Breakup Events Research Articles

A deep neural network framework with Analytic Continuation for predicting hypervelocity fragment flyout from satellite explosions

Hypervelocity breakup events contribute to the rapidly growing population of space debris orbiting Earth. To ensure a safe environment for future space missions, it is crucial to accurately characterize resulting fragments, which constitute a major portion of the orbital population but are often too small for conventional tracking methods. Currently, the Space Surveillance Network tracks satellites and debris within a specific altitude range and releases the data publicly as Two-Line Elements, though these datasets are limited in both size and accuracy. To supplement Two-Line Element data, this paper presents a novel Deep Neural Network approach to estimate orbital elements of hypervelocity fragments resulting from simulated satellite explosions. It employs initial conditions collected from realistic terrestrial explosions considered to be relative to 5 different detonation points on the polar orbit of the weather satellite, NOAA-16, to model the initial states of debris fragments immediately following an explosion. The debris trajectories are then propagated using a high-precision semi-analytic integration method, Analytic Continuation, considering J2−J6 zonal gravitational terms and Earth’s atmospheric drag perturbations. The collected data is used to train a Deep Neural Network for each of the orbital elements. Finally, a testing data set is used to validate the results, finding that this technique accurately estimates most of the orbital elements, but is not suited to predict the true anomaly of the fragments. Therefore, K-Nearest Neighbor regression is utilized instead to predict the nature of the final orbital element.

Drop breakup can occur inside the gap of a high-pressure homogenizer – New evidence from experimental breakup visualizations

High-pressure homogenizers are used extensively in food and beverage processing. For design and operation optimization, it is vital to understand where breakup takes place. Using an experimental high-speed camera setup on a scaled model, this contribution shows that breakup events can occur inside of the gap of a homogenizer valve. This contrasts with many previous studies which only observe breakup downstream of the gap. Results show that gap breakup occurs at a substantially lower rate than outlet chamber breakup. Comparisons with computational fluid dynamics suggest that a necessary (but not sufficient) condition for gap breakup, is that the drop passes into the high-shear region close to the separation zone at the seat wall. Implications for food emulsification are discussed.

Real-time prediction of river ice breakup phenomena: A jittered genetic programming model and wavelet analysis integrating remotely sensed imagery and machine learning

Forecasting the timing of breakup ice jams in rivers is crucial for early flood warning and effective management in cold regions where rising river flows can lead to significant damage. However, this task is hindered by insufficient data and the complex dynamics of river ice. These obstacles pose challenges in developing precise forecasting models. This study aimed to address the data scarcity issue by introducing innovative machine learning methods, focusing on classification and jittering (J), binary genetic programming (BGP), and wavelet transform (WT) for river ice forecasting (WT-JBGP) in the Tornio River, situated between Finland and Sweden. By considering time scales ranging from 2 to 32 days and time lags of 1 to 3 days, this method was applied to enhance the predictive capabilities of predictors. The findings reveal that certain predictors, with specific time scales and time lags, significantly influence the timing of breakup events. These include the 8-day temperature and 32-day discharge, both with a 2-day lag time, as well as the 4-day precipitation, approximation of albedo, and 16-day atmospheric pressure at ground level, all with a 1-day lag obtained from ERA5 and recorded data. Additionally, we conducted a quantitative evaluation of the effectiveness of the proposed model and contrasted its efficacy with that of BGP, WT-BGP, and advanced J-BGP techniques. The WT-JBGP model attains the highest overall classification accuracy of approximately 0.91, alongside a Heidke Skill Score exceeding 0.78, and a Positive Predictive Value surpassing 0.85, thereby demonstrating its superiority over competing methodologies. In summation, this study offers a promising approach to overcoming observed data scarcity in breakup date prediction, providing valuable insights into river ice dynamics.

Fragmentation characterization in the circular restricted three body problem for cislunar space domain awareness

With heightened international interest in spacecraft activities in the vicinity of the Moon, cislunar space debris is likely to follow. Even one fragmentation event can have catastrophic and far-reaching consequences, which drives the need for appropriate debris characterization tools. How a single fragmentation plays out is highly dependent on any given initial condition in the near-chaotic cislunar region. This paper offers a means of structuring the cislunar region in terms of dynamical flow, which enables global characterization of fragmentation events without propagation of every possible case. This work investigates patterns in fragment behaviour as a function of energy, Δv, and orbit location, and explores emergent dynamic structures in the vicinity of the Earth-Moon L2 Lagrange point. Subsequent findings are applied to analysis of a realistic breakup event for a 500 kg satellite on an L2 Lyapunov orbit with a Jacobi constant of 3.0165, modeled using an in–house modified version of the NASA Standard Breakup Model.

Simulating a breakup event and propagating the orbits of space debris

Explosions or collisions of satellites around the Earth generate space debris, whose uncontrolled dynamics might raise serious threats for operational satellites. Mitigation actions can be realized on the basis of our knowledge of the characteristics of the fragments produced during the breakup event and their subsequent propagation. In this context, important information can be obtained by implementing a breakup simulator, which provides, for example, the number of fragments, their area-to-mass ratio or the relative velocity distribution as a function of the characteristic length of the fragments. Motivated by the need to analyze the dynamics of the fragments, we reconstruct a simulator based on the NASA/JSC breakup model EVOLVE 4.0 that we review for self-consistency. This model, created at the beginning of the XXI century, is based on laboratory and on-orbit tests. Given that materials and methods for building satellites are constantly progressing, we leave some key parameters variable and produce results for different choices of the parameters. We will also present an application to the Iridium–Cosmos collision and we discuss the distribution function after a breakup event. The breakup model is strongly related to the propagation of the fragments; in this work, we discuss how to choose the models and the numerical integrators, we propose examples of how fragments can disperse in time, and we study the behavior of multiple simultaneous fragmentations. Finally, we compute some indicators for detecting streams of fragments. Breakup and propagation are performed using our own simulator SIMPRO, built from EVOLVE 4.0; the executable program will be freely available on GitHub.

A physics-informed machine learning model for the prediction of drop breakup in two-phase flows

Predictive simulations of two-phase flows are highly sought after because of their widespread applications in propulsion, energy, agriculture, and medicine. One crucial goal for many of these simulations is the accurate and efficient prediction of the size distribution and number density of atomized drops. The multi-scale nature of these flows makes it practically impossible to capture all scales within a single simulation. In particular, the breakup processes producing the smallest drops through secondary breakup often necessitate resolutions far below the Kolmogorov scale. Consequently, models must be employed for secondary breakup. Existing physics-based and stochastic breakup models are not universal and fail to account for the local and instantaneous flow field and drop geometry. We present a physics-informed machine learning model for predicting the statistics of daughter drops generated during the breakup of under-resolved drops. By training on high-fidelity simulations, the model can predict breakup outcomes from severely under-resolved input fields. This is made possible by a careful choice of quantities of interest and by taking inspiration from the discrete nature of breakup events to encode the temporal evolution via a mixture of sigmoid functions. We showcase proof-of-concept results from the canonical settings of 3D Taylor–Green vortex flows and homogeneous isotropic turbulence. Compared to results generated by low-resolution simulations (i.e., without a model) and baseline state-of-the-art models, our approach achieves superior accuracy in predicting drop size distribution and critical quantities of interest, such as surface area. This work paves the path towards the development of embedded machine learning models for the prediction of primary and secondary breakup.

From perturbative methods to machine learning techniques in space science

AbstractPerturbation theory is a very useful tool to investigate the dynamics of models in space science. We start by presenting some results obtained implementing classical perturbation theory to investigate the motion of space debris, which are objects that populate the sky around the Earth after a satellite break-up event. When dealing with two or more break-up events, a clusterization of the fragments can be computed using machine learning techniques. We also present the celebrated KAM theory for symplectic and conformally symplectic systems. We recall several computer-assisted results in Celestial Mechanics in conservative and dissipative settings. Finally, we consider the spin-orbit problem and we show how machine learning methods can be conveniently used to classify regular and chaotic motions.

Modeling Medium-Term Debris Cloud of Satellite Breakup via Probabilistic Method

Accurately modeling the evolution of debris clouds from satellite breakups is necessary for assessing the collision risk to space assets. Generally, the evolution of debris clouds can be divided into short-, medium-, and long-term phases. Compared to the short- and long-term phases, the study on the medium-term phase was insufficient. This paper proposes a probabilistic method to model the medium-term evolution of a debris cloud. First, a satellite breakup event can be characterized by a probabilistic density distribution of the initial velocity vectors of all fragments. Then, the distribution in the initial velocity can be transformed to that in three classic orbital elements, i.e., semimajor axis, eccentricity, and inclination. Given that the driving force of medium-term evolution is the J2 perturbation and that J2 has no secular contribution to these three classic orbital elements, the distribution of classic orbital elements remains stationary during the evolution. This feature can be exploited to express the probabilistic density distribution of any given target position in terms of the density distribution of the classic orbital elements by changing variables. Finally, 16 one-variable equations with analytical first derivatives were formulated to find the proper inverse mapping from the given position to the classic orbital elements, and the Jacobian matrix of the inverse mapping was derived. Medium-term debris clouds resulting from two typical breakup velocity distributions were tested using the proposed method. Results show that the proposed method can accurately simulate the evolution of the clouds’ geometrical extent and density flow.

Transient Plasma Wind Tunnel Testing Under Thermomechanical Loads for Reentry Break-Up Analysis

This paper introduces a novel approach for transient plasma wind tunnel testing in an arcjet facility, enabling the experimental simulation of the aerothermal loads along reentry trajectory segments. Such experiments newly allow for the investigation of the causes of break-up events. The trajectory segment is simulated by duplicating the time-resolved profiles of the characteristic flow parameters, namely, heat flux and stagnation pressure as well as the mechanical load, which represents the aerodynamic forces. In arcjet facilities, the parameters that govern the plasma condition are split into variable and constant parameters, which define the available altitude range that can be replicated. The variable conditions arc current and ambient pressure were determined with steady-state trajectory points and traces determined between these conditions resulting in a full trajectory segment. The test time then relates directly to an altitude on the trajectory segment, which allows for an experimental determination of the main break-up altitude. The methodology is applied to a trajectory segment of the transport vehicle CYGNUS OA6, covering an altitude range from 85 to 70 km. A transient break-up experiment on an aluminum bar yielded a failure at an altitude corresponding to 77.6 km, showing a thermomechanical characteristic. These results align well with the observed break-up altitude of CYGNUS OA6, showing the potential of the proposed method.

Cretaceous–Paleocene extension at the southwestern continental margin of India and opening of the Laccadive basin: constraints from geophysical data

Abstract. Previous geophysical investigations of the western continental margin of India (WCMI) confirm the two-phase breakup history of the margin with the first breakup taking place between India and Madagascar that created the Mascarene Basin in the Late Cretaceous and the second breakup event in Early Paleocene with Seychelles separating from India. Despite numerous geoscientific studies along the WCMI, the opening of the Laccadive basin, situated along the southern part of the margin, remains poorly constrained. In this study, we evaluate the multi-channel seismic reflection and gravity anomalies at the margin to identify the early rift signatures in conjunction with the magnetic anomaly identifications in the Mascarene Basin. The analysis led to the identification of two trends of extensional structures, a NNW–SSE-oriented structure over the Laccadive Ridge north of Tellicherry Arch, interpreted to result from ENE–WSW extension, and a SSW–NNE-oriented structure in the Laccadive basin region towards the south, interpreted to result from NW–SE extension. Previous plate reconstruction models of the Mascarene Basin using marine magnetic lineations suggest that the ENE–WSW extension observed over the Laccadive Ridge could be related to the India–Madagascar separation. We associate the pattern of sediment deposition and the presence of a Paleocene trap volcanics, linked with the NW–SE grabens observed in the Laccadive basin region, to the extension between the Laccadive Ridge and the western coast of India after the separation of Madagascar from India. We further propose that the anticlockwise rotation of India and the passage of the Réunion plume have facilitated the opening of the Laccadive basin.

The longitudinal correlates of breakup distress in early young adulthood: Future distress and future benefits

Objectives: Existing research on romantic breakups focused on the predictors of breakup, or on its emotional and behavioral sequelae. The current study examines the longitudinal correlates of a breakup experience over a period of eight years, and questions whether breakup experiences may also have negative and positive outcomes. Methods: Data were collected from 124 Israeli emerging adults (mean age 20.22 years; 79 females). Participants were approached again at ages 23, 25, and 28. Breakup distress was assessed at each wave. At age 28, participants’ well-being, as well as their romantic capacities, were evaluated. Results: The intensity of breakup distress at age 20 was not found to be associated with future well-being. However, increased accumulating distress explained a greater number of depressive and anxiety symptoms, and reports of feeling insecure about a partner’s availability and responsiveness, at age 28. In-depth interviews with participants about their romantic relationships at age 28 showed that breakup distress at age 20 was associated with greater romantic competence at age 28, explaining better capacity to learn from past romantic experiences and draw lessons for future behavior. In addition, earlier breakup distress was associated with more coherent accounts of romantic relationships at age 28. Conclusions: Findings suggest that young adults are likely to experience a number of breakup events during their twenties, and the accumulating breakup experiences can affect future well-being. The experience of a breakup might not necessarily associate with negative future outcomes, while an earlier breakup experience could also serve as a positive learning arena for future relationships. Social policy: Perception of romantic dissolution in a comprehensive manner could be helpful for understanding that breakups are probably part of the normative development of romantic relationships among young adults, and should not be perceived only from a deficit perspective.

Phase field modeling of hyperelastic material interfaces –Theory, implementation and application to phase transformations

Interface mechanics can significantly govern the evolution of multiple phases on smaller scales, e.g., determining the properties of TWIP- and TRIP-steels, geopolymers or Li-ion batteries. The present contribution is specifically centered around the influence of interface elasticity on mechanically induced phase transformations. A geometrically exact finite element framework is developed for this purpose based on incremental energy minimization. It is set up in three-dimensional space and comprises an Allen-Cahn type phase field formulation based on a Modica-Mortola double-well functional, as well as a Ginzburg-Landau type viscosity formulation. The phase field approximation of the interface deformation gradient is derived by means of homogenization theory. A monolithic solver is employed for the resulting set of non-linear coupled equations. The example of coalescing spheres shows that larger interface energies can amplify and accelerate coalescence. Lower interface energies, in contrast, allow for distinct spreading of the energetically favorable bulk phase. Deformation-dependent interface energies particularly add stress peaks to this process that are localized at the phase transition zone. The relaxation of a stepped interface shape showed that deformation-dependent interface energies favor a plane partition of the bulk phases. Yet, they also delay breakup events compared to simple constant interface energies. This peculiarity can be beneficial for calibration purposes. Strain dependence moreover causes an additional elastic stiffness in the direction of the interface tangent plane and constitutes thus another origin for anisotropy of the overall structure.

Generation of initial debris cloud distributions for breakup events based on CARDC-SBM

With the dramatic increase in the number of resident space objects, the risk of collision between space objects and debris is growing. To protect spacecraft from such collisions, it is crucial to determine the generation patterns of space debris and analyze the evolution of debris clouds. In this paper, a continuous distribution formula is derived for each parameter of the breakup debris based on the China Aerodynamics Research and Development Center spacecraft breakup model (CARDC-SBM). Using CARDC-SBM, we theoretically establish a normal distribution for the separation velocity of the breakup debris in relation to the breakup mass center. Based on this foundation, the mean and standard deviation of the debris separation velocity distribution are empirically modeled using polynomial and exponential functions. Consequently, an empirical formula with a broad range of applicability is derived, which significantly reduces the computation time of debris cloud simulations. The initial velocity distribution given by this empirical formula is employed as the initial condition for the evolution of debris clouds from the perspective of a boundary value problem. Simulations using CARDC-SBM and subsequent analysis of the debris cloud evolution resulting from a breakup event reveal that the distribution of each parameter is determined solely by the relative collision velocity and the spacecraft's nominal density in the impact breakup scenario. Our results show that the empirical formula for the debris cloud distribution provides good agreement with Monte Carlo simulations.

Breaking the Ice: Exploring the Changing Dynamics of Winter Breakup Events in the Beaufort Sea

AbstractThe Beaufort Sea has experienced a significant decline in sea ice, with thinner first‐year ice replacing thicker multi‐year ice. This transition makes the ice cover weaker and more mobile, making it more vulnerable to breakup during winter. Using a coupled ocean‐sea‐ice model, we investigated the impact of these changes on sea‐ice breakup events and lead formation from 2000 to 2018. The simulation shows an increasing trend in the Beaufort Sea lead area fraction during winter, with a pronounced transition around 2007. A high lead area fraction in winter leads to greater growth of new, thin ice within the Beaufort region while also leading to enhanced sea ice transport out of the area. Despite the large export, consisting primarily of thinner first‐year ice, we find little evidence that winter breakup amplifies the advection of multi‐year ice from the central Arctic into the Beaufort Sea. Overall, the export offsets ice growth, resulting in negative volume anomalies and preconditioning a thinner and weaker ice pack at the end of the cool season. Our results indicate that large breakup events may become more frequent as the sea‐ice cover thins and that such events only became common after 2007. This result highlights the need to represent these processes in global‐scale climate models to improve projections of the Arctic.

Monte Carlo simulation of spacecraft breakup events in Low Lunar Orbit

Monte Carlo simulations of spacecraft breakup events in Low Lunar Orbit are conducted to study the behavior of artificial debris across all orbit types in this environment. 2000 breakup events at random initial states in lunar orbit are simulated, and the resulting nearly 500,000 particles are propagated for five years using a high-fidelity lunar trajectory model. Debris from a smaller sample of 200 breakup events is also propagated for ten years. Trends in the rate of decay of debris from lunar orbit are analyzed to investigate the longevity of debris in lunar orbit, and the locations of lunar surface impacts are plotted to determine if some regions of the Moon would be at greater risk than others from an orbital breakup event. Across all orbits, about 38% of the debris remained in lunar orbit after five years, and the longevity of debris was found to depend significantly on the pre-breakup perilune and inclination. Debris generally remained in lunar orbit for less time as the pre-breakup perilune decreased, although an average of 19% the debris remained in lunar orbit after five years even for pre-breakup perilune altitudes below 50 km. Debris was also found to be highly unstable in certain inclinations. The rates of decay across all orbit types tended to slow greatly after two years, suggesting that a portion of the debris can often remain in lunar orbit for at least a decade. Finally, clusters of lunar surface debris impacts were identified, which could have applications for lunar satellite disposal after mission completion. The results of this study provide novel insights into the consequences of lunar breakup events, helping support the development of debris mitigation recommendations for lunar orbit as international interest in exploration of the Moon grows.

Celerity of Ice Breakup Front in the Regulated Peace River, Canada, and Implications for the Recharge of the Peace–Athabasca Delta

Timely release of flow from upstream hydropower generation facilities on the Peace River can enhance potential ice-jam flooding near the drying Peace–Athabasca Delta (PAD), a Ramsar wetland of international importance and homeland to Indigenous Peoples. An important consideration in deciding whether and when to commence a release is the celerity of the breakup front as it advances along the Peace River. Relevant historical data for a key stretch of the river are analyzed to determine average celerities, which can vary by an order of magnitude from year to year. Seven breakup events are identified that might have been candidates for a release, and the predictability of associated celerities is explored in terms of antecedent hydroclimatic variables, including cumulative winter snowfall, snow water equivalent on 1 April, ice cover thickness, coldness of the winter, and freezeup level. It is shown that celerity can be predicted to within a factor of two or less, with the freezeup level giving the best results. Three of the seven “promising” events culminated in PAD floods and were associated with the three highest celerities. The empirical findings are shown to generally align with physical understanding of breakup driving and resisting factors.

Late Paleoproterozoic Breakup Event in the Southern Margin of the North China Craton: Evidence from A-Type Granites

Late Paleoproterozoic Breakup Event in the Southern Margin of the North China Craton: Evidence from A-Type Granites

Breakup prediction of oscillating droplets under turbulent flow

Droplet and bubble breakup phenomena under turbulent flow have been widely studied for over 70 years through theoretical, experimental and numerical approaches. Despite significant progress, the dynamics of breakup remains an active research topic. The present study considers a database of breakup events under turbulent conditions. The database contains neutrally buoyant droplets obtained for a single moderate turbulent Reynolds number and a Weber number near the critical Weber number of the droplets, allowing for long time evolution prior to droplet breakage. Each droplet in the database follows a consistent behavior: the droplet undergoes (1) an initial shape deformation, then (2) an extended oscillatory regime, until (3) a critical large deformation starts, leading to (4) a capillary-driven breakup. While the first two stages have been investigated in our previous work using spherical harmonics decomposition, this study focuses on the last two stages, describing them qualitatively and quantitatively by means of seven different shape parameters. These shape parameters are based on different information of the specific droplet such as its surface, its volume or its averaged mean curvature, and provide a multidimensional analysis of the droplet breakup. They are used to measure the time spent in the final two stages prior to breakup, as well as the transition between these stages. Additionally, we establish breakup thresholds for each shape parameter to predict neutrally buoyant droplet breakup under turbulent flow conditions.

Linking kimberlite magmatism in the Brazilian Platform with Pangea break-up events using in situ Rb-Sr in phlogopite

Kimberlite magmatism provides insights into periodic tectonothermal processes linked to the evolution of supercontinents. Paleozoic and Mesozoic kimberlites overlapping with the Pangea cycle are exposed in the Amazonian Craton (Pimenta Bueno field) and the Neoproterozoic Brasília Belt. Phlogopite in mantle xenoliths in kimberlites from the Amazonian Craton are characterized by low Cr2O3 (< 1 wt%) and an enrichment in TiO2 (> 2 wt%), akin to secondary phlogopite formed by kimberlite magma infiltration in the mantle. Low Ti-Cr (< 1 wt%) and high #Mg (91–92) grains are linked to extensive metasomatism of garnet peridotites resulting in clinopyroxene-phlogopite rocks. In situ phlogopite Rb-Sr isochron ages of 250–220 Ma constrain the emplacement of pipes in the Amazonian Craton with no age difference between distinct phlogopite compositions (higher and lower TiO2 phlogopite) and microstructures (porphyroclasts, neoblasts, reaction rims). Mantle xenoliths in kimberlite pipes from the Brasília Belt present high TiO2 (> 2 wt%) akin to secondary phlogopite formed by magma infiltration, and low Ti-Cr (1 wt%), and high #Mg (> 92) phlogopite akin to primary grains in equilibrium with garnet. In situ phlogopite Rb-Sr isochron ages from all Brasília Belt phlogopite types span 90–80 Ma, constraining the emplacement of diamondiferous and barren pipes, with no relic of older metasomatic events. The kimberlites from the Pimenta Bueno field (Amazonian Craton) are coeval with the beginning of the extension within Pangea that culminated with the Central Atlantic rifting. In fact, the Permian-Triassic kimberlites occur close to intracratonic basins that are crosscut by ca. 200 Ma dykes and sills of the Central Atlantic Magmatic Province. In situ phlogopite Rb-Sr isochron ages spanning 90–80 Ma in the pipes from central and southeastern Brazil (Brasília Belt) may be associated with propagation of far-field stresses linked to opening of the South Atlantic Ocean during the Pangea break-up.

Zircon U[sbnd]Pb and Hf isotope insights into the Mesoproterozoic breakup of supercontinent Columbia from the Sausar Belt, Central Indian Tectonic Zone

Credible records of rifting and associated sedimentation and granitoid magmatism coinciding with the Columbia breakup event are not common in the Precambrian Indian continent. We report a 1322 ± 3 Ma concordia age for magmatic zircons from the granitoid rocks of the Sausar mobile belt, Central Indian Tectonic Zone (CITZ). The rocks exhibit geochemical characteristics of A-type granitoid rocks and were generated by the dehydration melting of shallow crust in an extensional tectonic setting. The predominantly negative εHf(t) values and partial melting modelling imply their origin by the reworking of pre-existing granitoid crust. TDM2 (Hf) model ages for these rocks range from 2856 Ma to 1885 Ma suggesting a prolonged period of crustal evolution and reworking of Archean to Paleoproterozoic basement rocks. The temperature for magma generation, determined from the calculated zircon saturation temperature of 874.2 °C is suggestive of melting of a thinned crust that was heated by the upwelling asthenosphere in an extensional tectonic setting. The obtained ages provide evidence for the existence of an extensional event during mid-Mesoproterozoic coinciding with the Columbia breakup event. The extension could also be argued as a local event related to far-field stresses generated due to the ca. 1.6 to 1.5 Ga subduction-collision event at the plate margin farther to the north of the studied region of the CITZ. The recrystallized margins of zircon grains yield 207Pb/206Pb ages between 0.95 Ga and 1.0 Ga implying their alteration during a metamorphic event that can be identified with the final amalgamation and stabilization of the northern and southern Indian blocks along the CITZ, coinciding with the Rodinia assembly, during which the regional structural fabric developed.