Relative Velocity Research Articles

Fluid-particle-structure interaction in single shot peening

Shot peening is a widely used cold-working process. Physical phenomena of shot peening are analyzed using the developed fluid-particle-structure coupled solver. The influences of the flow field and shot peening parameters such as the shot impact velocity and shot size are investigated in the case of the falling, impacting, and rebounding single particle. The weakly coupled solver applies the immersed boundary method which enables direct evaluation of the interactions between the unsteady flow field and moving/deforming objects. The elastoplastic object of AISI4340 during the collision of rigid steel shot is analyzed dynamically using the finite element method. Consequently, it is clarified that the flow field of the post-collision between the shot and structure can be characterized by the relative Reynolds number, which is based on the shot diameter and relative velocity between the uniform flow and rebounding shot velocities. As the relative Reynolds number increases, the complex flow field and vortex structures are generated at the collision location. These fluid structures affect the collision phenomena resulting in the random behavior of the shot and the asymmetric indentation in the structure.

Safe platooning and merging control using constructive barrier feedback

This paper proposes a novel formation control design for safe platooning and merging of a group of vehicles in multi-lane road scenarios. Provided a leader vehicle is independently controlled, the objective is controlling the follower vehicles to drive in the desired lane with a constant desired distance behind the neighboring (preceding) vehicle while preventing collisions with both the neighboring vehicle and the road’s edges. Inspired by the recent concept of constructive barrier feedback, the proposed controller for each follower vehicle is composed of two parts: one is the nominal controller that ensures its tracking of the neighboring vehicle; another is for collision avoidance by using divergent flow as a dissipative term, which slows down the relative velocity in the direction of the neighboring vehicle and road edges without compromising the nominal controller’s performance. The key contribution of this work is that the proposed control method ensures collision-free platooning and merging control in multi-lane road scenarios with computational efficiency and systematic stability analysis. Simulation results are provided to demonstrate the effectiveness of the proposed algorithms.

Comparative analysis of reactive routing protocols for vehicular adhoc network communications

In the recent past, vehicular adhoc networks (VANETs) have gained a lot of importance. The routing protocols play a vital role to deliver payloads from one vehicle to another one while they are moving at relative speeds. It is a challenging task to select a routing protocol for VANETs because of the uneven distribution and high mobility of vehicles. In this paper, we have analysed the two standard reactive protocols, adhoc on-demand distance vector (AODV) and ant colony optimization (ACO). The performance comparison of AODV and ACO routing protocols has been presented in this paper. The results show AODV performed better in terms of energy consumption and routing overhead. While considering the throughput, energy loss ratio, and delay ACO has performed. ACO resulted as upperhand.

Effect of fuel injection pressure on biodiesel blended combustion of Inland River diesel engine

Abstract Compared with ordinary diesel, biodiesel has greater viscosity, density, and flash point, especially under medium and low load, which is easy to cause poor atomization and inadequate combustion. In this paper, an in-line six-cylinder inland river ship diesel engine was used as a model to conduct simulation tests under 50% load of propulsion characteristics to explore the effects of different fuel injection pressures on oil-gas mixing, combustion, and emission of fuel blended with a small percentage of biodiesel. The results show that the increase of fuel injection pressure can enhance the average turbulence intensity in the cylinder as well as increase the relative flow velocity between oil and gas, which is beneficial to the mixture combustion. High fuel injection pressure will promote flame propagation, increasing the maximum burst pressure and the average temperature in the cylinder. Compared to the fuel injection pressure of 24 MPa, NOx emission increases by 5.5% and 15.6% respectively at 27 MPa and 30 MPa, and decreases by 10% and 25% respectively by SOOT.

Dragonfly-Inspired Blades for high Aerodynamic Performance small Horizontal Axis Wind Turbine

Inspired from the fascinating realm of Dragonfly features, this study intricately investigates the aerodynamic performance of a distinctive 1 m diameter small-scale Horizontal Axis Wind Turbine characterized by a unique bio-inspired tandem-blades configuration. Based on experimental wind tunnel tests and computational fluid dynamics simulations, the turbine performance is explored at different Tip Speed Ratios (TSRs). Remarkably, the bio-inspired turbine exhibits exceptional traits, achieving a notable peak power coefficient of approximately 0.35 at a low TSR of 3. A detailed investigation includes thorough analyses of pressure contours, relative velocity distributions, and individual blade contributions, revealing unique dynamics within the tandem configuration. The fore blade notably prevails in extracting wind energy, showcasing superior performance. While the hind blade influence in enhancing the fore blade efficiency emerges, underscoring the role of blade interactions in this bio-inspired designs. This study contributes significantly to the comprehension of the new design dragonfly-inspired wind turbine aerodynamics.

Evolution of the Disk in the Be Binary δ Scorpii Probed during Three Periastron Passages

We examine the evolution of the disk surrounding the Be star in the highly eccentric 10.8 yr binary system δ Scorpii over its three most recent periastron passages. V-band and B − V photometry, along with Hα spectroscopy, are combined with a new set of extensive multiband polarimetry data to produce a detailed comparison of the disk's physical conditions during the time periods surrounding each closest approach of the secondary star. We use the three-dimensional Monte Carlo radiative transfer code HDUST and a smoothed particle hydrodynamics code to support our observations with models of disk evolution, discussing the behavior of the Hα and He i 6678 Å lines, V-band magnitude, and polarization degree. We compare the characteristics of the disk immediately before each periastron passage to create a baseline for the unperturbed disk. We find that the extent of the Hα emitting region increased between each periastron passage, and that transient asymmetries in the disk become more pronounced with each successive encounter. Asymmetries of the Hα and He i 6678 Å lines in 2011 indicate that perturbations propagate inward through the disk near periastron. When the disk’s direction of orbit is opposite to that of the secondary, the parameters used in our models do not produce spiral density enhancements in the Hα emitting region because the tidal interaction time is short due to the relative velocities of the disk particles with the secondary. The effects of the secondary star on the disk are short-lived and the disk shows independent evolution between each periastron event.

ICM-SHOX. I. Methodology Overview and Discovery of a Gas–Dark Matter Velocity Decoupling in the MACS J0018.5+1626 Merger

Galaxy cluster mergers are rich sources of information to test cluster astrophysics and cosmology. However, cluster mergers produce complex projected signals that are difficult to interpret physically from individual observational probes. Multi-probe constraints on the gas and dark matter (DM) cluster components are necessary to infer merger parameters that are otherwise degenerate. We present Improved Constraints on Mergers with SZ, Hydrodynamical simulations, Optical, and X-ray (ICM-SHOX), a systematic framework to jointly infer multiple merger parameters quantitatively via a pipeline that directly compares a novel combination of multi-probe observables to mock observables derived from hydrodynamical simulations. We report a first application of the ICM-SHOX pipeline to MACS J0018.5+1626, wherein we systematically examine simulated snapshots characterized by a wide range of initial parameters to constrain the MACS J0018.5+1626 merger geometry. We constrain the epoch of MACS J0018.5+1626 to the range 0–60 Myr post-pericenter passage, and the viewing angle is inclined ≈27°–40° from the merger axis. We obtain constraints for the impact parameter (≲250 kpc), mass ratio (≈1.5–3.0), and initial relative velocity when the clusters are separated by 3 Mpc (≈1700–3000 km s−1). The primary and secondary clusters initially (at 3 Mpc) have gas distributions that are moderately and strongly disturbed, respectively. We discover a velocity space decoupling of the DM and gas distributions in MACS J0018.5+1626, traced by cluster-member galaxy velocities and the kinematic Sunyaev–Zel'dovich effect, respectively. Our simulations indicate this decoupling is dependent on the different collisional properties of the two distributions for particular merger epochs, geometries, and viewing angles.

Improved control of permanent magnet synchronous motors using adaptive nonlinear control with Deadbeat Observer

Permanent Magnet Synchronous Motor (PMSM) control optimization is crucial for a variety of applications, including electric vehicles, industrial automation, and renewable energy systems (RESs). However, traditional control methods often struggle to adapt to the dynamic and non-linear nature of PMSMs, leading to sub-optimal performance. To address these challenges, this paper proposes a hybrid adaptive nonlinear control strategy with a deadbeat observer (DO) designed to improve the performance of PMSMs. This approach aims to improve the accuracy and robustness of the control while taking into account the system parameters variations and disturbances. Simulation tests comparing the proposed method with an adaptive nonlinear control (ANLC) are presented, highlighting its superior effectiveness in controlling PMSMs under varying load conditions and speed fluctuations. The proposed strategy achieves a maximum relative speed error around of 6% at 0.4 s under gradually varying load torque disturbances, which is better than the ANLC with 8%. Furthermore, under large speed variations, the suggested method maintains a maximum relative speed error of 0.82% at 0.85 s. Furthermore, the robustness assessment under system parameters variations, stator resistance, and inductance, shows extraordinary performances of the proposed scheme. These results highlight the effectiveness and robustness of the proposed strategy in achieving precise PMSM control while dynamically adapting to changing conditions. This research underscores the potential of our approach to advance key technologies, including electric vehicles, industrial automation, and renewable energy systems. By optimizing PMSM control, this strategy contributes to increased efficiency, reliability, and adaptability, facilitating broader adoption of electric propulsion systems and sustainable energy solutions.

Determination of Ship Collision Avoidance Timing Using Machine Learning Method

The accurate timing for collision avoidance actions is crucial for preventing maritime collisions. Traditional methods often rely on collision risk assessments, using quantitative indicators like the Distance to the Closest Point of Approach (DCPA) and the Time to the Closest Point of Approach (TCPA). Ship Officers on Watch (OOWs) are required to execute avoidance maneuvers once these indicators reach or exceed preset safety thresholds. However, the effectiveness of these indicators is limited by uncertainties in the maritime environment and the human behaviors of OOWs. To address these limitations, this study introduces a machine learning method to learn collision avoidance behavior from empirical data of ship collision avoidance, particularly in cross-encounter situations. The research utilizes Automatic Identification System (AIS) data from the open waters around Ningbo Zhoushan Port. After data preprocessing and applying spatio-temporal constraints, this study identifies ship trajectory pairs in crossing scenarios and calculates their relative motion parameters. The Douglas–Peucker algorithm is used to identify the timing of ship collision avoidance actions and a collision avoidance decision dataset is constructed. The Random Forest algorithm was then used to analyze the factors affecting the timing of collision avoidance, and six key factors were identified: the distance, relative speed, relative bearing, DCPA, TCPA, and the ratio of the lengths of the giving-way and stand-on ships. These factors serve as inputs for the XGBoost algorithm model, which is enhanced with Particle Swarm Optimization (PSO), and thus constructing a ship collision avoidance decision model. In addition, considering the inherent errors in any model and the dynamic nature of the ship collision avoidance process, an action time window for collision avoidance is introduced, which provides a more flexible time range for ships to make timely collision avoidance responses based on actual conditions and the specific encounter environment. This model provides OOWs with accurate timing for taking collision avoidance decisions. Case studies have validated the practicality and effectiveness of this model, offering new theoretical foundations and practical guidance for maritime collision avoidance.

Mining Associations between Air Quality and Natural and Anthropogenic Factors

The urbanization and industrialization of human society boost the socioeconomic growth but yet inevitably result in unprecedented damages to environment and organisms. One of the threats is the air pollution produced from anthropogenic activities. Moreover, the pollution concentrates longer in certain meteorological phenomena and exacerbates the impact on nature species and human health. This paper presents an association mining approach to identify the influential factors which result in a high volume of air pollution concentration, in particular, the particulate matter with aerodynamic diameter ≤ 2.5 μm (PM2.5). Since the literature showed that the identified factors are location and spatial-scale dependent, we chose a basin geography, Puli township, Taiwan, and inferred the association relationships with two different-scaled monitoring stations. The government-built supersite at Puli estimates the PM2.5 concentration for the entire township of the area around 150 km2, while the participatory microsites monitor air quality in a smaller region of a hundred thousand square meters. Our research was conducted with relevant data during 2017–2019. The mining result has unique findings as compared to the literature. The relative humidity, precipitation, wind speed and direction, which were identified as major factors in many previous studies, have less impact on air quality of our studied field than temperature and atmospheric pressure. The remarkable distinction is mainly attributed to the special weather patterns of basin geography. We investigated the impact of all national festivals and identified the most significant ones. The probability of observing PM2.5 concentrations greater than 35 μg/m3 in the activity hours of New Year’s Eve is 50% which is significantly greater than 11.74%, the probability of observing the same concentration range over all days in the investigated years, while the Tomb Sweeping Day (TSD) has a varying impact on air quality depending on the order of the TSD date within the long holiday. The increase of PM2.5 concentration is remarkably more significant if the TSD is the last day in the long holiday than if it is the middle day. This finding can be taken into consideration when the government agent makes schedules for national festivals. Finally, it was learned in our study that different landmarks and land uses have various significant impacts on micro-scale air quality. The microsites monitor high PM2.5 concentrations at particular landmarks with a greater confidence than the mean confidence over all microsites. These pollution-associated landmarks with the confidence ranked from highest to lowest are night markets, crossroads, paper mills, temples, and highway exits. It is worth noting that the PM2.5 increase contributed by temples is negligible, which may be attributed to the citizen action for promoting reduction in joss paper and incense stick burning. The land uses have diverse impacts on air quality. Anthropogenic activities contribute higher PM2.5 concentrations in business districts and residential areas. The PM2.5 concentration monitored at high lands and agricultural lands is lower than the overall background due to fewer mass gathering and combustion activities in these land uses.

Metabolic plasticity drives mismatches in physiological traits between prey and predator

Metabolic rate, the rate of energy use, underpins key ecological traits of organisms, from development and locomotion to interaction rates between individuals. In a warming world, the temperature-dependence of metabolic rate is anticipated to shift predator-prey dynamics. Yet, there is little real-world evidence on the effects of warming on trophic interactions. We measured the respiration rates of aquatic larvae of three insect species from populations experiencing a natural temperature gradient in a large-scale mesocosm experiment. Using a mechanistic model we predicted the effects of warming on these taxa’s predator-prey interaction rates. We found that species-specific differences in metabolic plasticity lead to mismatches in the temperature-dependence of their relative velocities, resulting in altered predator-prey interaction rates. This study underscores the role of metabolic plasticity at the species level in modifying trophic interactions and proposes a mechanistic modelling approach that allows an efficient, high-throughput estimation of climate change threats across species pairs.

Do galaxy mergers prefer under-dense environments?

Context. Galaxy mergers play a crucial role in galaxy evolution. However, the correlation between mergers and the local environment of galaxies is not fully understood. Aims. We aim to address the question of whether galaxy mergers prefer denser or less dense environments by quantifying the spatial clustering of mergers and non-mergers. We use two different indicators to classify mergers and non-mergers – classification based on a deep learning technique (f) and non-parametric measures of galaxy morphology, Gini-M20 (g). Methods. We used a set of galaxy samples in the redshift range 0.1 < z < 0.15 from the Galaxy and Mass Assembly (GAMA) survey with a stellar mass cut of log(M⋆/M⊙) > 9.5. We measured and compared the two-point correlation function (2pCF) of the mergers and non-mergers classified using the two merger indicators f and g. We measured the marked correlation function (MCF), in which the galaxies were weighted by f to probe the environmental dependence of galaxy mergers. Results. We do not observe a statistically significant difference between the clustering strengths of mergers and non-mergers obtained using 2pCF. However, using the MCF measurements with f as a mark, we observe an anti-correlation between the likelihood of a galaxy being a merger and its environment. Our results emphasise the advantage of MCF over 2pCF in probing the environmental correlations. Conclusions. Based on the MCF measurements, we conclude that the galaxy mergers prefer to occur in the under-dense environments on scales > 50 h−1 kpc of the large-scale structure (LSS). We attribute this observation to the high relative velocities of galaxies in the densest environments that prevent them from merging.

An analytical evaluation of tools for lipid isomer differentiation in imaging mass spectrometry

Imaging mass spectrometry has emerged as a powerful tool to map the spatial distributions of lipids and metabolites in biological tissues. However, these analyses are challenged by the multitude of isobaric (i.e., same nominal mass) and isomeric compounds present in most samples. Failure to adequately separate these compounds results in inaccurate or incomplete chemical identifications and produces composite images of spatial distribution arising from multiple compounds. A number of techniques have been developed to more completely resolve and identify this complex chemical milieu. These include methods that rely on condensed-phase chemical derivatization and gas-phase ion chemistry, or some combination thereof. This Young Scientist Feature focuses on summarizing the analytical figures of merit of these tools, highlighting their relative speeds, limits of detection, molecular specificities, and eases-of-use. It will also include current challenges and future perspectives for resolving structural isomers in imaging mass spectrometry experiments.

Quantitative correlation of ENPP1 pathogenic variants with disease phenotype

Ectonucleotide pyrophosphatase/phosphodiesterase 1 (ENPP1) codes for a type 2 transmembrane glycoprotein which hydrolyzes extracellular phosphoanhydrides into bio-active molecules that regulate, inter alia, ectopic mineralization, bone formation, vascular endothelial proliferation, and the innate immune response. The clinical phenotypes produced by ENPP1 deficiency are disparate, ranging from life-threatening arterial calcifications to cutaneous hypopigmentation. To investigate associations between disease phenotype and enzyme activity we quantified the enzyme velocities of 29 unique ENPP1 pathogenic variants in 41 patients enrolled in an NIH study along with 33 other variants reported in literature. We correlated the relative enzyme velocities with the presenting clinical diagnoses, performing the catalytic velocity measurements simultaneously in triplicate using a high-throughput assay to reduce experimental variation. We found that ENPP1 variants associated with autosomal dominant phenotypes reduced enzyme velocities by 50 % or more, whereas variants associated with insulin resistance had non-significant effects on enzyme velocity. In Cole disease the catalytic velocities of ENPP1 variants associated with AD forms trended to lower values than those associated with autosomal recessive forms – 8-32 % vs. 33 % of WT, respectively. Additionally, ENPP1 variants leading to life-threatening vascular calcifications in GACI patients had widely variable enzyme activities, ranging from no significant differences compared to WT to the complete abolishment of enzyme velocity. Finally, disease severity in GACI did not correlate with the mean enzyme velocity of the variants present in affected compound heterozygotes but did correlate with the more severely damaging variant. In summary, correlation of ENPP1 enzyme velocity with disease phenotypes demonstrate that enzyme velocities below 50 % of WT levels are likely to occur in the context of autosomal dominant disease (due to a monoallelic variant), and that disease severity in GACI infants correlates with the more severely damaging ENPP1 variant in compound heterozygotes, not the mean velocity of the pathogenic variants present.

Effects of phase angle and sensor properties on on-orbit debris detection using commercial star trackers

The recent proliferation of resident space objects (RSOs) in low Earth orbit (LEO) threatens the sustainability of space as a resource and requires persistent monitoring to avoid collisions involving valuable space assets. State-of-the-art ground-based space surveillance techniques, due to their susceptibility to atmosphere, weather, and lighting conditions, tend to focus on RSOs with characteristic length greater than 10 cm or 1 dm. Consequently, millions of smaller LEO RSOs remain untracked by ground-based methods, which reduces overall space situational awareness. Onboard satellite sensors offer a space-based method for tracking RSOs. Prior research has investigated the feasibility of using commercial star trackers (CSTs) — optical sensors prevalent on most active spacecraft — to observe, detect, and estimate the position and velocity of RSOs larger than 10 cm. In a recent effort, we expanded on these feasibility studies by assessing the capabilities of CSTs to detect debris particles smaller than 10 cm in characteristic length. We modeled the particles as Lambertian spheres with zero phase angle and ten percent reflectivity and found that typical CSTs can detect properly illuminated debris of characteristic length between 1 cm and 10 cm even at distances of tens of kilometers. More sensitive CSTs can characterize decimeter-scale RSOs hundreds of kilometers away; alternatively, they can track centimeter-scale and smaller RSOs at closer distances. In this paper, we summarize these key results and extend our previous study by relaxing its zero-phase-angle assumption and characterizing the effect of Sun-RSO-CST phase angle on debris detection range. We identify a number of representative CSTs with publicly available optical characteristics and consider the effects of properties such as pixel pitch, focal length, aperture diameter, and field of view (FOV) on the capability of each CST to detect debris at a given distance and relative velocity (in the form of streak speed). We find that, for debris particles modeled as diffuse Lambertian spheres, Sun-RSO-CST phase angles as high as 57° result in no more than 20% reduction to the useful RSO-CST detection range. In addition, we find that pixel pitch and focal length, rather than aperture diameter, tend to determine the capability of a given CST to resolve two distinct RSOs. Furthermore, streak speed may serve as a stronger limiting factor for detection of smaller debris particles than for larger ones. Despite these limitations, the overall results indicate that CSTs have the potential to substantially enhance space-based debris detection capability.

A Multi-UAV cooperative mission planning method based on SA-WOA algorithm for three-dimensional space atmospheric environment detection

AbstractIn the application of rotorcraft atmospheric environment detection, to reflect the distribution of atmospheric pollutants more realistically and completely, the sampling points must be spread throughout the entire three-dimensional space, and the cooperation of multiple unmanned aerial vehicles (multi-UAVs) can ensure real-time performance and increase operational efficiency. In view of the problem of coordinated detection by multi-UAVs, the region division and global coverage path planning of the stereo space to be detected are studied. A whale optimization algorithm based on the simulated annealing-whale optimization algorithm (SA-WOA) is proposed, which introduces adaptive weights with the Levy flight mechanism, improves the metropolis criterion, and introduces an adaptive tempering mechanism in the SA stage. Path smoothing is subsequently performed with the help of nonuniform rational B-spline (NURBS) curves. The comparison of algorithms using the eil76 dataset shows that the path length planned by the SA-WOA algorithm in this paper is 10.15% shorter than that of the WOA algorithm, 13.25% shorter than the SA planning result, and only 0.95% difference from the optimal path length in the dataset. From the perspective of planning time, its speed is similar to WOA, with a relative speed increase of 27.15% compared to SA, proving that the algorithm proposed in this paper has good planning performance. A hardware system platform is designed and built, and environmental gas measurement experiments were conducted. The experimental results indicate that the multi-UAV collaborative environment detection task planning method proposed in this paper has certain practical value in the field of atmospheric environment detection.

Research of the Influence of Lateral Inflow Angles on the Cavitation Flow and Movement Characteristics of Underwater Moving Objects

This study examined the multi-phase flow field for a single object and two parallel/series objects under different incoming angles of lateral flow. The volume of fluid model, the Sauer–Schnerr cavitation model, and the six degrees of freedom (DOF) method were adopted to consider simulations of multi-phase flow, phase change, and object movement, respectively. The results show that, for a single object, the degree of asymmetry in the cavity profile depends on the component (the z-component) of the lateral inflow velocity in the direction perpendicular to the initial velocity of the object. As this component increases, the asymmetry of the cavity increases. The cavity length is related to the relative axial speed between the object and the water. For parallel objects, the cavity asymmetry is determined by the superimposed influence of the z-component of the lateral incoming speed and the high-pressure zone induced by the nearby object. The object located downstream relative to the lateral flow has a stronger cavity asymmetry than that of the upstream object, and the trajectory of the downstream object is more easily deviated than that of the upstream object. For tandem objects, with the increase in the lateral incoming angle, the supercavity length increases after the rear object enters into the front cavity. With the increase in the z-component of the lateral flow velocity, the deviation speed increases.

Realistic 3D human saccades generated by a 6-DOF biomimetic robotic eye under optimal control.

We recently developed a biomimetic robotic eye with six independent tendons, each controlled by their own rotatory motor, and with insertions on the eye ball that faithfully mimic the biomechanics of the human eye. We constructed an accurate physical computational model of this system, and learned to control its nonlinear dynamics by optimising a cost that penalised saccade inaccuracy, movement duration, and total energy expenditure of the motors. To speed up the calculations, the physical simulator was approximated by a recurrent neural network (NARX). We showed that the system can produce realistic eye movements that closely resemble human saccades in all directions: their nonlinear main-sequence dynamics (amplitude-peak eye velocity and duration relationships), cross-coupling of the horizontal and vertical movement components leading to approximately straight saccade trajectories, and the 3D kinematics that restrict 3D eye orientations to a plane (Listing's law). Interestingly, the control algorithm had organised the motors into appropriate agonist-antagonist muscle pairs, and the motor signals for the eye resembled the well-known pulse-step characteristics that have been reported for monkey motoneuronal activity. We here fully analyse the eye-movement properties produced by the computational model across the entire oculomotor range and the underlying control signals. We argue that our system may shed new light on the neural control signals and their couplings within the final neural pathways of the primate oculomotor system, and that an optimal control principle may account for a wide variety of oculomotor behaviours. The generated data are publicly available at https://data.ru.nl/collections/di/dcn/DSC_626870_0003_600.

Functional Forms for Lorentz Invariant Velocities

Lorentz invariance lies at the very heart of Einstein’s special relativity, and both the energy formula and the relative velocity formula are well-known to be invariant under a Lorentz transformation. Here, we investigate the spatial and temporal dependence of the velocity field itself u(x,t) and we pose the problem of the determination of the functional form of those velocity fields u(x,t) which are automatically invariant under a Lorentz transformation. For a single spatial dimension, we determine a first-order partial differential equation for the velocity u(x,t), which appears to be unknown in the literature, and we investigate its main consequences, including demonstrating that it is entirely consistent with many of the familiar outcomes of special relativity and deriving two new partial differential relations connecting energy and momentum that are fully compatible with the Lorentz invariant energy–momentum relations.

Varying primordial state fractions in exo- and endothermic SIDM simulations of Milky Way-mass haloes

Abstract Self-interacting dark matter (SIDM) is increasingly studied as a potential solution to small-scale discrepancies between simulations of cold dark matter (CDM) and observations. We examine a physically motivated two-state SIDM model with both elastic and inelastic scatterings. In particular, endothermic, exothermic, and elastic scattering have equal transfer cross sections at high relative velocities (vrel ≳ 400 km s−1). In a suite of cosmological zoom-in simulation of Milky Way-size haloes, we vary the primordial state fractions to understand the impact of inelastic dark matter self-interactions on halo structure and evolution. In particular, we test how the initial conditions impact the present-day properties of dark matter haloes. Depending on the primordial state fraction, scattering reactions will be dominated by either exothermic or endothermic effects for high and low initial excited state fractions respectively. We find that increasing the initial excited fraction reduces the mass of the main halo, as well as the number of subhaloes on all mass scales. The main haloes are cored, with lower inner densities and higher outer densities compared with CDM. Additionally, we find that the shape of the main halo becomes more spherical the higher the initial excited state fraction is. Finally, we show that the number of satellites steadily decreases with initial excited state fraction across all satellite masses.