal-rich stars display a higher line-of-sight velocity dispersion compared to metal-poor stars, while at higher latitudes metal-rich stars have lower velocity dispersions than metal-poor stars, similar to what is found in the Galactic disc. In this work, we re-examine this issue, by studying the dependence of line-of-sight velocity dispersions on metallicity and latitude in APOGEE Data Release 17, confirming the results of previous works. We then analyse an $N$-body simulation of a Milky Way-like galaxy, also taking into account observational biases introduced by the APOGEE selection function. We show that the inversion in the line-of-sight velocity dispersion-latitude relation observed in the Galactic bulge -- where the velocity dispersion of metal-rich stars becomes greater than that of metal-poor stars as latitude decreases -- can be reproduced by our model. We show that this inversion is a natural consequence of a scenario in which the bulge is a boxy or peanut-shaped structure, whose metal-rich and metal-poor stars mainly originate from the thin and thick disc of the Milky Way, respectively. Due to their cold kinematics, metal-rich, thin disc stars are efficiently trapped in the boxy, peanut-shaped bulge, and at low latitudes show a strong barred morphology, which -- given the bar orientation with respect to the Sun-Galactic centre direction -- results in high velocity dispersions that are larger than those attained by the metal-poor populations. Extremely metal-rich stars in the Galactic bulge, which have received renewed attention in the literature, do follow the same trends as those of the metal-rich populations. The line-of-sight velocity-latitude relation observed in the Galactic bulge for metal-poor and metal-rich stars are thus both an effect of the intrinsic nature of the Galactic bulge (i.e. mostly secular) and of the angle at which we observe it from the Sun.

Secondary halo bias through cosmic time II. Reconstructing halo properties using clustering information

When constructing mock galaxy catalogs based on suites of dark matter halo catalogs generated with approximated, calibrated, or machine-learning approaches, assigning intrinsic properties for these tracers is a step of paramount importance, given that they can shape the abundance and spatial distribution of mock galaxies and galaxy clusters. We explore the possibility of assigning properties of dark matter halos within the context of calibrated or learning approaches, explicitly using clustering information. The goal is to retrieve the correct signal of primary and secondary large-scale effective bias as a function of properties reconstructed solely based on phase-space properties of the halo distribution and dark matter density field. The algorithm reconstructs a set of halo properties (such as virial mass, maximum circular velocity, concentration, and spin) constrained to reproduce both primary and secondary (or assembly) bias. The key ingredients of the algorithm are the implementation of individually-assigned large-scale effective bias, a multi-scale approach to account for halo exclusion, and a hierarchical assignment of halo properties. The method facilitates the assignment of halo properties, aiming to replicate the large-scale effective bias, both primary and secondary. This constitutes an improvement over previous methods in the literature, especially for the high-mass end population. We have designed a strategy for reconstructing the main properties of dark matter halos obtained using calibrated or learning algorithms, such that the one- and two-point statistics (on large scales) replicate the signal from detailed $N$-body simulations. We encourage the application of this strategy (or the implementation of our algorithm) for the generation of mock catalogs of dark matter halos based on approximated methods.

The e-MANTIS emulator: Fast and accurate predictions of the halo mass function in f(R)CDM and wCDM cosmologies

In this work, we present a novel emulator of the halo mass function (HMF), which we implemented in the framework of the e-MANTIS emulator of $f(R)$ gravity models. We also extended e-MANTIS to cover a larger cosmological parameter space and to include models of dark energy with a constant equation of state $w$CDM. We used a Latin hypercube sampling of the $w$CDM and $f(R)$CDM cosmological parameter spaces, over a wide range, and carried out a large suite of more than $10000$ $N$-body simulations with a different volume, mass resolution, and random phase for the initial conditions. For each simulation in the suite, we generated halo catalogues using the friends-of-friends (FoF) halo finder, as well as the spherical overdensity (SO) algorithm for different overdensity thresholds (200, 500, and 1000 times the critical density). We decomposed the corresponding HMFs on a B-spline basis, while adopting a minimal set of assumptions on their shape. We used this decomposition to train an emulator based on Gaussian processes. The resulting emulator is able to predict the HMF for redshifts $ 1.5$ and for halo masses $M_h M_ The typical HMF errors for SO haloes with $ c $ at $z=0$ in $w$CDM (respectively $f(R)$CDM) are of the order of $ up to a transition mass $M_t M_ ($M_t M_ For larger masses, the errors are dominated by the shot noise and scale as $ with $ up to $M_h M_ Independently of this general trend, the emulator is able to provide an estimation of its own error as a function of the cosmological parameters, halo mass, and redshift. We have performed an extensive comparison against analytical parametrizations and shown that e-MANTIS is able to better capture the cosmological dependence of the HMF, while being complementary to other existing emulators. The e-MANTIS emulator, which is publicly available, can be used to obtain fast and accurate predictions of the HMF in the $f(R)$CDM and $w$CDM non-standard cosmological models. As such, it represents a useful theoretical tool to constrain the nature of dark energy using data from galaxy cluster surveys.

Strongly Coupled Simulation of Magnetic Rigid Bodies

Strongly Coupled Simulation of Magnetic Rigid Bodies

A speech-based convolutional neural network for human body posture classification

Abstract Problem In recent years, computing and sensing advances have helped to develop efficient human posture classification systems, which assist in creating health systems that contribute to enhancing elder’s and disable’s life quality in context-aware and ambient assistive living applications. Other applications of body posture classification include the simulation of human bodies into virtual characters, security applications such as kidnapping and the body position of the kidnapper or victim, which can provide useful information to the negotiator or the rescue team, and other sports applications. Aim This work aims to propose a body posture classification system based on speech using deep learning techniques. Methods All samples pass through the preprocessing phase. The Mel-frequency cepstral coefficient (MFCC) with 12 coefficients was used as features, and the best features were selected by the correlation-based feature selection method. Two supervised learning techniques called artificial hydrocarbon networks (AHN) and convolutional neural networks (CNN) were deployed to efficiently classify body postures and movements. This research aims to detect six human positions through speech, which include walking downstairs, sitting, walking upstairs, running, laying, and walking. The dataset used in this work was prepared by the authors, named the human activity speech dataset. Results The best performance gained was with the AHN classifier of 68.9% accuracy and 67.1% accuracy with the CNN. Conclusion It was concluded that the MFCC features are the most powerful features in body position classification, and the deep learning methods are powerful in classifying body positions.

Dynamical friction from self-interacting dark matter

Context. Merging compact objects such as binary black holes provide a promising probe for the physics of dark matter (DM). The gravitational waves emitted during inspiral potentially allow one to detect DM spikes around black holes. This is because the dynamical friction force experienced by the inspiralling black hole alters the orbital period and thus the gravitational wave signal. Aims. The dynamical friction arising from DM can potentially differ from the collisionless case when DM is subject to self-interactions. This paper aims to understand how self-interactions impact dynamical friction. Methods. To study the dynamical friction force, we use idealised N-body simulations, where we include self-interacting dark matter. Results. We find that the dynamical friction force for inspiralling black holes would be typically enhanced by DM self-interactions compared to a collisionless medium (ignoring differences in the DM density). At lower velocities below the sound speed, we find that the dynamical friction force can be reduced by the presence of self-interactions. Conclusions. DM self-interactions have a significant effect on the dynamical friction for black hole mergers. Assuming the Chandrasekhar formula may underpredict the deceleration due to dynamical friction.

Tidal mass loss in the Fornax dwarf spheroidal galaxy through N-body simulations with Gaia DR3-based orbits

Aims. The Fornax dwarf spheroidal galaxy (dSph) represents a challenge for some globular cluster (GC) formation models, because an exceptionally high fraction of its stellar mass is locked in its GC system. In order to shed light on our understanding of GC formation, we aim to constrain the amount of stellar mass that Fornax has lost via tidal interaction with the Milky Way (MW). Methods. Exploiting the flexibility of effective multi-component N-body simulations and relying on state-of-the-art estimates of Fornax’s orbital parameters, we study the evolution of the mass distribution of the Fornax dSph in observationally justified orbits in the gravitational potential of the MW over 12 Gyr. Results. We find that, though the dark-matter mass loss can be substantial, the fraction of stellar mass lost by Fornax to the MW is always negligible, even in the most eccentric orbit considered. Conclusions. We conclude that stellar-mass loss due to tidal stripping is not a plausible explanation for the unexpectedly high stellar mass of the GC system of the Fornax dSph and we discuss quantitatively the implications for GC formation scenarios.

Fatigue assessment for back-support exoskeletons during repetitive lifting tasks.

Fatigue is a major cause of low back pain for workers in various fields, including industry and agriculture. It has a negative impact on workers' safety, decreases their productivity, and causes a reduction in their occupational career. An exoskeleton is expected to be a solution for reducing workers' fatigue. However, assessing the safety and effectiveness of exoskeletons, except for the direct measurement of electromyography (EMG) in the human body, is challenging in real-case scenarios. Recently, simulations have been widely used to estimate biomechanical variables. Thus, we aimed to develop a method that combines an exoskeleton model and human body simulation to evaluate the effects of exoskeletons on lumbar fatigue. The strength and tendency estimated using this method are similar to those obtained from EMG devices in symmetrical repetitive lifting tasks. In addition, this method can be used to predict and simulate fatigue after a recorded motion. Our findings will help guide manufacturers in designing their products.

A machine learning framework to generate star cluster realisations

Computational astronomy has reached the stage where running a gravitational $N$-body simulation of a stellar system, such as a Milky Way star cluster, is computationally feasible, but a major limiting factor that remains is the ability to set up physically realistic initial conditions. We aim to obtain realistic initial conditions for $N$-body simulations by taking advantage of machine learning, with emphasis on reproducing small-scale interstellar distance distributions. The computational bottleneck for obtaining such distance distributions is the hydrodynamics of star formation, which ultimately determine the features of the stars, including positions, velocities, and masses. To mitigate this issue, we introduce a new method for sampling physically realistic initial conditions from a limited set of simulations using Gaussian processes. We evaluated the resulting sets of initial conditions based on whether they meet tests for physical realism. We find that direct sampling based on the learned distribution of the star features fails to reproduce binary systems. Consequently, we show that physics-informed sampling algorithms solve this issue, as they are capable of generating realisations closer to reality.

Cluster membership analysis with supervised learning and N-body simulations

Context. Membership analysis is an important tool for studying star clusters. There are various approaches to membership determination, including supervised and unsupervised machine-learning (ML) methods. Aims. We perform membership analysis using the supervised ML approach. Methods. We trained and tested our ML models on two sets of star cluster data: snapshots from N-body simulations, and 21 different clusters from the Gaia Data Release 3 data. Results. We explored five different ML models: random forest (RF), decision trees, support vector machines, feed-forward neural networks, and K-nearest neighbors. We find that all models produce similar results, and the accuracy of RF is slightly better. We find that a balance of classes in the datasets is optional for a successful learning. The classification accuracy strongly depends on the astrometric parameters. The addition of photometric parameters does not improve the performance. We find no strong correlation between the classification accuracy and the cluster age, mass, and half-mass radius. At the same time, models trained on clusters with a larger number of members generally produce better results.

Bounds on galaxy stochasticity from halo occupation distribution modeling

The joint probability distribution of matter overdensity and galaxy counts in cells is a powerful probe of cosmology, and the extent to which variance in galaxy counts at fixed matter density deviates from Poisson shot noise is not fully understood. The lack of informed bounds on this stochasticity is currently the limiting factor in constraining cosmology with the galaxy–matter probability distribution function (PDF). We investigate stochasticity in the conditional distribution of galaxy counts along lines of sight with fixed matter density, and we present a halo occupation distribution (HOD)-based approach for obtaining plausible ranges for stochasticity parameters. To probe the high-dimensional space of possible galaxy–matter connections, we derive a set of HODs that conserve the galaxies’ linear bias and number density to produce REDMAGIC-like galaxy catalogs within the ABACUSSUMMIT suite of N-body simulations. We study the impact of individual HOD parameters and cosmology on stochasticity and perform a Monte Carlo search in HOD parameter space subject to the constraints on bias and density. In mock catalogs generated by the selected HODs, shot noise in galaxy counts spans both sub-Poisson and super-Poisson values, ranging from 80% to 133% of Poisson variance for cells with mean matter density. Nearly all of the derived HODs show a positive relationship between local matter density and stochasticity. For galaxy catalogs with higher stochasticity, modeling galaxy bias to second order is required for an accurate description of the conditional PDF of galaxy counts at fixed matter density. The presence of galaxy assembly bias also substantially extends the range of stochasticity in the super-Poisson direction. This HOD-based approach leverages degrees of freedom in the galaxy–halo connection to obtain informed bounds on nuisance model parameters and can be adapted to study other parametrizations of shot noise in galaxy counts, in particular to motivate prior ranges on stochasticity for cosmological analyses.

Examining the effects of dark matter spikes on eccentric intermediate-mass ratio inspirals using N-body simulations

ABSTRACT Recent studies suggest that dark matter (DM) spikes around intermediate-mass black holes could cause observable dephasing in gravitational wave (GW) signals from intermediate-mass ratio inspirals (IMRIs). Previous research primarily used non-self-consistent analytic methods to estimate the impact of DM spikes on eccentric IMRIs. Our study provides the first self-consistent treatment of this phenomenon using N-body simulations, incorporating post-Newtonian effects up to the 2.5 order for accurate and robust results. Contrary to prior works, which posited that the cumulative effect of two-body encounters (dynamical friction; DF) is the primary mechanism for energy dissipation, we reveal that a three-body effect (slingshot mechanism) plays a more significant role in driving the binary system’s energy loss and consequent orbital shrinkage. We find that binaries counter-rotating with respect to the DM spike merge faster, while corotating binaries merge slower, contrary to expectations from the DF theory. Using Fokker–Planck methods, we also assess the presence and detectability of spikes in realistic environments. When interacting with surrounding materials, DM spikes can have shallower slopes and lower densities than previously considered, leading to smaller signals and lower detection prospects via dephasing. Our results suggest that ‘deshifting’ rather than dephasing might be a more optimistic signature, as it is more robust even in low-density environments.

A Human Body Simulation Using Semantic Segmentation and Image-Based Reconstruction Techniques for Personalized Healthcare

The global healthcare market is expanding, with a particular focus on personalized care for individuals who are unable to leave their homes due to the COVID-19 pandemic. However, the implementation of personalized care is challenging due to the need for additional devices, such as smartwatches and wearable trackers. This study aims to develop a human body simulation that predicts and visualizes an individual’s 3D body changes based on 2D images taken by a portable device. The simulation proposed in this study uses semantic segmentation and image-based reconstruction techniques to preprocess 2D images and construct 3D body models. It also considers the user’s exercise plan to enable the visualization of 3D body changes. The proposed simulation was developed based on human-in-the-loop experimental results and literature data. The experiment shows that there is no statistical difference between the simulated body and actual anthropometric measurement with a p-value of 0.3483 in the paired t-test. The proposed simulation provides an accurate and efficient estimation of the human body in a 3D environment, without the need for expensive equipment such as a 3D scanner or scanning uniform, unlike the existing anthropometry approach. This can promote preventive treatment for individuals who lack access to healthcare.

Compliance control of a rehabilitation massage robot in dynamic scenes

Abstract Medical robots encounter challenges when interacting with people or operating in complex and dynamic environments due to the variability of human morphology and the unpredictability of environmental changes. Compliance of human-robot interaction is the primary goal of medical robots when in contact with the human body. Therefore, robots must be able to adaptively adjust their forces and actions to ensure safety and comfort during the contact process. This paper focuses on the compliance control of rehabilitation massage robots in dynamic scenes. We propose a mechanical arm compliance control method based on the Soft Actor-Critic (SAC) algorithm. We construct a simulated massage environment in a dynamic scene according to the task requirements and design a massage path covering the entire back. Under the framework of deep reinforcement learning, the optimal reward function is designed to achieve constant force control under dynamic scenes. Through numerous simulation experiments, we have verified that the robotic arm can move along the predetermined path under the massage while maintaining a constant contact force with the body simulation module. The actual contact force and target contact force control are realized within 0.1 N.