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Finite-volume gravity currents frequently encounter bottom obstacles, particularly in underwater environments such as lakes and oceans. However, how obstacle–current interactions reorganize Lagrangian transport pathways and ultimately determine the fate of fluid elements over the full current life cycle remains unclear. Using large-eddy simulations, we focus on a low-volume lock-exchange gravity current impinging on an isolated two-dimensional triangular obstacle. Fluid-element trajectories are tracked from collapse through propagation, obstacle interaction, and final dilution and decay, and are classified using K-means clustering into five transport modes linked to characteristic flow structures. We find that increasing obstacle slenderness strengthens upstream reflection and reduces downstream overflow, thereby shifting the fate of tracer particles from downstream delivery toward upstream retention. In addition, the obstacle standoff distance controls the dynamical state of the current at impact, producing systematic yet non-monotonic changes in the fractional population of the transport modes. This study establishes an explicit correspondence between evolving flow structures and clustered Lagrangian pathways. Comparative cases with varying geometric configuration, density contrast, flow depth, and release volume indicate that the identified transport patterns are reasonably robust. Therefore, the present results provide a fate-oriented predictive framework and theoretical basis for the transport of finite-volume gravity currents near obstacles, with important implications for engineering applications.

In this paper, the physical simulation of filling process of vertical centrifugal casting (VCC) of complex titanium alloy casting was studied. Combined with the mature PTV particle tracking technology, the high-speed photography pictures of the filling process of VCC at different rotational speeds were obtained. The trajectory and velocity information of tracer particles in the rotating flow field were obtained by the corresponding analysis software. Then, through the analysis and modeling of quantitative experimental data, the flow behavior characteristics and movement law of titanium alloy melt in the mold cavity under different mold speeds were studied. The results show that: 1. When the mold is still, the front edge of the filling fluid forms a curved surface with the curvature center pointing to the outside of the mold; when the mold rotates, the front edge of the liquid flow forms a curved surface with the curvature center pointing to the inside of the mold; 2. With the increase of the mold rotation speed, the speed of the fluid filling the mold increases significantly; when the rotational speed is greater than 120 rpm, the fluid still has a certain driving force in the mold center far away from the gate; it is good for filling the inner corner of mold with fluid; and 3. When the rotational speed of centrifugal casting of titanium alloy reaches 45 rpm or above, typical turbulent vortices appear in the wake; with the increase of rotating speed to 180 rpm, the average curvature radius of turbulent vortices first increases and then decreases, and reaches the minimum value of 0.67 cm at 120 rpm.

Radio relics are diffuse synchrotron sources that illuminate shock waves in the intracluster medium. In recent years, radio telescopes have provided detailed observations about relics. Consequently, cosmological simulations of radio relics need to provide a similar amount of detail. In this methodological work, we include information on adiabatic compression and expansion, which have been neglected in the past in the modelling of relics. In a cosmological simulation of a merging galaxy cluster, we follow the energy spectra of shock accelerated cosmic-ray electrons using Lagrangian tracer particles. On board of each tracer particle, we compute the temporal evolution of the energy spectrum under the influence of synchrotron radiation, inverse Compton scattering, and adiabatic compression and expansion. Exploratory tests show that the total radio power and, hence, the integrated radio spectrum are not sensitive to the adiabatic processes. This is attributed to small changes in the compression ratio over time.

Internal gravity waves can cause mixing in the radiative interiors of stars. We study this mixing by introducing tracer particles into 2D hydrodynamic simulations. Following the work of Rogers & McElwaine, we extend our study to different masses (3, 7, and 20 M ⊙) and ages (ZAMS, midMS, and TAMS). The diffusion profiles of these models are influenced by various parameters such as the Brunt–Väisälä frequency, density, thermal damping, the geometric effect, and the frequencies of waves contributing to these mixing profiles. We find that the mixing profile changes dramatically across age. In younger stars, we noted that the diffusion coefficient increases toward the surface, whereas in older stars the initial increase in the diffusion profile is followed by a decreasing trend. We also find that mixing is stronger in more massive stars. Hence, future stellar evolution models should include this variation. In order to aid the inclusion of this mixing in 1D stellar evolution models, we determine the dominant waves contributing to these mixing profiles and present a prescription that can be included in 1D models.

Spontaneous formation of colonies of bacteria or flocks of birds are examples of self-organization in active living matter. Here, we demonstrate a form of self-organization from nonequilibrium driving forces in a suspension of synthetic photoactivated colloidal particles. They lead to two-dimensional \"living crystals,\" which form, break, explode, and re-form elsewhere. The dynamic assembly results from a competition between self-propulsion of particles and an attractive interaction induced respectively by osmotic and phoretic effects and activated by light. We measured a transition from normal to giant-number fluctuations. Our experiments are quantitatively described by simple numerical simulations. We show that the existence of the living crystals is intrinsically related to the out-of-equilibrium collisions of the self-propelled particles.

Stellar streams that emerge from globular clusters (GCs) are thin stellar structures spread along the orbits of progenitor clusters. Numerical modeling of these streams is essential for understanding their interaction with the host galaxy's mass distribution. Traditional methods are either computationally expensive or oversimplified, motivating us to develop a fast and accurate approach using a particle spray algorithm. By conducting a series of N-body simulations of GCs orbiting a host galaxy, we find that the position and velocity distributions of newly escaped stream particles are consistent across various GC masses and orbital parameters. Based on these distributions, we develop a new algorithm that avoids computing the detailed internal cluster dynamics by directly drawing tracer particles from these distributions. This algorithm correctly reproduces the action space distribution of stream particles and achieves a 10% accuracy in stream morphology and velocities compared to N-body simulations. To facilitate broader use, we have implemented this algorithm in galactic dynamics codes agama, gala, galax, and galpy.

After decades, the theoretical study of core-collapse supernova explosions is moving from parameterized, spherically symmetric models to increasingly realistic multidimensional simulations. However, obtaining nucleosynthesis yields based on such multidimensional core-collapse supernova simulations is not straightforward. Frequently, tracer particles are employed. Tracer particles may be tracked in situ during the simulation, but often they are reconstructed in a post-processing step based on the information saved during the hydrodynamic simulation. Reconstruction can be done in a number of ways, and here we compare the approaches of backward and forward integration of the equations of motion to the results based on inline particle trajectories. We find that both methods agree reasonably well with the inline results for isotopes for which a large number of particles contribute. However, for rarer isotopes that are produced only by a small number of particle trajectories, deviations can be large. For our setup, we find that backward integration leads to better agreement with the inline particles by more accurately reproducing the conditions following freeze-out from nuclear statistical equilibrium, because the establishment of nuclear statistical equilibrium erases the need for detailed trajectories at earlier times. Based on our results, if inline tracers are unavailable, we recommend backward reconstruction to the point when nuclear statistical equilibrium was last applied, with an interval between simulation snapshots of at most 1 ms for nucleosynthesis post-processing.

A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells.

The driving of turbulence in galaxies is deeply connected with the physics of feedback, star formation, outflows, accretion, and radial transport in disks. The velocity dispersion of gas in galaxies therefore offers a promising observational window into these processes. However, the relative importance of each of these mechanisms remains controversial. In this work we revisit the possibility that turbulence on galactic scales is driven by the direct impact of accreting gaseous material on the disk. We measure this effect in a disk-like star-forming galaxy in IllustrisTNG, using the high-resolution cosmological magnetohydrodynamical simulation TNG50. We employ Lagrangian tracer particles with a high time cadence of only a few million years to identify accretion and other events. The energies of particles are measured by stacking the events in bins of time around the event. The average effect of each event is measured by fitting explicit models for the kinetic and turbulent energies as a function of time. These measurements are corroborated by cross-correlating the turbulent energy with other time series and searching for signals of causality, i.e., asymmetries across zero time lag. We find that accretion contributes to the large-scale turbulent kinetic energy even if it does not dominate in this ∼5 × 109 M ⊙ stellar mass galaxy. Extrapolating this finding to a range of galaxy masses, we find that there are regimes where energy from direct accretion may dominate the turbulent energy budget, particularly in disk outskirts, galaxies less massive than the Milky Way, and at redshift ∼2.

Neutron star mergers produce r-process elements, with yields that are sensitive to the kinematic and thermodynamic properties of the ejecta. These ejecta properties are potentially affected by dynamically important feedback from r-process heating, which is usually not coupled to the hydrodynamics in postmerger simulations modeling the ejecta launching and expansion. The multimessenger detection of GW170817 showed the importance of producing reliable ejecta predictions to maximize the diagnostic potential of future events. In this paper, we develop a prescription for including r-process heating as a source term in the hydrodynamic equations. This prescription depends on local fluid properties and the Ye history as recorded by dedicated tracer particles, which exchange information with the grid using the cloud-in-cell method. The method is implemented in long-term viscous hydrodynamic simulations of accretion disk outflows to investigate its feedback on ejecta properties. We find that r-process heating can increase the unbound disk ejecta mass by ∼10% relative to a baseline case that only considers alpha particle recombination. Nuclear heating also enhances the radial velocity of the ejecta with Ye < 0.25 by up to a factor of 2 while concurrently suppressing marginally bound convective ejecta.