Breakup Events Research Articles

Ice regime of the lower Peace River and ice‐jam flooding of the Peace‐Athabasca Delta

AbstractThe Peace‐Athabasca Delta (PAD) in northern Alberta is one of the world's largest inland freshwater deltas, home to large populations of waterfowl, muskrat, beaver, and free‐ranging wood bison. Beginning in the mid‐1970s, a paucity of ice‐jam flooding in the lower Peace River has resulted in prolonged dry periods and considerable reduction in the area covered by lakes and ponds that provide a habitat for aquatic life in the PAD region. Using archived hydrometric data and in situ observations, the ice regime of the lower Peace is described and quantified, setting the stage for identification of the conditions that lead to ice‐jam flooding and replenishment of Delta habitat. The first such condition is the occurrence of a mechanical, as opposed to a thermal, breakup event; second, the river flow should be at least 4000 m3/s; and third, an ice jam should form within the last 50 km of the Peace River. The type of breakup event depends on the freeze‐up stage and spring flow. The former has increased as a result of flow regulation, and the latter has decreased owing to changing climatic patterns. Both trends tend to inhibit the occurrence of mechanical breakups and contribute to less frequent ice‐jam flooding. Potential mitigation strategies are discussed. Copyright © 2006 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.

Noble gas and oxygen isotope studies of aubrites: A clue to origin and histories

Noble gas measurements were performed for nine aubrites: Bishopville, Cumberland Falls, Mayo Belwa, Mount Egerton, Norton County, Peña Blanca Spring, Shallowater, ALHA 78113 and LAP 02233. These data clarify the origins and histories, particularly cosmic-ray exposure and regolith histories, of the aubrites and their parent body(ies). Accurate cosmic-ray exposure ages were obtained using the 81Kr–Kr method for three meteorites: 52 ± 3, 49 ± 10 and 117 ± 14 Ma for Bishopville, Cumberland Falls and Mayo Belwa, respectively. Mayo Belwa shows the longest cosmic-ray exposure age determined by the 81Kr–Kr method so far, close to the age of 121 Ma for Norton County. These are the longest ages among stony meteorites. Distribution of cosmic-ray exposure ages of aubrites implies 4–9 break-up events (except anomalous aubrites) on the parent body. Six aubrites show “exposure at the surface” on their parent body(ies): (i) neutron capture 36Ar, 80Kr, 82Kr and/or 128Xe probably produced on the respective parent body (Bishopville, Cumberland Falls, Mayo Belwa, Peña Blanca Spring, Shallowater and ALHA 78113); and/or (ii) chondritic trapped noble gases, which were likely released from chondritic inclusions preserved in the aubrite hosts (Cumberland Falls, Peña Blanca Spring and ALHA 78113). The concentrations of 128Xe from neutron capture on 127I vary among four measured specimens of Cumberland Falls (0.5–76 × 10 −14 cm 3STP/g), but are correlated with those of radiogenic 129Xe, implying that the concentrations of ( 128Xe) n and ( 129Xe) rad reflect variable abundances of iodine among specimens. The ratios of ( 128Xe) n/( 129Xe) rad obtained in this work are different for Mayo Belwa (0.045), Cumberland Falls (0.015) and Shallowater (0.001), meaning that neutron fluences, radiogenic 129Xe retention ages, or both, are different among these aubrites. Shallowater contains abundant trapped Ar, Kr and Xe (2.2 × 10 −7, 9.4 × 10 −10 and 2.8 × 10 −10 cm 3STP/g, respectively) as reported previously ( Busemann and Eugster, 2002). Isotopic compositions of Kr and Xe in Shallowater are consistent with those of Q (a primordial noble gas component trapped in chondrites). The Ar/Kr/Xe compositions are somewhat fractionated from Q, favoring lighter elements. Because of the unbrecciated nature of Shallowater, Q-like noble gases are considered to be primordial in origin. Fission Xe is found in Cumberland Falls, Mayo Belwa, Peña Blanca Spring, ALHA 78113 and LAP 02233. The majority of fission Xe is most likely 244Pu-derived, and about 10–20% seems to be 238U-derived at 136Xe. The observed ( 136Xe) Pu corresponds to 0.019–0.16 ppb of 244Pu, from which the 244Pu/U ratios are calculated as 0.002–0.009. These ratios resemble those of chondrites and other achondrites like eucrites, suggesting that no thermal resetting of the Pu–Xe system occurred after ∼4.5 Ga ago. We also determined oxygen isotopic compositions for four aubrites with chondritic noble gases and a new aubrite LAP 02233. In spite of their chondritic noble gas signatures, oxygen with chondritic isotopic compositions was found only in a specimen of Cumberland Falls (Δ 17O of ∼0.3‰). The other four aubrites and the other two measured specimens of Cumberland Falls are concurrent with the typical range for aubrites.

Formation of Breakup Ice Jams at Bridges

Bridges can impede the passage of river ice during the breakup event and promote formation of ice jams, with adverse socioeconomic and ecological impacts. Design for ice passage at bridges has largely been empirical and qualitative so that avoidance of ice-jam instigation is often uncertain. It is thus important to develop rational design criteria, based on a thorough understanding of the factors governing the interaction between bridges and ice. This concern is quantified by utilizing recent advances on breakup initiation and comparing driving and resisting forces when the sheet ice cover is about to be set in motion. Retention of ice sheets by in-stream piers can lead to jamming via accumulation of ice rubble that may be arriving from upriver. The resulting methodology is applied to two case studies and yields results that are in full accord with local experience. Though the present findings pertain to the obstruction created by in-stream piers, similar reasoning can be applied to constrictions that may be caused by protruding bridge abutments.

Petrology of silicate inclusions in the Sombrerete ungrouped iron meteorite: Implications for the origins of IIE‐type silicate‐bearing irons

Abstract— The petrography and mineral and bulk chemistries of silicate inclusions in Sombrerete, an ungrouped iron that is one of the most phosphate‐rich meteorites known, was studied using optical, scanning electron microscopy (SEM), electron microprobe analysis (EMPA), and secondary ion mass spectrometry (SIMS) techniques. Inclusions contain variable proportions of alkalic siliceous glass (˜69 vol% of inclusions on average), aluminous orthopyroxene (˜9%, Wo1–4Fs25–35, up to ˜3 wt% Al), plagioclase (˜8%, mainly An70–92), Cl‐apatite (˜7%), chromite (˜4%), yagiite (˜1%), phosphate‐rich segregations (˜1%), ilmenite, and merrillite. Ytterbium and Sm anomalies are sometimes present in various phases (positive anomalies for phosphates, negative for glass and orthopyroxene), which possibly reflect phosphate‐melt‐gas partitioning under transient, reducing conditions at high temperatures. Phosphate‐rich segregations and different alkalic glasses (K‐rich and Na‐rich) formed by two types of liquid immiscibility. Yagiite, a K‐Mg silicate previously found in the Colomera (IIE) iron, appears to have formed as a late‐stage crystallization product, possibly aided by Na‐K liquid unmixing. Trace‐element phase compositions reflect fractional crystallization of a single liquid composition that originated by low‐degree (˜4–8%) equilibrium partial melting of a chondritic precursor. Compositional differences between inclusions appear to have originated as a result of a “filter‐press differentiation” process, in which liquidus crystals of Cl‐apatite and orthopyroxene were less able than silicate melt to flow through the metallic host between inclusions. This process enabled a phosphoran basaltic andesite precursor liquid to differentiate within the metallic host, yielding a dacite composition for some inclusions. Solidification was relatively rapid, but not so fast as to prevent flow and immiscibility phenomena. Sombrerete originated near a cooling surface in the parent body during rapid, probably impact‐induced, mixing of metallic and silicate liquids. We suggest that Sombrerete formed when a planetesimal undergoing endogenic differentiation was collisionally disrupted, possibly in a breakup and reassembly event. Simultaneous endogenic heating and impact processes may have widely affected silicate‐bearing irons and other solar system matter.

Investigation of the influence of the architectures of poly(vinyl pyrrolidone) polymers made via the reversible addition–fragmentation chain transfer/macromolecular design via the interchange of xanthates mechanism on the stabilization of suspension polymerizations

AbstractLinear, star, and block copolymers based on poly(vinyl pyrrolidone) (PVP) were synthesized with the macromolecular design via the interchange of xanthates (MADIX) process for use as potential stabilizers in suspension polymerization. The design of the leaving group of the dithioxanthate‐based transfer agent was shown to be key to the successful preparation of well‐defined PVP architectures. A linear correlation of the monomer conversion and molecular weight was found in the synthesis of star polymers, whereas the molecular weight distribution remained narrow (polydispersity index < 1.3). Significant side reactions, which typically broaden the molecular weight distribution when R‐designed MADIX agents are used, were absent. The living behavior of the PVP polymerization was furthermore confirmed via chain extension with vinyl acetate, which resulted in the formation of PVP–PVAc block copolymers [where PVAc is poly(vinyl acetate)]. The prepared polymers were used as stabilizers in suspension polymerization to prepare crosslinked poly(vinyl neodecanoate)/ethylene glycol dimethacrylate microspheres. The ratio of the interfacial tension of the aqueous and monomer phases and the overall viscosity were found to have an effect on the diameter of the particles, with PVP star polymers as stabilizers resulting in smaller particles. A smaller interfacial tension, measured when star polymers and block copolymers were used, resulted in the appearance of smaller particles, probably because of more breakup events of the monomer droplets and the enhanced stabilization of the particle surface area. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4372–4383, 2006

Extraterrestrial chromite in Middle Ordovician marine limestone at Kinnekulle, southern Sweden—Traces of a major asteroid breakup event

Abstract— The distribution of sediment‐dispersed extraterrestrial chromite grains and other Cr‐rich spinels (>63 μm) has been studied in Middle Ordovician Orthoceratite Limestone from two quarries at Kinnekulle, southern Sweden. In the Thorsberg quarry, an ˜3.2 m thick sequence of beds previously shown to be rich in fossil meteorites is also rich in sediment‐dispersed extraterrestrial chromite grains. Typically, 1–3 grains are found per kilogram of limestone. In the nearby Hällekis quarry, the same beds show similarly high concentrations of extraterrestrial chromite grains, but in samples representing the 9 m downward continuation of the section exposed at this site, only 5 such grains were found in a total of 379 kg of limestone. The extraterrestrial (equilibrated ordinary chondritic) chromite grains can be readily distinguished by a homogeneous and characteristic major element chemistry, including 2.0–3.5 wt% TiO2 and stable V2O3 concentrations close to 0.7 wt%. Terrestrial Cr‐rich spinels have a wide compositional range and co‐exist with extraterrestrial chromite in some beds. These grains may be derived, for example, from mafic dykes exposed and weathered at the sea floor.Considering lithologic and stratigraphic aspects variations in sedimentation rate cannot explain the dramatic increase in extraterrestrial chromite seen in the upper part of the composite section studied. Instead, the difference may be primarily related to an increase in the ancient flux of extraterrestrial matter to Earth in connection with the disruption of the L chondrite parent body in the asteroid belt at about this time. The coexistence in some beds of high concentrations of chondritic chromite and terrestrial Cr‐rich spinels, however, indicates that redistribution of heavy minerals on the sea floor, related to changes in sea level and sea‐floor erosion and currents, must also be considered.

Synthesis of the proterozoic evolution of the Mt Isa Inlier

By virtue of its large area of exposure of different crustal levels, and preservation of a protracted (∼400 million years) Palaeoproterozoic to Mesoproterozoic tectonic evolution, the Mt Isa Inlier is an excellent natural laboratory to study Proterozoic tectonic processes. The inlier preserves evidence of intracontinental basin development, plutonism, low-pressure metamorphism, orogenesis at different crustal levels, and crustal-scale metasomatism. In addition, the Mt Isa Inlier is endowed with a variety of ore deposits, including the Mt Isa Pb – Zn – Ag and Cu deposits, Century Zn – Pb – Ag deposit, Cannington Ag – Pb – Zn deposit, and the Osborne and Ernest Henry iron oxide Cu – Au deposits. Basement rocks were deformed and metamorphosed during the ca 1900 – 1870 Ma Barramundi Orogeny and intruded by the granitic rocks of the ca 1850 Ma Kalkadoon and Ewen Batholiths and their coeval Leichhardt Volcanics. Three stacked and superimposed superbasins evolved between ca 1800 and ca 1595 Ma. These basins evolved in an environment characterised by elevated heat flow and transient episodes of magmatism and basin inversion in an inferred continental backarc setting. The ca 1600 – 1500 Ma Isan Orogeny probably records two phases of orogenesis. The first phase (ca 1600 – 1570 Ma) involved approximately north – south to northwest – southeast shortening in which a northwest-vergent fold-thrust belt evolved in the Eastern Fold Belt and localised basin inversion occurred in the Western Fold Belt. The second phase (ca 1550 – 1500) involved thick-skinned deformation in the Eastern and Western Fold Belts, characterised by upright folding, reverse faulting, and dextral wrenching. Voluminous granites were emplaced throughout the Eastern Fold Belt between ca 1550 and 1500 Ma. Exhumation and cooling of the crustal pile following the Isan Orogeny were related to crustal extension and widespread erosion in eastern and southern Australia. Subtle reactivation of faults within the inlier following the Isan Orogeny records the distal effects of Mesoproterozoic to Neoproterozoic breakup events and orogenesis in central Australia.

Factors affecting fast-ice break-up frequency in Lützow-Holm Bay, Antarctica

AbstractAntarctic fast-ice variation is investigated using satellite images and ship’s ice navigation logs, focusing on break-up phenomena in Lützow-Holm Bay. Although spatio-temporal scales for breakup events vary somewhat for each event, their commencement is generally in autumn and almost always in the same region. Specifically, the 1997/98 break-up event occurred over a wide area and continued for a long time after the initial break-up. Since then, break-ups have recurred until 2004, and a total of 20 annual events have been detected and monitored since 1980. Moreover, information from icebreaker navigation logs shows that unstable fast-ice conditions occurred in the 1980s and after the late 1990s. From the analysis of surface meteorological data and the offshore pack-ice distribution, anomalously shallow snow-cover depths and a peculiar retreat pattern of the ice edge are found to be factors that favour fast-ice break-up. The pack-ice distribution controls the propagation of ocean swell inside the bay; encroaching swells are likely to mechanically disintegrate fast-ice during autumn prior to the annual formation of the protective pack-ice cover to the north. Less snow cover also leads to fast-ice weakening as the melt season progresses and broken floes are then transported offshore by prevailing southerly winds.

Characteristics of Sea-ice thickness and Snow-depth distributions of the Summer landfast ice in Lützow-Holm Bay, East Antarctica

AbstractSea-ice observations have been conducted on board icebreakershiraseas a part of the Scientific programs of the Japanese Antarctic Research Expedition. We Summarize these to investigate Spatial and interannual variability of ice thickness and Snow depth of the Summer landfast ice in Lützow-Holm Bay, East Antarctica. Electromagnetic–inductive observations, which have been conducted Since 2000, provide total thickness distributions with high Spatial resolution. A clear discontinuity, which Separates thin first-year ice from thick multi-year ice, was observed in the total thickness distributions in two voyages. Comparison with Satellite images revealed that Such phenomena reflected the past breakup of the landfast ice. Within 20–30km from the Shore, total thickness as well as Snow depth decrease toward the Shore. This is due to the Snowdrift by the Strong northeasterly wind. Video observations of Sea-ice thickness and Snow depth were conducted on 11 voyages Since December 1987. Probability density functions derived from total thickness distributions in each year are categorized into three types: a thin-ice, thick-ice and intermediate type. Such interannual variability primarily depends on the extent and duration of the Successive break-up events.

Dynamical transport of asteroid fragments from the ν6 resonance

A large disruption in the main asteroid belt can cause a large flux, an “asteroid shower”, on the terrestrial planets. We quantitatively examine the hypothesis that such an event was the cause of the lunar late heavy bombardment (LHB). We performed numerical integrations of about 20,000 test particles starting in the vicinity of the ν 6 secular resonance in the main asteroid belt. The purpose of these integrations is to calculate, for each of the terrestrial planets, the collision probability of asteroids coming from an asteroid break-up event in the inner part of the main belt. Compared with previous studies, we simulate nearly two orders of magnitude larger number of particles, and we include the orbital effects of the eight planets, Mercury to Neptune. We also examined in detail the orbital evolution of asteroid fragments once they enter the Earth’s activity sphere, including the effect of the Earth–Moon orbit. We obtained the collision probability, the distributions of impact velocities, impact positions, and impact angles of asteroid fragments on the Moon. The collision probability with the Moon (∼0.1%) suggests that a fairly large parent body, 1000–1500 km in diameter, is required if the LHB event is to be ascribed to a single asteroid disruption. An even larger parent body is required for less favorable initial conditions than we investigated here. We conclude that an asteroid disruption event is not a viable explanation for the LHB.

On scaling of diffuse–interface models

Application of diffuse–interface models (DIM) yields a system of partial differential equations (PDEs) that generally requires a numerical solution. In the analyses of multiphase flows with DIM usually an artificial enlargement of the interface thickness is required for numerical reasons. Replacing the real interface thickness with a numerically acceptable one, while keeping the surface tension constant, can be justified based on the analysis of the equilibrium planar interface, but demands a change in the local part of the free energy. In a non-equilibrium situation, where the interface position and shape evolve with time, we need to know how to change the mobility in order to still model the same physical problem. Here we approach this question by studying the mixing of two immiscible fluids in a lid-driven cavity flow where the interface between the two fluids is stretched roughly linearly with time, before break-up events start. Scaling based on heuristics, where the mobility is taken inversely proportional to the interface thickness, was found to give fairly well results over the period of linear interface stretching for the range of Péclet numbers and viscosity ratios considered when the capillary number is O(10). None of the scalings studied was, however, able to capture the break-up events accurately.

Atomistic study of the dissolution of small boron interstitial clusters in c-Si

The dissolution of boron-interstitial clusters (BICs) in crystalline silicon, often formed after ion implantation, is investigated by temperature accelerated dynamics of their formation using the Si–B Stillinger-Weber potential. We find that the dominant breakup event for small BICs is the emission of either Si mono- or di-interstitials, though the dominant reaction for the reactivation of boron is via emission of a boron interstitial defect B1I1. Most reactions are well approximated by the assumption that they are diffusion limited. Finally, the rate limiting step for breakup of clusters with three B atoms involves the B3I2 cluster, which also dissolves via emission of B1I1.

Paleomagnetism of the Baiyisi volcanic rocks (ca. 740 Ma) of Tarim, Northwest China: A continental fragment of Neoproterozoic Western Australia?

We report a paleomagnetic pole from the SHRIMP U-Pb zircon dated Baiyisi volcanic rocks in the Xishankou area at the northern edge of the Tarim Block, Northwest China. Rock magnetic and microscopic observations indicate that the characteristic remanent magnetization (ChRM) isolated by both thermal and alternating-field demagnetization is preserved in original single domain (SD) or pseudo-single domain (PSD) low-titanium titanomagnetite grains. The new paleomagnetic pole ( Q = 5) indicates that the Tarim Block was located in equatorial paleolatitudes at ca. 740 Ma and was most likely situated against Western Australia during the most of Neoproterozoic and the early Paleozoic. We suggest that the Tarim Block could be a continental fragment rifted from Western Australia during the break-up event of the Rodinia supercontinent at ca. 820–750 Ma.

Thermal stability of polycrystalline nanowires

Abstract The equilibrium shape of a polycrystalline cylindrical nanowire with bamboo microstructure is determined. It is shown that for a certain ratio of grain boundary and surface energies a critical grain length exists above which the integrity of a nanowire cannot be preserved. Numerical calculations of the kinetics of nanowire shape evolution controlled by surface diffusion are performed. It is shown that the rate of thinning of unstable nanowires in the region of grain boundaries diverges as a break-up event is approached.

Integração de métodos geofísicos na modelagem crustal da Bacia de Santos

A Bacia de Santos e uma bacia de margem passiva gerada durante o Neocomiano, associado com o evento de ruptura do Supercontinente de Gondwana. A espessura da secao sedimentar pode alcancar 15 km, incluindo a sequencia rifte, e foi depositada sobre uma crosta afinada cuja espessura original era de cerca de 35 km. Foi realizada uma modelagem crustal em 8 linhas, aproximadamente perpendiculares ao mergulho deposicional da bacia, objetivando o reconhecimento da geometria da fase rifte e a estimativa do estiramento crustal. Foram utilizados durante a modelagem quatro horizontes sismicos em profundidade, mapas magnetico e gravimetrico alem de dados da profundidade do embasamento magnetico. Foi reconhecido um pronunciado estiramento crustal em toda a bacia (fatores de estiramento crustal variando entre 1.2 e 3.1), evidenciando ampla acomodacao da deformacao. Os resultados da modelagem necessitaram, ainda, de espessas e continuas camadas de rochas vulcânicas para ajuste do modelo. Estas cunhas de rochas vulcânicas, limitadas lateralmente por falhas normais, sao feicoes comuns em bacias rifte. Os resultados da modelagem foram confrontados com dados da profundidade do embasamento magnetico, obtidos anteriormente, e evidenciaram forte correlacao, sobretudo nas areas rasas da bacia.

Determining ice-jam-surge characteristics from measured wave forms

Upon the release of an ice jam, a wave or surge results that generates increased water stages and much higher flow velocities, posing various risks to local river ecology as well as to river structures and riverside communities. The temporal waveform can be easily measured, using water-level sensors, but the hydrodynamic characteristics of the surge, such as celerity, flow velocity, discharge, and shear stress, remain difficult to determine. An analytical method to deduce these parameters is developed herein, based on the equations of motion and plausible approximations for natural stream geometry. Preliminary comparisons with recent field measurements show promising results and demonstrate the degree to which a surge can magnify hydrodynamic forces. The methodology can be used in various applications, such as assessing the severity of a breakup event, estimating flow discharge during the passage of a wave, or evaluating scour potential in ecologically sensitive reaches and at river crossings.Key words: breakup, celerity, equations of motion, ice jam, shear stress, surge, velocity, wave.

Early Palaeozoic crustal melting in an extensional setting: petrological and Sm–Nd evidence from the Izera granite-gneisses, Polish Sudetes

The Izera Block in the West Sudetes, which is composed of granites, gneisses (and transitional granite-gneisses) and minor mica schists, is one of the largest outcrops of Early Palaeozoic (ca. 500 Ma) metagranitoid rocks in the basement units of the Variscides of Central Europe. The Izera granites show S-type features: magmatic cordierite, relict garnet and sillimanite, lack of mafic enclaves, and absence of coexisting tonalites and diorites. The paucity of pegmatites indicates that the granitic magma was relatively dry. The S-type character of these granites is further supported by their peraluminous character (A/CNK 1.0–1.63), high content of normative corundum (up to 3.5%) and relatively high 87Sr /86Sr initial ratio. The chemical variation of these rocks was controlled by the fractional crystallization of plagioclase (CaO, Sr, Eu/Eu*), biotite and cordierite (Al2O3, MgO, FeO), zircon (Zr, Hf) and monazite (REE). Initial eNd values range from −5.2 to −6.9 (mean: −5.9, SD=0.6). These largely negative eNd values imply that the granitic magmas emplaced ca. 500 Ma were extracted from a source reservoir that was strongly enriched in LREE (i.e., with low Sm/Nd ratio) on a time-integrated basis. The relatively consistent depleted mantle model ages (1,730–2,175 Ma; mean: 1,890 Ma) is in agreement with the earlier reported presence of ca. 2.1 Ga old inherited Pb component in zircon from the closely related Rumburk granite. This points to an old (Early Proterozoic) crustal residence age of the inferred metasedimentary protoliths of the Izera granitoids, with only minor contribution to their protoliths of juvenile components of Late Proterozoic/Early Palaeozoic age. Although the Izera granites show some trace element features reminiscent of syn-collisional or post-collisional granitoids, they more likely belong to the broad anorogenic class. Our data corroborate some previous interpretations that granite generation was connected with the Early Palaeozoic rifting of the passive margin of the Saxothuringian block, well documented in the region by bimodal volcanic suites of similar age (Kaczawa Unit, eastern and southern envelope of the Karkonosze–Izera Block). In this scenario, granite magmatism and bimodal volcanism would represent two broadly concomitant effects of a single major event of lithospheric break-up at the northern edge of Gondwana.

Interpretation of size reduction data via moment models

Modeling breakage by a rate kernel that is power-law in particle size and with self-similar daughters yields similarity solutions of the population balance equations. For rate exponents that are inverses of integers, the moments of the similarity solution are easily found. Using a generalized power-law product daughter distribution that is self-similar and obeys the Hill–Ng exchangeability principle provides a very flexible description of the daughters. This paper explores how to interpret milling data to extract the parameters of the model, including the power-law exponent and either the sharpness parameter of the daughter distribution or the number of daughters in a breakup event.

Archaeobatrachian Paraphyly and Pangaean Diversification of Crown-Group Frogs

Current models for the early diversification of living frogs inferred from morphological, ontogenetic, or DNA sequence data invoke very different scenarios of character evolution and biogeography. To explore central controversies on the phylogeny of Anura, we analyzed nearly 4000 base pairs of mitochondrial and nuclear DNA for the major frog lineages. Likelihood-based analyses of this data set are congruent with morphological evidence in supporting a paraphyletic arrangement of archaeobatrachian frogs, with an (Ascaphus + Leiopelma) clade as the sister-group of all other living anurans. The stability of this outcome is reinforced by screening for phylogenetic bias resulting from site-specific rate variation, homoplasy, or the obligatory use of distantly related outgroups. Twenty-one alternative branching and rooting hypotheses were evaluated using a nonparametric multicomparison test and parametric bootstrapping. Relaxed molecular clock estimates situate the emergence of crown-group anurans in the Triassic, approximately 55 million years prior to their first appearance in the fossil record. The existence of at least four extant frog lineages on the supercontinent Pangaea before its breakup gains support from the estimation that three early splits between Laurasia- and Gondwana-associated families coincide with the initial rifting of these landmasses. This observation outlines the potential significance of this breakup event in the formation of separate Mesozoic faunal assemblages in both hemispheres.

An Algorithm for the Orbital Evolution of Space Debris from Breakup Events

Space debris created by man's space activities has brought great risks to launch and operation of spacecrafts, especially in the following few years, there will be more and more space activities in the world. So it is necessary to know situation of current space debris environment and predict its development in the future, thus to provide important reference to protection design and operation of spacecrafts and measures of diminishing amount of space debris. An important component of the debris population that is presented in this paper is the debris generated by on-orbit breakup events. It is collision and explosion event that inflames most the increasing rate of the total amount of the space debris. Breakup events include collision and explosion events. Consequently the ability to model different breakup events is a vital part of a long-term debris environment model. In this paper, the orbital evolution of space debris from the spacecraft breakups has been done a through mathematical analysis. A detailed research on the mechanisms of space debris generation, evolution and annihilation from the view point of evolutionary mode is also given. The velocity increments of space debris from spacecraft breakups are presented. Based on the velocity increments, the orbital elements of space debris are gained. Then the cumulative number and orbital distribution of space debris are analyzed due to atmospheric drag perturbation. Finally, the relevant results are gave and compared with the results of CODRM. The results indicate the feasibility of the algorithm.