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Fragmentation under the Scaling Symmetry and Turbulent Cascade with Intermittency

Fragmentation plays an important role in a variety of physical, chemical, and geological processes. Examples include atomization in sprays, crushing of rocks, explosion and impact of solids, polymer degradation, etc. Although each individual action of fragmentation is a complex process, the number of these elementary actions is large. It is natural to abstract a simple 'effective' scenario of fragmentation and to represent its essential features. One of the models is the fragmentation under the scaling symmetry: each breakup action reduces the typical length of fragments, r (right arrow) alpha r, by an independent random multiplier alpha (0 < alpha < 1), which is governed by the fragmentation intensity spectrum q(alpha), integral(sup 1)(sub 0) q(alpha)d alpha = 1. This scenario has been proposed by Kolmogorov (1941), when he considered the breakup of solid carbon particle. Describing the breakup as a random discrete process, Kolmogorov stated that at latest times, such a process leads to the log-normal distribution. In Gorokhovski & Saveliev, the fragmentation under the scaling symmetry has been reviewed as a continuous evolution process with new features established. The objective of this paper is twofold. First, the paper synthesizes and completes theoretical part of Gorokhovski & Saveliev. Second, the paper shows a new application of the fragmentation theory under the scale invariance. This application concerns the turbulent cascade with intermittency. We formulate here a model describing the evolution of the velocity increment distribution along the progressively decreasing length scale. The model shows that when the turbulent length scale gets smaller, the velocity increment distribution has central growing peak and develops stretched tails. The intermittency in turbulence is manifested in the same way: large fluctuations of velocity provoke highest strain in narrow (dissipative) regions of flow.

Gorokhovski, M.↗

Characterization of the Catalog Fengyun-1C Fragments and Their Long-term Effect on the LEO Environment

The intentional breakup of Fengyun-1C on 11 January 2007 created the most severe orbital debris cloud in history. More than 2500 large fragments were identified and tracked by the U.S. Space Surveillance Network by the end of the year. The altitude where the event occurred was probably the worst location for a major breakup in the low Earth orbit (LEO) region, since it was already highly populated with operational satellites and debris generated from previous breakups. The addition of so many fragments not only poses a realistic threat to operational satellites in the region, but also increases the instability (i.e., collision cascade effect) of the debris population there. Preliminary analysis of the large Fengyun-1C fragments indicates that their size and area-to-mass ratio (A/M) distributions are very different from those of other known events. About half of the fragments appear to be composed of light-weight materials and more than 100 of them have A/M values exceeding 1 square meter per kilogram, consistent with thermal blanket pieces. In addition, the orbital elements of the fragments suggest nontrivial velocity gain by the fragment cloud during the impact. These important characteristics were incorporated into a numerical simulation to assess the long-term impact of the Fengyun-1C fragments to the LEO debris environment. The main objectives of the simulation were to evaluate (1) the collision probabilities between the Fengyun-1C fragments and the rest of the catalog population and (2) the collision activities and population growth in the region in the next 100 years.

Liou, J.-C.↗

Observations of Titan IIIC Transtage Fragmentation Debris

The fragmentation of a Titan IIIC Transtage (1968-081) on 21 February 1992 is one of only two known break-ups in or near geosynchronous orbit. The original rocket body and 24 pieces of debris are currently being tracked by the U. S. Space Surveillance Network (SSN). The rocket body (SSN# 3432) and several of the original fragments (SSN# 25000, 25001, 30000, and 33511) were observed in survey mode during 2004-2010 using the 0.6-m Michigan Orbital DEbris Survey Telescope (MODEST) in Chile using a broad R filter. This paper presents a size distribution for all calibrated magnitude data acquired on MODEST. Size distribution plots are also shown using historical models for small fragmentation debris (down to 10 cm) thought to be associated with the Titan Transtage break-up. In November 2010, visible broadband photometry (Johnson/Kron-Cousins BVRI) was acquired with the 0.9-m Small and Moderate Aperture Research Telescope System (SMARTS) at the Cerro Tololo Inter-American Observatory (CTIO) in Chile on several Titan fragments (SSN 25001, 33509, and 33510) and the parent rocket body (SSN 3432). Color index data are used to determine the fragment brightness distribution and how the data compares to spacecraft materials measured in the laboratory using similar photometric measurement techniques. In order to better characterize the break-up fragments, spectral measurements were acquired on three Titan fragments (one fragment observed over two different time periods) using the 6.5-m Magellan telescopes at Las Campanas Observatory in Chile. The telescopic spectra of SSN 25000 (May 2012 and January 2013), SSN 38690, and SSN 38699 are compared with laboratory acquired spectra of materials (e.g., aluminum and various paints) to determine the surface material.

Cowardin, Heather↗

A Monte Carlo Approach to Modeling the Breakup of the Space Launch System EM-1 Core Stage with an Integrated Blast and Fragment Catalogue

The Liquid Propellant Fragment Overpressure Acceleration Model (L-FOAM) is a tool developed by Bangham Engineering Incorporated (BEi) that produces a representative debris cloud from an exploding liquid-propellant launch vehicle. Here it is applied to the Core Stage (CS) of the National Aeronautics and Space Administration (NASA) Space Launch System (SLS launch vehicle). A combination of Probability Density Functions (PDF) based on empirical data from rocket accidents and applicable tests, as well as SLS specific geometry are combined in a MATLAB script to create unique fragment catalogues each time L-FOAM is run-tailored for a Monte Carlo approach for risk analysis. By accelerating the debris catalogue with the BEi blast model for liquid hydrogen / liquid oxygen explosions, the result is a fully integrated code that models the destruction of the CS at a given point in its trajectory and generates hundreds of individual fragment catalogues with initial imparted velocities. The BEi blast model provides the blast size (radius) and strength (overpressure) as probabilities based on empirical data and anchored with analytical work. The coupling of the L-FOAM catalogue with the BEi blast model is validated with a simulation of the Project PYRO S-IV destruct test. When running a Monte Carlo simulation, L-FOAM can accelerate all catalogues with the same blast (mean blast, 2 σ blast, etc.), or vary the blast size and strength based on their respective probabilities. L-FOAM then propagates these fragments until impact with the earth. Results from L-FOAM include a description of each fragment (dimensions, weight, ballistic coefficient, type and initial location on the rocket), imparted velocity from the blast, and impact data depending on user desired application. LFOAM application is for both near-field (fragment impact to escaping crew capsule) and far-field (fragment ground impact footprint) safety considerations. The user is thus able to use statistics from a Monte Carlo set of L-FOAM catalogues to quantify risk for a multitude of potential CS destruct scenarios. Examples include the effect of warning time on the survivability of an escaping crew capsule or the maximum fragment velocities generated by the ignition of leaking propellants in internal cavities.

Richardson, Erin↗

Comparison of Gas Phase Fragmentation Behaviors of Nuclear Fuel Cycle Ligands in Lanthanide and Americium Metal Ligand Nitrate Clusters

Introduction (120 words): Transport of metal ions across the aqueous-organic phase boundary is an essential step in a hydrometallurgical nuclear fuel reprocessing strategy. The study of transport agents for nuclear fuel elements is imperative to guide the design of ligands that boost the separation efficiency of the recovery process from fission products. However, limited studies have been made on the chemistry of these transport agents when complexing with transuranic elements in gas-phase where all surrounding factors are essentially excluded. This work investigates the reagent ligand complexations to transuranic and other metals and their dissociations in the gas phase. Comparisons are made between 4f and 5f elements and between ligands. Methods (120 words): (N,N-diisobutylcarbamoylmethyl)phenyloctylphosphine oxide (CMPO) and N,N,N',N'-tetraoctyldiglycolamide (TODGA) have been selected to complex with metal nitrates. The actinide americium and lanthanides neodymium, samarium, and europium were investigated as part of this work. The lanthanides were selected to act as size and electron configuration analogues of the minor actinides. Metal complexes with two ligands and two nitrates ([M(NO3)2(CMPO)2]+, for example) are studied in Bruker micrOTOF-Q II mass spectrometer equipped with collision-induced dissociation capability. The comparisons of the mass spectra are made in groups of homogenous ligands and mixed TODGA-CMPO ligands clusters. Comparisons are also made based on the complexed metals (Am and lanthanides). Preliminary data (300 words): Collision-induced dissociation mass spectrometry data are collected on two ligands complexed with metal nitrates where the two ligands are homogenous, with (CMPO)2 or (TODGA)2, or heterogeneous, with (TODGA)(CMPO). Several fragmentation patterns are observed among complexes with the CMPO ligand whereas the TODGA ligand commonly dissociates intact from the complex. Most of the metal complexes exhibit similar fragmentation patterns, but there are a few notable deviations in fragmentation patterns between the Am and Ln-bearing complexes. For the [M(CMPO)2(NO3)2]+ complexes, the initial loss of nitrate in the form of nitric acid is observed in all four complexes. However, [Am(CMPO)2(NO3)2]+ exhibits an additional fragmentation not found in the lanthanide complexes. Also, a significantly different ratio of the second nitric acid loss is found in the Am complex. These deviations may indicate the different interaction behaviors between actinides and lanthanides. The [M(TODGA)2(NO3)2]+ complexes exhibit the fragmentation as the loss of one TODGA ligand as an intact form and the loss of nitrate as nitric acid. The Am complex exhibits an additional fragmentation after losing the TOGDA ligand, which is not observed among the Ln complexes. The heterogeneous [M(TODGA)(CMPO)(NO3)2]+ complexes exhibit both similarities and differences between the Am and Ln complexes. For example, the heterogenous Am complex does not exhibit the loss of an intact TODGA ligand while all three Ln complexes do. This indicates that TODGA may bind more strongly to Am than Ln. Additionally, the intensity of the loss of CMPO ligand (as partially or whole) is found to be significantly larger than that of the loss of TODGA (as partially of whole) indicating that TODGA is bound to the metal significantly stronger than CMPO. Planned computational analysis will help understand the deviation in fragmentation behaviors between americium and lanthanide metal centers, or between TODGA and CMPO ligands. Novel aspect (20 words): Gas-phase actinide and lanthanide complex formation and fragmentation provide insight into the coordination environment differences of f-element metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Fragment-Cloud Model for Breakup of Asteroids with Varied Internal Structures

As an asteroid descends toward Earth, it deposits energy in the atmosphere through aerodynamic drag and ablation. Asteroid impact risk assessments rely on energy deposition estimates to predict blast overpressures and ground damage that may result from an airburst, such as the one that occurred over Chelyabinsk, Russia in 2013. The rates and altitudes at which energy is deposited along the entry trajectory depend upon how the bolide fragments, which in turn depends upon its internal structure and composition. In this work, we have developed an analytic asteroid fragmentation model to assess the atmospheric energy deposition of asteroids with a range of structures and compositions. The modeling approach combines successive fragmentation of larger independent pieces with aggregate debris clouds released with each fragmentation event. The model can vary the number and masses of fragments produced, the amount of mass released as debris clouds, the size-strength scaling used to increase the robustness of smaller fragments, and other parameters. The initial asteroid body can be seeded with a distribution of independent fragment sizes amid a remaining debris mass to represent loose rubble pile conglomerations, can be given an outer regolith later, or can be defined as a coherent or fractured monolith. This approach enables the model to represent a range of breakup behaviors and reproduce detailed energy deposition features such as multiple flares due to successive burst events, high-altitude regolith blow-off, or initial disruption of rubble piles followed by more energetic breakup of the constituent boulders. These capabilities provide a means to investigate sensitivities of ground damage to potential variations in asteroid structure.

Asteroid↗

Meteorite Falls and the Fragmentation of Meteorites

In order to understand the fragmentation of objects entering the atmosphere and why some produce more fragments than others, I have searched the Meteoritical Society database for meteorites greater than 20 kilograms that fell in the USA, China, and India. I also studied the video and film records of 21 fireballs that produced meteorites. A spreadsheet was prepared that noted smell, fireball, explosion, whistling, rumbling, the number of fragments, light, and impact sounds. Falls with large numbers of fragments were examined to look for common traits. These were: the Norton County aubrite, explosion and a flare greater than 100 fragments; the Forest City H5 chondrite explosion, a flare, a dust trail, 505 specimens; the Richardton H5 chondrite explosion and light, 71 specimens; the Juancheng H5 chondrite explosion, a rumbling, a flare, a dust trail,1000 specimens; the Tagish Lake C2 chondrite explosion, flare, dust trail, 500 specimens. I conclude that fragmentation is governed by the following: (1) Bigger meteors undergo more stress which results in more specimens; (2) Harder meteorites also require more force to break them up which will cause greater fragmentation; (3) Force and pressure are directly proportional during falls. General observations made were; (1) Meteorites produce fireballs sooner due to high friction; (2) Meteors tend to explode as well because of high stress; (3) Softer meteorites tend to cause dust trails; (4) Some falls produce light as they fall at high velocity. I am grateful to NASA Ames for this opportunity and Derek Sears, Katie Bryson, and Dan Ostrowski for discussions.

fragmentations↗

Microscopic theory of angular momentum distributions across the full range of fission fragments

Modern nuclear theory provides qualitative insights into the fundamental mechanisms of nuclear fission and is increasingly capable of making reliable quantitative predictions. Most quantities of interest pertain to the primary fission fragments, whose subsequent decay is typically modeled using statistical reaction models. Consequently, a key objective of fission theory is to inform these models by predicting the initial conditions of the primary fragments. Here, in this work, we employ a framework that combines joint angular momentum and particle number projection with time-dependent configuration mixing to calculate the angular momentum distributions of primary fragments. Focusing on the benchmark cases of neutron-induced fission of 235 U and 239 Pu , we predict—for the first time—microscopic angular momentum distributions for all fragments observed in experiments. Our results reveal a pronounced sawtooth pattern in the average angular momentum as a function of fragment mass, consistent with recent measurements. Additionally, we observe substantial variations in angular momentum distributions along isobaric chains, indicating that commonly used empirical formulas lack sufficient accuracy. We also quantify a strong correlation between the angular momentum and the deformation of the fragments at scission, and a weak correlation in the magnitude of the angular momentum between fragment partners. The generated data will enable estimation of the impact of microscopic distributions on fission spectra, paving the way toward fission modeling based on microscopic inputs.

Physics - Nuclear physics and radiation physics↗

Heavy Ion Fragmentation Experiments at the Bevatron

Fragmentation processes of heavy nuclei in matter using the heavy-ion capability of the Bevatron were studied. The purpose was to obtain the single particle inclusive spectra of secondary nuclei produced at 0 deg by the fragmentation of heavy ion beam projectiles. The process being examined is B+T yields F + anything, where B is the beam nucleus, T is the target nucleus, and F is the detected fragment. The fragments F are isotopically identified by experimental procedures involving magnetic analysis, energy loss and time-of-flight measurements. Attempts were also made to: (1) measure the total and partial production cross section for all isotopes, (2) test the applicability of high-energy multi-particle interaction theory to nuclear fragmentation, (3) apply the cross-section data and fragmentation probabilities to cosmic ray transport theory, and (4) search for systematic behavior of fragment production as a means to improve existing semi-empirical theories of cross sections.

Heckman, H. H.↗

Heavy ion fragmentation experiments at the bevatron

Collaborative research efforts to study the fragmentation processes of heavy nuclei in matter using heavy ion beams of the Bevatron/Bevalac are described. The goal of the program is to obtain the single particle inclusive spectra of secondary nuclei produced at 0 deg by the fragmentation of heavy ion beam projectiles. The process being examined is B+T yields F + anything, where B is the beam nucleus, T is the target nucleus, and F is the detected fragment. The fragments F are isotopically identified by experimental procedures involving magnetic analysis, energy loss and time-of-flight measurements. Effects were also made to: (a) study processes of heavy nuclei in matter, (b) measure the total and partial production cross section for all isotopes, (c) test the applicability of high energy multiparticle interaction theory to nuclear fragmentation, (d) apply the cross section data and fragmentation probabilities to cosmic ray transport theory, and (e) search for systematic behavior of fragment production as a means to improve existing semi-empirical theories of cross-sections.

Heckman, H. H.↗

Derivation of a heterogeneous lithic fragment in the Bovedy L-group chondrite from impact-melted porphyritic chondrules

Results are presented of petrographic, compositional and dating analyses of a light-colored lithic fragment in the L-group Bovedy meteorite that has a composition different from that of the host chondrite. Polished thin sections of the lithic fragment, host, and the fragment-host boundary were examined microscopically and analyzed by electron microprobe, metallic Ni-Fe, and instrumental neutron activation techniques; chips of the fragment were also used for Ar-39/Ar-40 dating and oxygen isotope analyses. The poikilitic textures, olivine, low-Ca pyroxene and kamacite composition and low Na2O, K2O and P2O5 contents of the fragment indicate that it represents a solidified, slightly fractionated impact melt formed from a source rich in porphyritic chondrules. A progressive increase on MgO content across the fragment is accounted for by the heterogeneous nucleation of MgO-rich phases. The Ar data indicate that the Bovedy lithic fragment and its host were partly degassed of radiogenic Ar less than 0.94 billion years ago, probably due to shock. The data are consistent with a cooling rate of about 5 C/million years through 500 C, which must have resulted from the burial of the assemblage beneath insulating material on the parent body at depths of at least several km.

Rubin, A. E.↗

Fragmentation of ice by low velocity impact

Low-velocity impact experiments (0.14 to 1 km/s) carried out in polycrystalline water ice targets at 257 and 81 K reveal interactions which are assigned to four fragmentation classes: cratering, erosion, disruption, and total fragmentation. The specific kinetic energies for the transitions between these classes are found to be about one to two orders of magnitude below those for silicate rocks. The mass vs. cumulative number distribution of fragments in the experiments is described by a simple power law, similar to that observed in fragmented rocks both in the laboratory and in nature. The logarithmic slopes of cumulative number vs. fragment weight range from -0.9 to -1.8; they decrease with increasing projectile energy and are approximately independent of target temperature. The shapes of fragments resulting from erosion and disruption of ice targets are found to be significantly less spherical for 257 K targets than for 81 K targets. Fragment sphericity increases with increasing projectile energy at 257 K; however, no similar trend is observed for 81 K ice.

Lange, M. A.↗

Fractals and fragmentation

The use of renormalization group techniques on fragmentation problems is examined. The equations which represent fractals and the size-frequency distributions of fragments are presented. Method for calculating the size distributions of asteriods and meteorites are described; the frequency-mass distribution for these interplanetary objects are due to fragmentation. The application of two renormalization group models to fragmentation is analyzed. It is observed that the models yield a fractal behavior for fragmentation; however, different values for the fractal dimension are produced . It is concluded that fragmentation is a scale invariant process and that the fractal dimension is a measure of the fragility of the fragmented material.

Turcotte, D. L.↗

Biological effectiveness of high-energy protons - Target fragmentation

High-energy protons traversing tissue produce local sources of high-linear-energy-transfer ions through nuclear fragmentation. The contribution of these target fragments to the biological effectiveness of high-energy protons using the cellular track model is examined. The effects of secondary ions are treated in terms of the production collision density using energy-dependent parameters from a high-energy fragmentation model. Calculations for mammalian cell cultures show that at high dose, at which intertrack effects become important, protons deliver damage similar to that produced by gamma rays, and with fragmentation the relative biological effectiveness (RBE) of protons increases moderately from unity. At low dose, where sublethal damage is unimportant, the contribution from target fragments dominates, causing the proton effectiveness to be very different from that of gamma rays with a strongly fluence-dependent RBE. At high energies, the nuclear fragmentation cross sections become independent of energy. This leads to a plateau in the proton single-particle-action cross section, below 1 keV/micron, since the target fragments dominate.

Cucinotta, Francis A.↗

History of on-orbit satellite fragmentations

Since the first serious satellite fragmentation occurred in Jun. 1961, and instantaneously increased the total Earth satellite population by more than 400 percent, the issue of space operations within the finite region of space around the Earth has been the subject of increasing interest and concern. The prolific satellite fragmentations of the 1970's and the marked increase in the number of fragmentations in the 1980's served to widen international research into the characteristics and consequences of such events. Plans for large, manned space stations in the next decade and beyond demand a better understanding of the hazards of the dynamic Earth satellite population. The contribution of satellite fragmentations to the growth of the Earth satellite population is complex and varied. The majority of detectable fragmentation debris have already fallen out of orbit, and the effects of 40 percent of all fragmentations have completely disappeared. In this volume, satellite fragmentations are categorized by their assessed nature and to a lesser degree by their effect on the near-Earth space environment. A satellite breakup is the usually destructive disassociation of an orbital payload, rocket body, or structure, often with a wide range of ejecta velocities. A satellite breakup may be accidental or the result of intentional actions, e.g., due to a propulsion system malfunction or a space weapons test, respectively. An anomalous event is the unplanned separation, usually at low velocity, of one or more detectable objects from a satellite which remains essentially intact. Anomalous events can be caused by material deterioration of items such as thermal blankets, protective shields, or solar panels. As a general rule, a satellite breakup will produce considerably more debris, both trackable and non-trackable, than an anomalous event. From one perspective, satellite breakups may be viewed as a measure of the effects of man's activity on the environment, while anomalous events may be a measure of the environment on man-made objects.

Nauer, David J.↗

A thermodynamic theory of dynamic fragmentation

We present a theory of dynamic fragmentation of brittle materials based on thermodynamic arguments. We recover the expressions for average fragment size and number as originally derived by Grady. We extend the previous work by obtaining descriptions of fragment size distribution and compressibility change due to the fragmentation process. The size distribution is assumed to be proportional to the spectral power of the strain history and a sample distribution is presented for a fragmentation process corresponding to a constant rate strain history. The description of compressibility change should be useful in computational studies of fragmentation. These results should provide insight into the process of fragmentation of brittle materials from hypervelocity impact.

Ching H Yew↗

Proton-induced fragmentation of carbon at energies below 100 MeV

Radiation effects caused by single cosmic ray particles have been studied for many years in radiobiological experiments for different biological objects and biological end-points. Additionally, single event effects in microelectronic devices have gained large interest. There are two fundamental mechanisms by which a single particle can cause radiation effects. On the one hand, a cosmic ray ion with high linear energy transfer can deposit a high dose along its path. On the other hand, in a nuclear collision, a high dose can be deposited by short range particles emitted from the target nucleus. In low earth orbits a large contribution to target fragmentation events originates from trapped protons which are encountered in the South Atlantic Anomaly. These protons have energies up to a few hundred MeV. We study the fragmentation of C, O and Si nuclei - the target nuclei of biological material and microelectronic devices - in nuclear collisions. Our aim is to measure production cross sections, energy spectra, emission directions and charge correlations of the emitted fragments. The present knowledge concerning these data is rather poor. M. Alurralde et al. have calculated cross sections and average energies of fragments produced from Si using the cascade-evaporation model. D.M. Ngo et al. have used the semiempirical cross section formula of Silberberg and Tsao to calculate fragment yields and the statistical model of Goldhaber to describe the reaction kinematics. Cross sections used in these models have uncertainties within a factor of two. Our data will help to test and improve existing models especially for energies below 300 MeV/nucleon. Charge correlations of fragments emitted in the same interaction are of particular importance, since high doses can be deposited if more than one heavy fragment with a short range is produced.

Schmitz, M.↗

Repair of x-ray-induced DNA double-strand breaks in specific Not I restriction fragments in human fibroblasts: joining of correct and incorrect ends

An assay that allows measurement of absolute induction frequencies for DNA double-strand breaks (dsbs) in defined regions of the genome and that quantitates rejoining of correct DNA ends has been used to study repair of dsbs in normal human fibroblasts after x-irradiation. The approach involves hybridization of single-copy DNA probes to Not I restriction fragments separated according to size by pulsed-field gel electrophoresis. Induction of dsbs is quantitated from the decrease in the intensity of the hybridizing restriction fragment and an accumulation of a smear below the band. Rejoining of dsbs results in reconstitution of the intact restriction fragment only if correct DNA ends are joined. By comparing results from this technique with results from a conventional electrophoresis assay that detects all rejoining events, it is possible to quantitate the misrejoining frequency. Three Not I fragments on the long arm of chromosome 21 were investigated with regard to dsb induction, yielding an identical induction rate of 5.8 X 10(-3) break per megabase pair per Gy. Correct dsb rejoining was measured for two of these Not I fragments after initial doses of 80 and 160 Gy. The misrejoining frequency was about 25% for both fragments and was independent of dose. This result appears to be representative for the whole genome as shown by analysis of the entire Not I fragment distribution. The correct rejoining events primarily occurred within the first 2 h, while the misrejoining kinetics included a much slower component, with about half of the events occurring between 2 and 24 h. These misrejoining kinetics are similar to those previously reported for production of exchange aberrations in interphase chromosomes.

NASA Discipline Radiation Health↗