Freely Expanding X-ray Ejecta Knots in Kepler's Supernova Remnant
Hughes, John Patrick; Sato, Toshiki
2017-08-01
Using archival data from the Chandra X-ray Observatory, we measure the proper motions and radial velocities of compact X-ray bright knots in Kepler's supernova remnant (SNR). The high speed ejecta knots are morphologically and kinematically distinct from the rest of the ejecta and appear only in specific, limited locations. The highest speed knots show both large proper motions and high radial velocities with estimated space velocities of 10,000 km/s, similar to the typical Si velocity seen in Type Ia supernovae near maximum light. The proper motions of five knots extrapolate back over the age of the remnant to a consistent central position, defining a kinematic center for Kepler's SNR. Our new explosion center agrees well with previous determinations, but suffers less from systematic uncertainty. These five knots are expanding at close to the free expansion rate (expansion indices of 0.75 speeds and expansion indices consistent with decelerated ejecta knots. The differences in the expansion rates are likely a function of differences in the ambient medium density surrounding Kepler’s SNR.
A DECADE-BASELINE STUDY OF THE PLASMA STATES OF EJECTA KNOTS IN CASSIOPEIA A
Rutherford, John; Dewey, Daniel; Figueroa-Feliciano, Enectali; Heine, Sarah N. T.; Canizares, C. R.; Bastien, Fabienne A.; Sato, Kosuke, E-mail: enectali@mit.edu, E-mail: jmrv@mit.edu [Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2013-05-20
We present the analysis of 21 bright X-ray knots in the Cassiopeia A supernova remnant from observations spanning 10 yr. We performed a comprehensive set of measurements to reveal the kinematic and thermal state of the plasma in each knot, using a combined analysis of two high energy resolution High Energy Transmission Grating (HETG) and four medium energy resolution Advanced CCD Imaging Spectrometer (ACIS) sets of spectra. The ACIS electron temperature estimates agree with the HETG-derived values for approximately half of the knots studied, yielding one of the first comparisons between high resolution temperature estimates and ACIS-derived temperatures. We did not observe the expected spectral evolution-predicted from the ionization age and density estimates for each knot-in all but three of the knots studied. The incompatibility of these measurements with our assumptions has led us to propose a dissociated ejecta model, with the metals unmixed inside the knots, which could place strong constraints on supernova mixing models.
Effects of knots on protein folding properties.
Miguel A Soler
Full Text Available This work explores the impact of knots, knot depth and motif of the threading terminus in protein folding properties (kinetics, thermodynamics and mechanism via extensive Monte Carlo simulations of lattice models. A knotted backbone has no effect on protein thermodynamic stability but it may affect key aspects of folding kinetics. In this regard, we found clear evidence for a functional advantage of knots: knots enhance kinetic stability because a knotted protein unfolds at a distinctively slower rate than its unknotted counterpart. However, an increase in knot deepness does not necessarily lead to more effective changes in folding properties. In this regard, a terminus with a non-trivial conformation (e.g. hairpin can have a more dramatic effect in enhancing kinetic stability than knot depth. Nevertheless, our results suggest that the probability of the denatured ensemble to keep knotted is higher for proteins with deeper knots, indicating that knot depth plays a role in determining the topology of the denatured state. Refolding simulations starting from denatured knotted conformations show that not every knot is able to nucleate folding and further indicate that the formation of the knotting loop is a key event in the folding of knotted trefoils. They also show that there are specific native contacts within the knotted core that are crucial to keep a native knotting loop in denatured conformations which otherwise have no detectable structure. The study of the knotting mechanism reveals that the threading of the knotting loop generally occurs towards late folding in conformations that exhibit a significant degree of structural consolidation.
Duality properties of indicatrices of knots
Adams, Colin; Hawkins, Katherine; Sia, Charmaine; Silversmith, Robert; Tshishiku, Bena
2012-01-01
The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.
Material Properties of Wire for the Fabrication of Knotted Fences
Dirk J. Pons
2014-01-01
Full Text Available This paper describes the materials properties of galvanised fencing wire, as used in the fabrication of knotted wire fences. A range of physical properties are investigated: tensile strength, ductility in tension, Young’s modulus, three-point bending, and bending span. A range of commercially available wire products were tested. The results show that most, but not all, high tensile wire samples met the minimum tensile and ductility requirements. Young’s modulus results failed to provide any meaningful insights into wire quality. Flexural modulus results also failed to provide any insight into wire quality issues, with no statistically significant differences existing between acceptable and problematic wire batches. The implications are that premature fence failures are unlikely to be caused solely by reduced tensile properties. Existing test methods, including tensile strength and ductility, are somewhat incomplete, perhaps even unreliable, as measures of wire quality.
Lunar crater ejecta: Physical properties revealed by radar and thermal infrared observations
Ghent, R. R.; Carter, L. M.; Bandfield, J. L.; Tai Udovicic, C. J.; Campbell, B. A.
2016-07-01
We investigate the physical properties, and changes through time, of lunar impact ejecta using radar and thermal infrared data. We use data from two instruments on the Lunar Reconnaissance Orbiter (LRO) - the Diviner thermal radiometer and the Miniature Radio Frequency (Mini-RF) radar instrument - together with Earth-based radar observations. We use this multiwavelength intercomparison to constrain block sizes and to distinguish surface from buried rocks in proximal ejecta deposits. We find that radar-detectable rocks buried within the upper meter of regolith can remain undisturbed by surface processes such as micrometeorite bombardment for >3 Gyr. We also investigate the thermophysical properties of radar-dark haloes, comprised of fine-grained, rock-poor ejecta distal to the blocky proximal ejecta. Using Diviner data, we confirm that the halo material is depleted in surface rocks, but show that it is otherwise thermophysically indistinct from background regolith. We also find that radar-dark haloes, like the blocky ejecta, remain visible in radar observations for craters with ages >3 Ga, indicating that regolith overturn processes cannot replenish their block populations on that timescale.
Discovery of Outlying, High-Velocity Oxygen-Rich Ejecta in Cassiopeia A
Fesen, R A; Morse, J; Chevalier, R A; Borkowski, K J; Dopita, M A; Gerardy, C L; Lawrence, S S; Raymond, J C; Van den Bergh, S
2006-01-01
Hubble Space Telescope images of the young Galactic supernova remnant Cassiopeia A reveal a far larger population of outlying, high-velocity knots of ejecta with a broader range of chemical properties than previously suspected. We identify three main classes of outer ejecta: 1) Knots dominated by [N II] 6548,6583 emission; 2) Knots dominated by oxygen emission lines especially [O II] 7319,7330; and 3) Knots with emission line strengths similar to the [S II] strong FMK ejecta commonly seen in the main emission shell. The discovery of a significant population of O-rich ejecta situated in between the suspected N-rich outer photospheric layer and S-rich FMK-like ejecta suggests that the Cas A progenitor's chemical layers were not completely disrupted by the supernova explosion outside of the remnant's NE and SW high velocity `jet' regions. In addition, we find the majority of O-rich outer ejecta at projected locations out beyond (v = 6500 - 9000 km/s) the remnant's fastest moving Fe-rich X-ray emission material (...
Asteroid Impact Deflection and Assessment (AIDA) mission - Properties of Impact Ejecta
Hamilton, Douglas P.; Fahnestock, Eugene G.; Schwartz, Stephen R.; Murdoch, Naomi; Asphaug, Erik; Cheng, Andrew F.; Housen, Kevin R.; Michel, Patrick; Miller, Paul L.; Stickle, Angela; Tancredi, Gonzalo; Vincent, Jean-Baptiste; Wuennemann, Kai; Yu, Yang; AIDA Impact Simulation Working Group
2016-10-01
The Asteroid Impact Deflection and Assessment (AIDA) mission is composed of NASA's Double Asteroid Redirection Test (DART) mission and ESA's Asteroid Impact Monitor (AIM) rendezvous mission. The DART spacecraft is designed to impact the small satellite of near-Earth asteroid 65803 Didymos in October 2022, while the in-situ AIM spacecraft observes. AIDA's Modeling and Simulation of Impact Outcomes Working Group is tasked with investigating properties of the debris ejected from the impact. The orbital evolution of this ejecta has important implications for observations that the AIM spacecraft will take as well as for the safety of the spacecraft itself. Ejecta properties including particle sizes, bulk densities, and velocities all depend on the poorly-known physical properties of Didymos' moon. The moon's density, internal strength, and especially its porosity have a strong effect on all ejecta properties. Making a range of assumptions, we perform a suite of numerical simulations to determine the fate of the ejected material; we will use simulation predictions to optimize AIM observations and safety. Ultimately, combining AIM's observations of the ejecta with detailed numerical simulations will help constrain key satellite parameters.We use distinct types of numerical tools to explore ejecta properties based on additional target parameters (different forms of friction, cohesion), e.g., the shock physics code iSALE, smoothed particle hydrodynamics codes, and the granular code PKDGRAV. Given the large discrepancy between the 6 km/s impact speed of DART and the moon's 6 cm/s escape speed, a great challenge will be to determine properties of the low-speed ejecta. Very low-speed material relevant to the safety of the AIM spacecraft and its ability to conduct its observations may loft from the crater at late stages of the impact process, or from other locations far from the impact site due to seismic energy propagation. The manner in which seismic waves manifests in
Myagkov, N. N.; Shumikhin, T. A.; Bezrukov, L. N.
2013-08-01
The series of impact experiments were performed to study the properties of ejecta generated at high-velocity perforation of thin bumpers. The bumpers were aluminum plates, fiber-glass plastic plates, and meshes weaved of steel wire. The projectiles were 6.35 mm diameter aluminum spheres. The impact velocities ranged from 1.95 to 3.52 km/s. In the experiments the ejecta particles were captured with low-density foam collectors or registered with the use of aluminum foils. The processing of the experimental results allowed us to estimate the total masses, spatial and size distributions, and perforating abilities of the ejecta produced from these different bumpers. As applied to the problem of reducing the near-Earth space pollution caused by the ejecta, the results obtained argue against the use of aluminum plates as first (outer) bumper in spacecraft shield protection.
The Links Between Target Properties and Layered Ejecta Craters in Acidalia and Utopia Planitiae Mars
Jones, E.; Osinski, G. R.
2013-08-01
Layered ejecta craters on Mars may form from excavation into subsurface volatiles. We examine a new catalogue of martian craters to decipher differences between the single- and double-layered ejecta populations in Acidalia and Utopia.
Yacov Kantov
2005-06-01
Knots and topological entanglements play an important role in the statistical mechanics of polymers. While topological entanglement is a global property, it is possible to study the size of a knotted region both numerically and analytically. It can be shown that long-range repulsive interactions, as well as entropy favor small knots in dilute systems. However, in dense systems and at the -point in two dimensions the uncontracted knot configuration is the most likely.
Fujibayashi, Sho; Sekiguchi, Yuichiro; Kiuchi, Kenta; Shibata, Masaru
2017-09-01
We performed general relativistic, long-term, axisymmetric neutrino radiation hydrodynamics simulations for the remnant formed after a binary neutron star merger, which consists of a massive neutron star and a torus surrounding it. As an initial condition, we employ the result derived in a three-dimensional, numerical relativity simulation for the binary neutron star merger. We investigate the properties of neutrino-driven ejecta. Due to the pair-annihilation heating, the dynamics of the neutrino-driven ejecta are significantly modified. The kinetic energy of the ejecta is about two times larger than that in the absence of pair-annihilation heating. This suggests that the pair-annihilation heating plays an important role in the evolution of merger remnants. The relativistic outflow, which is required for driving gamma-ray bursts, is not observed because the specific heating rate around the rotational axis is not sufficiently high, due to the baryon loading caused by the neutrino-driven ejecta from the massive neutron star. We discuss the condition for launching the relativistic outflow and the nucleosynthesis in the ejecta.
Properties of Ejecta Blanket Deposits Surrounding Morasko Meteorite Impact Craters (Poland)
Szokaluk, M.; Muszyński, A.; Jagodziński, R.; Szczuciński, W.
2016-08-01
Morasko impact craters are a record of the fall of a meteorite into the soft sediments. The presented results illustrate the geological structure of the area around the crater as well as providing evidence of the occurrence of ejecta blanket.
The properties of conformal blocks, the AGT hypothesis, and knot polynomials
Morozov, A. A.
2016-09-01
Various properties of correlators of the two-dimensional conformal field theory are discussed. Specifically, their relation to the partition function of the four-dimensional supersymmetric theory is analyzed. In addition to being of interest in its own right, this relation is of practical importance. For example, it is much easier to calculate the known expressions for the partition function of supersymmetric theory than to calculate directly the expressions for correlators in conformal theory. The examined representation of conformal theory correlators as a matrix model serves the same purpose. The integral form of these correlators allows one to generalize the obtained results for the Virasoro algebra to more complicated cases of the W algebra or the quantum Virasoro algebra. This provides an opportunity to examine more complex configurations in conformal field theory. The three-dimensional Chern-Simons theory is discussed in the second part of the present review. The current interest in this theory stems largely from its relation to the mathematical knot theory (a rather well-developed area of mathematics known since the 17th century). The primary objective of this theory is to develop an algorithm that allows one to distinguish different knots (closed loops in three-dimensional space). The basic way to do this is by constructing the so-called knot invariants.
Proteins analysed as virtual knots
Alexander, Keith; Dennis, Mark R
2016-01-01
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or disappear rapidly under manipulation and interaction. Knotting has been previously identified in protein backbone chains, for which these mechanical constraints are of fundamental importance to their molecular functionality, despite their being open curves in which the knots are not mathematically well defined; knotting can only be identified by closing the termini of the chain somehow. We introduce a new method for resolving knotting in open curves using virtual knots, a wider class of topological objects that do not require a classical closure and so naturally capture the topological ambiguity inherent in open curves. We describe the results of analysing proteins in the Protein Data Bank by this new scheme, recovering and extending previous knotting results, and identify...
Safavieh, Roozbeh; Zhou, Gina Z; Juncker, David
2011-08-07
We present and characterize cotton yarn and knots as building blocks for making microfluidic circuits from the bottom up. The yarn used is made up of 200-300 fibres, each with a lumen. Liquid applied at the extremity of the yarn spontaneously wets the yarn, and the wetted length increases linearly over time in untreated yarn, but progresses according to a square root relationship as described by Washburn's equation upon plasma activation of the yarn. Knots are proposed for combining, mixing and splitting streams of fluids. Interestingly, the topology of the knot controls the mixing ratio of two inlet streams into two outlet yarns, and thus the ratio can be adjusted by choosing a specific knot. The flow resistance of a knot is shown to depend on the force used to tighten it and the flow resistance rapidly increases for single-stranded knots, but remains low for double-stranded knots. Finally, a serial dilutor is made with a web made of yarns and double-stranded overhand knots. These results suggest that yarn and knots may be used to build low cost microfluidic circuits.
OKeefe, John D.; Stewart, Sarah T.; Ahrens, Thomas J.
2001-01-01
We modeled in detail the ejecta dynamics associated with the Chicxulub impact. We determined: (1) ejecta trajectories, (2) stratigraphic motions, (3) depth of ejecta stages, (4) thermodynamic histories of the ejecta particles, and (5) the final ejecta distribution. Additional information is contained in the original extended abstract.
Knot theory in modern chemistry.
Horner, Kate E; Miller, Mark A; Steed, Jonathan W; Sutcliffe, Paul M
2016-11-21
Knot theory is a branch of pure mathematics, but it is increasingly being applied in a variety of sciences. Knots appear in chemistry, not only in synthetic molecular design, but also in an array of materials and media, including some not traditionally associated with knots. Mathematics and chemistry can now be used synergistically to identify, characterise and create knots, as well as to understand and predict their physical properties. This tutorial review provides a brief introduction to the mathematics of knots and related topological concepts in the context of the chemical sciences. We then survey the broad range of applications of the theory to contemporary research in the field.
Dessart, Luc; Woosley, Stan; Livne, Eli; Waldman, Roni; Yoon, Sung-Chul; Langer, Norbert
2016-01-01
We present 1-D non-Local-Thermodynamic-Equilibrium time-dependent radiative-transfer simulations for a large grid of supernovae (SNe) IIb/Ib/Ic that result from the terminal explosion of the mass donor in a close-binary system. Our sample covers ejecta masses $M_{\\rm e}$ of 1.7$-$5.2M$_\\odot$, kinetic energies $E_{\\rm kin}$ of 0.6$-$5.0$\\times$10$^{51}$erg, and $^{56}$Ni masses of 0.05$-$0.30M$_\\odot$. We find a strong correlation between the $^{56}$Ni mass and the photometric properties at maximum, and between the rise time to bolometric maximum and the post-maximum decline rate. We confirm the small scatter in ($V-R$) at 10d past $R$-band maximum. The quantity $V_{\\rm m} \\equiv \\sqrt{2E_{\\rm kin}/M_{\\rm e}}$ is comparable to the Doppler velocity measured from HeI 5875\\AA\\ at maximum in SNe IIb/Ib, although some scatter arises from the uncertain level of chemical mixing. The OI7772\\AA\\ line may be used for SNe Ic, but the correspondence deteriorates with higher ejecta mass/energy. We identify a temporal reve...
2003-01-01
[figure removed for brevity, see original site] Released 4 September 2003In the heavily cratered southern highlands of Mars, the type of crater seen in this THEMIS visible image is relatively rare. Elliptical craters with 'butterfly' ejecta patterns make up roughly 5% of the total crater population of Mars. They are caused by impactors which hit the surface at oblique, or very shallow angles. Similar craters are also seen in about the same abundance on the Moon and Venus.Image information: VIS instrument. Latitude -24.6, Longitude 41 East (319 West). 19 meter/pixel resolution.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
2003-01-01
[figure removed for brevity, see original site] Released 4 September 2003In the heavily cratered southern highlands of Mars, the type of crater seen in this THEMIS visible image is relatively rare. Elliptical craters with 'butterfly' ejecta patterns make up roughly 5% of the total crater population of Mars. They are caused by impactors which hit the surface at oblique, or very shallow angles. Similar craters are also seen in about the same abundance on the Moon and Venus.Image information: VIS instrument. Latitude -24.6, Longitude 41 East (319 West). 19 meter/pixel resolution.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
Proteins analysed as virtual knots
Alexander, Keith; Taylor, Alexander J.; Dennis, Mark R.
2017-02-01
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or disappear rapidly under manipulation and interaction. Knotting has been previously identified in protein backbone chains, for which these mechanical constraints are of fundamental importance to their molecular functionality, despite their being open curves in which the knots are not mathematically well defined; knotting can only be identified by closing the termini of the chain somehow. We introduce a new method for resolving knotting in open curves using virtual knots, which are a wider class of topological objects that do not require a classical closure and so naturally capture the topological ambiguity inherent in open curves. We describe the results of analysing proteins in the Protein Data Bank by this new scheme, recovering and extending previous knotting results, and identifying topological interest in some new cases. The statistics of virtual knots in protein chains are compared with those of open random walks and Hamiltonian subchains on cubic lattices, identifying a regime of open curves in which the virtual knotting description is likely to be important.
Proteins analysed as virtual knots
Alexander, Keith; Taylor, Alexander J.; Dennis, Mark R.
2017-01-01
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or disappear rapidly under manipulation and interaction. Knotting has been previously identified in protein backbone chains, for which these mechanical constraints are of fundamental importance to their molecular functionality, despite their being open curves in which the knots are not mathematically well defined; knotting can only be identified by closing the termini of the chain somehow. We introduce a new method for resolving knotting in open curves using virtual knots, which are a wider class of topological objects that do not require a classical closure and so naturally capture the topological ambiguity inherent in open curves. We describe the results of analysing proteins in the Protein Data Bank by this new scheme, recovering and extending previous knotting results, and identifying topological interest in some new cases. The statistics of virtual knots in protein chains are compared with those of open random walks and Hamiltonian subchains on cubic lattices, identifying a regime of open curves in which the virtual knotting description is likely to be important. PMID:28205562
2004-01-01
[figure removed for brevity, see original site] Released 15 July 2004 The atmosphere of Mars is a dynamic system. Water-ice clouds, fog, and hazes can make imaging the surface from space difficult. Dust storms can grow from local disturbances to global sizes, through which imaging is impossible. Seasonal temperature changes are the usual drivers in cloud and dust storm development and growth. Eons of atmospheric dust storm activity has left its mark on the surface of Mars. Dust carried aloft by the wind has settled out on every available surface; sand dunes have been created and moved by centuries of wind; and the effect of continual sand-blasting has modified many regions of Mars, creating yardangs and other unusual surface forms. The yardangs in today's image are the remains of the rim and ejecta of the large impact crater at the top right of the image. The black pixels are due to exposure saturation. Image information: VIS instrument. Latitude -1.9, Longitude 152.8 East (207.2 West). 19 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter
Friedman, Greg
2004-01-01
This is an introduction to the construction of higher-dimensional knots by spinning methods. Simple spinning of classical knots was introduced by E. Artin in 1926, and several generalizations have followed. These include twist spinning, superspinning or p-spinning, frame spinning, roll spinning, and deform spinning. We survey these constructions and some of their most important applications, as well as some newer hybrids due to the author. The exposition, meant to be accessible to a broad aud...
How to fold intricately: using theory and experiments to unravel the properties of knotted proteins
Jackson, Sophie E; Micheletti, Cristian
2016-01-01
Over the years, advances in experimental and computational methods have helped us to understand the role of thermodynamic, kinetic and active (chaperone-aided) effects in coordinating the folding steps required to achieving a knotted native state. Here, we review such developments by paying particular attention to the complementarity of experimental and computational studies. Key open issues that could be tackled with either or both approaches are finally pointed out.
Ejecta evolution during cone impact
Marston, Jeremy; Vakarelski, Ivan; Thoroddsen, Sigurdur
2013-11-01
We present results from an experimental study of the impact of conical shaped bodies into a pool of liquid. By varying the cone angle, impact speed and liquid physical properties, we examine a broad parameter space and seek to find conditions when self-similarity can be observed during this phenomena. We use high-speed imaging to capture the early-time motion of the liquid ejecta which emanates from the tip of the cone and travels up along the cone surface. Surprisingly, we find that the detachment of the ejecta can be simply described by air entrainment relationships derived from coating experiments.
Ejecta evolution during cone impact
Marston, Jeremy
2014-07-07
We present findings from an experimental investigation into the impact of solid cone-shaped bodies onto liquid pools. Using a variety of cone angles and liquid physical properties, we show that the ejecta formed during the impact exhibits self-similarity for all impact speeds for very low surface tension liquids, whilst for high-surface tension liquids similarity is only achieved at high impact speeds. We find that the ejecta tip can detach from the cone and that this phenomenon can be attributed to the air entrainment phenomenon. We analyse of a range of cone angles, including some ogive cones, and impact speeds in terms of the spatiotemporal evolution of the ejecta tip. Using superhydrophobic cones, we also examine the entry of cones which entrain an air layer.
Nullification of knots and links
Diao, Yuanan; Montemayor, Anthony
2011-01-01
In this paper, we study a geometric/topological measure of knots and links called the nullification number. The nullification of knots/links is believed to be biologically relevant. For example, in DNA topology, one can intuitively regard it as a way to measure how easily a knotted circular DNA can unknot itself through recombination of its DNA strands. It turns out that there are several different ways to define such a number. These definitions lead to nullification numbers that are related, but different. Our aim is to explore the mathematical properties of these nullification numbers. First, we give specific examples to show that the nullification numbers we defined are different. We provide detailed analysis of the nullification numbers for the well known 2-bridge knots and links. We also explore the relationships among the three nullification numbers, as well as their relationships with other knot invariants. Finally, we study a special class of links, namely those links whose general nullification numbe...
Werle, M; Kafedjiiski, K; Kolmar, H; Bernkop-Schnürch, A
2007-03-06
Cystine-knot microproteins exhibit several properties that make them highly interesting as scaffolds for oral peptide drug delivery. It was therefore the aim of the study to evaluate the novel clinically relevant cystine-knot microprotein McoEeTI regarding its potential for oral delivery. Additionally, based on the gained results, important features of McoEeTI were improved. Enzymatic degradation was caused by chymotrypsin, trypsin and porcine small intestinal juice whereas McoEeTI was stable towards elastase, membrane bound proteases, pepsin and porcine gastric juice. Only minor McoEeTI degradation was observed during a 24h incubation period in rat plasma. In the presence of various physiological ions about 50% of McoEeTI formed di- and/or trimers. P(app) value of McoEeTI was determined to be (7.4+/-0.4)x10(-6)cm/s. Sodium caprate and polycarbophil-cysteine (PCP-Cys) had no beneficial effect on McoEeTI permeation, whereas the utilization of a chitosan-thiobutylamidine (Chito-TBA) system improved McoEeTI permeation 3-fold. Enzymatic stability could be strongly improved by the utilization of Bowman-Birk-Inhibitor (BBI) as well as PCP-Cys. In conclusion, this study indicates that McoEeTI represents a promising candidate as a novel scaffold for oral peptide drug delivery.
Henrich, Allison; Narayan, Sneha; Pechenik, Oliver; Silversmith, Robert; Townsend, Jennifer
2010-01-01
In this paper, we introduce playing games on shadows of knots. We demonstrate two novel games, namely, To Knot or Not to Knot and Much Ado about Knotting. We also discuss winning strategies for these games on certain families of knot shadows. Finally, we suggest variations of these games for further study.
Studying uniform thickness II: Transversely nonsimple iterated torus knots
LaFountain, Douglas
2011-01-01
We prove that an iterated torus knot type in the standard contact 3-sphere fails the uniform thickness property (UTP) if and only if it is formed from repeated positive cablings, which is precisely when an iterated torus knot supports the standard contact structure. This is the first complete UTP...... classification for a large class of knots. We also show that all iterated torus knots that fail the UTP support cabling knot types that are transversely non-simple....
Mechanical Normal Forms of Knots and Flat Knots
Sossinsky, A B
2010-01-01
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely determined (up to isometry) normal form at least when the original knot diagram has a small number of crossings, thus outperforming the famous M\\"obius energy due to Jun O'Hara and studied by Michael Freedman et al. Various properties of the device are described (under certain conditions it does the Reidemeister and Markov moves, it beautifully performs the Whitney trick by uniformizing its own local curvature). If the device is constrained between two parallel planes (e.g. glass panes), it yields a real life model of a flat knot (class of knot diagrams equivalent under Reidemeister $\\Omega_2$ and $\\Omega_3$ moves) also leading to uniquely determined "flat normal forms" (for a small number of crossing points of the given flat knot diagram). The paper concludes with two mathematical theorems, one reducing the knot recognition problem t...
X-RAY EJECTA KINEMATICS OF THE GALACTIC CORE-COLLAPSE SUPERNOVA REMNANT G292.0+1.8
Bhalerao, Jayant; Park, Sangwook [Department of Physics, University of Texas at Arlington, P.O. Box 19059, Arlington, TX 76019 (United States); Dewey, Daniel [MIT Kavli Institute, Cambridge, MA 02139 (United States); Hughes, John P. [Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854-8019 (United States); Mori, Koji [Department of Applied Physics, University of Miyazaki, 1-1 Gakuen Kibanadai-nishi, Miyazaki 889-2192 (Japan); Lee, Jae-Joon, E-mail: jayant.bhalerao@mavs.uta.edu [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of)
2015-02-10
We report on the results from the analysis of our 114 ks Chandra High Energy Transmision Grating Spectrometer observation of the Galactic core-collapse supernova remnant G292.0+1.8. To probe the three-dimensional structure of the clumpy X-ray emitting ejecta material in this remnant, we measured Doppler shifts in emission lines from metal-rich ejecta knots projected at different radial distances from the expansion center. We estimate radial velocities of ejecta knots in the range of –2300 ≲ v{sub r} ≲ 1400 km s{sup –1}. The distribution of ejecta knots in velocity versus projected-radius space suggests an expanding ejecta shell with a projected angular thickness of ∼90'' (corresponding to ∼3 pc at d = 6 kpc). Based on this geometrical distribution of the ejecta knots, we estimate the location of the reverse shock approximately at the distance of ∼4 pc from the center of the supernova remnant, putting it in close proximity to the outer boundary of the radio pulsar wind nebula. Based on our observed remnant dynamics and the standard explosion energy of 10{sup 51} erg, we estimate the total ejecta mass to be ≲8 M {sub ☉}, and we propose an upper limit of ≲35 M {sub ☉} on the progenitor's mass.
An HST Survey of the Highest-Velocity Ejecta in Cassiopeia A
Fesen, Robert A
2015-01-01
We present Hubble Space Telescope WFC3/IR images of the Cassiopeia A supernova remnant that survey its high-velocity, S-rich debris in the NE jet and SW counterjet regions through [S III] 9069, 9531 and [S II] 10,287 - 10,370 line emissions. We identify nearly 3400 sulfur emitting knots concentrated in ~120 degree wide opposing streams, almost triple the number previously known. The vast majority of these ejecta knots lie at projected distances well out ahead of the remnant's forward blast wave and main shell ejecta, extending to angular distance of 320" to the NE and 260" to the SW from the center of expansion. Such angular distances imply undecelerated ejecta knot transverse velocities of 15,600 and 12,700 km/s respectively, assuming an explosion date ~1670 AD and a distance of 3.4 kpc. Optical spectra of knots near the outermost tip of the NE ejecta stream show strong emission lines of S, Ca, and Ar. We estimate a total mass ~0.1 Msun and a kinetic energy of at least ~1 x10^50 erg for S-rich ejecta in the ...
Practical and ornamental knots
Shaw, George Russell
2008-01-01
For centuries, everyone from sailors, fishermen, and cowboys to explorers, hunters, and mountaineers have known about - and relied on - the indispensable knot. Many of them also knew that the diversity of knot crafting was limited only by the imagination. In this classic guide, George Russell Shaw reveals the unlimited potential of the knot as not only a basic tool, but as a beautiful work of art.Filled with easy-to-follow and accurate instructions on creating scores of useful and decorative knots, 193 hand-drawn illustrations will guide you in creating: Braids Angler Knots Japanese Knots L
Interstellar and Ejecta Dust in the Cas A Supernova Remnant
Arendt, Richard G.; Dwek, Eli; Kober, Gladys; Rho, Jonghee; Hwang, Una
2013-01-01
The ejecta of the Cas A supernova remnant has a complex morphology, consisting of dense fast-moving line emitting knots and diffuse X-ray emitting regions that have encountered the reverse shock, as well as more slowly expanding, unshocked regions of the ejecta. Using the Spitzer 5-35 micron IRS data cube, and Herschel 70, 100, and 160 micron PACS data, we decompose the infrared emission from the remnant into distinct spectral components associated with the different regions of the ejecta. Such decomposition allows the association of different dust species with ejecta layers that underwent distinct nuclear burning histories, and determination of the dust heating mechanisms. Our decomposition identified three characteristic dust spectra. The first, most luminous one, exhibits strong emission features at approx. 9 and 21 micron, and a weaker 12 micron feature, and is closely associated with the ejecta knots that have strong [Ar II] 6.99 micron and [Ar III] 8.99 micron emission lines. The dust features can be reproduced by magnesium silicate grains with relatively low MgO-to-SiO2 ratios. A second, very different dust spectrum that has no indication of any silicate features, is best fit by Al2O3 dust and is found in association with ejecta having strong [Ne II] 12.8 micron and [Ne III] 15.6 micron emission lines. A third characteristic dust spectrum shows features that best matched by magnesium silicates with relatively high MgO-to-SiO2 ratio. This dust is primarily associated with the X-ray emitting shocked ejecta and the shocked interstellar/circumstellar material. All three spectral components include an additional featureless cold dust component of unknown composition. Colder dust of indeterminate composition is associated with [Si II] 34.8 micron emission from the interior of the SNR, where the reverse shock has not yet swept up and heated the ejecta. The dust mass giving rise to the warm dust component is about approx. 0.1solar M. However, most of the dust mass
Star-formation knots in IRAS galaxies
Hutchings, J B
1995-01-01
Images of IRAS galaxies with a range of IR properties are examined for bright knots, both within and outside the galaxy. These are found almost exclusively in galaxies with steep IR spectra, but over a wide range of IR luminosity, and usually without strong nuclear activity. In most cases, the knots are likely to be star-formation induced by tidal interactions, and are seen in the early stages of such interactions. Detailed photometry is presented of knots in six representative galaxies. The knots appear to have a wide range of colour and luminosity, but it is argued that many are heavily reddened. Knots formed outside the parent galaxy may be a new generation of what later become globular clusters, but they appear to have a wide range of luminosities.
Rolfsen, Dale
2003-01-01
Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners with a basic background find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide
Menasco, William
2005-01-01
This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry.* Survey of mathematical knot theory* Articles by leading world authorities* Clear exposition, not over-technical* Accessible to readers with undergraduate background in mathematics
Avoine, Xytilis; Lussier, Bertrand; Brailovski, Vladimir; Inaekyan, Karine; Beauchamp, Guy
2016-04-01
The influence of the type of material used, knot configuration, and use of an additional throw on the tensile force at failure, the elongation, and the mode of failure of different configurations of linear sutures and knotted suture loops was evaluated in this in-vitro mechanical study. We hypothesized that all types of knots would significantly influence the initial force and elongation of suture materials and would influence the force and elongation at which the knotted loops break, but not their mode of failure. A total of 432 samples of 4 types of size 3-0 suture material (polydioxanone, polyglecaprone 25, polyglactin 910, and nylon), representing 9 configurations, were tested in a tensiometer. The configurations were 1 linear suture without a knot and the following loops: square (SQ) knot; surgeon's (SU) knot; granny (GR) knot; and sliding half-hitch (SHH) knot using either 4 and 5 or 3 and 4 throws, depending on the material. For polydioxanone, SQ and SU knots did not decrease the initial force at failure of the suture. Granny (GR) and SHH knots decreased the tensile force at failure and elongation by premature failure of the loop. For polyglecaprone 25, all knots decreased the initial force at failure of the suture, with SHH being weaker than the other knots. For coated polyglactin 910, all knots decreased the initial force at failure of the suture and slippage increased significantly compared with the other 3 sutures. The use of SQ knots with 3 throws did not result in a safe knot. For nylon, knots did not alter the original mechanics of the suture. In conclusion, all knots and types of suture material do not necessarily have the same effect on the initial tensile force at failure of suture materials.
Cherchneff, Isabelle
2011-01-01
The first molecules detected at infrared wavelengths in the ejecta of a Type II supernova, namely SN1987A, consisted of CO and SiO. Since then, confirmation of the formation of these two species in several other supernovae a few hundred days after explosion has been obtained. However, supernova environments appear to hamper the synthesis of large, complex species due to the lack of microscopically-mixed hydrogen deep in supernova cores. Because these environments also form carbon and silicate dust, it is of importance to understand the role played by molecules in the depletion of elements and how chemical species get incorporated into dust grains. In the present paper, we review our current knowledge of the molecular component of supernova ejecta, and present new trends and results on the synthesis of molecules in these harsh, explosive events.
Tabulating knot polynomials for arborescent knots
Mironov, A; Morozov, An; Sleptsov, A; Ramadevi, P; Singh, Vivek Kumar
2016-01-01
Arborescent knots are the ones which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present knowledge is enough for lifting topological description to the level of effective analytical formulas. The paper describes the origin and structure of the new tables of colored knot polynomials, which will be posted at the dedicated site. Even if formal expressions are known in terms of modular transformation matrices, the computation in finite time requires additional ideas. We use the "family" approach, and apply it to arborescent knots in Rolfsen table by developing a Feynman diagram technique, associated with an auxiliary matrix model field theory. Gauge invariance in this theory helps to provide meaning to Racah matrices in the case of non-trivial multiplicities and explains the need for peculiar sign prescriptions in the calculation of [21]-colored HOMFLY polynomials.
Discovery of Outlying, High-Velocity O-Rich Ejecta in Cas A
Fesen, R.; Hammell, M.; Morse, J.; Borkowski, K.; Chevalier, R.; Dopita, M.; Lawrence, S.; Raymond, J.; van den Bergh, S.
2004-12-01
We present Hubble Space Telescope WFPC2 and ACS images of the Galactic supernova remnant Cas A taken in 2000, 2002, and 2004 which reveal the presence of numerous outlying ejecta knots whose optical emission is dominated by oxygen lines including [O I] 6300,6364 A, and [O II] 7319,7330 A. These ejecta are found immediately behind the faster moving [N II] 6548,6583 A dominated ejecta knots and are seen (in projection) to lie slightly ahead or roughly coincident with the remnant's forward blast wave as detected in deep Chandra X-ray images (Hwang et al. 2004, ApJL, in press). Proper motion derived projected expansion velocities indicate this O-rich layer is expanding at 8000 -- 8500 km/s, or some 500 km/s slower than the outer N-rich material. Location of O-dominated ejecta knots in the eastern portion of the remnant behind N-rich ejecta but ahead of the remnant's outermost S,Si-rich ejecta as seen in X-ray emission maps, suggests that: 1) With the exception of the NE-SW jet regions, the Cas A SN largely retained the progenitor's He,N -- O -- S,Si abundance zones, and 2) Fingers of X-ray emitting, Fe-rich material seen along the eastern limb at larger radial distances than S,Si-rich ejecta did not significantly penetrate the progenitor's O-rich or He,N-rich outer layers. This research was funded by NASA HST GO programs 8281, 9238, and 9890.
Phase behaviour of polyethylene knotted ring chains
Wen Xiao-Hui; Zhang Lin-Xi; Xia A-Gen; Chen Hong-Ping
2011-01-01
The phase behaviour of polyethylene knotted ring chains is investigated by using molecular dynamics simulations.In this paper, we focus on the collapse of the polyethylene knotted ring chain, and also present the results of linear and ring chains for comparison. At high temperatures, a fully extensive knot structure is observed. The mean-square radius of gyration per bond〈S2〉/(Nb2)and the shape factor(δ*)depend on not only the chain length but also the knot type.With temperature decreasing, chain collapse is observed, and the collapse temperature decreases with the chain length increasing. The actual collapse transition can be determined by the specific heat capacity Cv, and the knotted ring chain undergoes gas-liquid-solid-like transition directly. The phase transition of a knotted ring chain is only one-stage collapse, which is different from the polyethylene linear and ring chains. This investigation can provide some insights into the statistical properties of knotted polymer chains.
EVOLUTION OF THE 1919 EJECTA OF V605 AQUILAE
Clayton, Geoffrey C.; Montiel, Edward [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Bond, Howard E.; Sparks, William B.; Meakes, M. G. [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Long, Lindsey A.; Meyer, Paul I.; Sugerman, Ben E. K. [Department of Physics and Astronomy, Goucher College, 1021 Dulaney Valley Road, Baltimore, MD 21204 (United States); Chesneau, O. [Observatoire de la Cote d' Azur-CNRS-UMR 6203, Dept Gemini, Avenue Copernic, F-06130 Grasse (France); De Marco, O., E-mail: gclayton@fenway.phys.lsu.edu, E-mail: emonti2@lsu.edu, E-mail: bond@stsci.edu, E-mail: sparks@stsci.edu, E-mail: mgmeakes@gmail.com, E-mail: ben.sugerman@goucher.edu, E-mail: olivier.chesneau@ob-azur.fr, E-mail: orsola@science.mq.edu.au [Department of Physics, Macquarie University, Sydney, NSW 2109 (Australia)
2013-07-10
New imaging of V605 Aql, was obtained in 2009 with HST/WFPC2, which had a nova-like outburst in 1919, and is located at the center of the planetary nebula (PN), A58. This event has long been ascribed to a final helium shell flash, but it has been suggested recently that it may instead have been an ONe nova. The new images provide an 18 yr baseline for the expansion of the ejecta from the 1919 event. In addition, the central star has been directly detected in the visible for the first time since 1923, when it faded from sight due to obscuration by dust. The expansion of the ejecta has a velocity of {approx}200 km s{sup -1}, and an angular expansion rate of {approx}10 mas yr{sup -1}, consistent with a 1919 ejection. This implies a geometric distance of 4.6 kpc for V605 Aql, consistent with previous estimates. The gas mass in the central knot of ejecta was previously estimated to be 5 Multiplication-Sign 10{sup -5} M{sub Sun }. It is estimated that warm dust associated with this gas has a mass of {approx}10{sup -5} M{sub Sun }. There is also evidence for a significant amount, 10{sup -3} M{sub Sun }, of cold (75 K) dust, which may be associated with its PN. The knot ejected in 1919 is asymmetrical and is approximately aligned with the asymmetry of the surrounding PN. Polarimetric imaging was obtained to investigate whether the 2001 spectrum of V605 Aql was obtained primarily in scattered light from dust in the central knot, but the signal-to-noise in the data was insufficient to measure the level of polarization.
Interstellar and ejecta dust in the cas a supernova remnant
Arendt, Richard G. [CRESST, University of Maryland, Baltimore County, Baltimore, MD 21250 (United States); Dwek, Eli; Kober, Gladys [NASA Goddard Space Flight Center, Code 665, Greenbelt, MD 20771 (United States); Rho, Jeonghee [SETI Institute, 189 Bernardo Avenue, Mountain View, CA 94043 (United States); Hwang, Una, E-mail: Richard.G.Arendt@nasa.gov [NASA Goddard Space Flight Center, Code 662, Greenbelt, MD 20771 (United States)
2014-05-01
Infrared continuum observations provide a means of investigating the physical composition of the dust in the ejecta and swept up medium of the Cas A supernova remnant (SNR). Using low-resolution Spitzer IRS spectra (5-35 μm), and broad-band Herschel PACS imaging (70, 100, and 160 μm), we identify characteristic dust spectra, associated with ejecta layers that underwent distinct nuclear burning histories. The most luminous spectrum exhibits strong emission features at ∼9 and 21 μm and is closely associated with ejecta knots with strong Ar emission lines. The dust features can be reproduced by magnesium silicate grains with relatively low Mg to Si ratios. Another dust spectrum is associated with ejecta having strong Ne emission lines. It has no indication of any silicate features and is best fit by Al{sub 2}O{sub 3} dust. A third characteristic dust spectrum shows features that are best matched by magnesium silicates with a relatively high Mg to Si ratio. This dust is primarily associated with the X-ray-emitting shocked ejecta, but it is also evident in regions where shocked interstellar or circumstellar material is expected. However, the identification of dust composition is not unique, and each spectrum includes an additional featureless dust component of unknown composition. Colder dust of indeterminate composition is associated with emission from the interior of the SNR, where the reverse shock has not yet swept up and heated the ejecta. Most of the dust mass in Cas A is associated with this unidentified cold component, which is ≲ 0.1 M {sub ☉}. The mass of warmer dust is only ∼0.04 M {sub ☉}.
Turner, J C
1996-01-01
This book brings together twenty essays on diverse topics in the history and science of knots. It is divided into five parts, which deal respectively with knots in prehistory and antiquity, non-European traditions, working knots, the developing science of knots, and decorative and other aspects of knots.Its authors include archaeologists who write on knots found in digs of ancient sites (one describes the knots used by the recently discovered Ice Man); practical knotters who have studied the history and uses of knots at sea, for fishing and for various life support activities; a historian of l
Zou, L P; Pak, D G
2013-01-01
We consider topological structure of classical vacuum solutions in quantum chromodynamics. Topologically non-equivalent vacuum configurations are classified by non-trivial second and third homotopy groups for coset of the color group SU(N) (N=2,3) under the action of maximal Abelian stability group. Starting with explicit vacuum knot configurations we study possible exact classical solutions as vacuum excitations. Exact analytic non-static knot solution in a simple CP^1 model in Euclidean space-time has been obtained. We construct an ansatz based on knot and monopole topological vacuum structure for searching new solutions in SU(2) and SU(3) QCD. We show that singular knot-like solutions in QCD in Minkowski space-time can be naturally obtained from knot solitons in integrable CP^1 models. A family of Skyrme type low energy effective theories of QCD admitting exact analytic solutions with non-vanishing Hopf charge is proposed.
Chicxulub Impact Ejecta From Albion Island, Belize
Ocampo, A.; Pope, K.; Fischer, A.; Alvarez, W.; Fouke, B.; Webster, C.; Vega, F.; Smit, J.; Fritsche, A.; Claeys, P.
1999-01-01
Impact ejecta from the Albion Formation are exposed in northern Belize. The ejecta come from the outer portion of the continuous ejecta blanket of the Chicxulub crater, which is located 360 km to the northwest.
The Wiese Knot: A Sliding-Locking Arthroscopic Knot.
Parada, Stephen A; Shaw, K Aaron; Eichinger, Josef K; Boykin, Nathan T; Gloystein, David M; Ledford, Cheryl L; Arrington, Edward D; Wiese, Paul T
2017-02-01
Despite recent advances in knotless suture devices for arthroscopic surgical procedures, arthroscopic knot tying remains a necessary skill for the arthroscopic surgeon. Successful completion of arthroscopic knot tying relies on a thorough understanding of the chosen technique, proper suture management, adequate knot tensioning and securement, and the ability to reproducibly create the knot. We introduce a technique that serves as both a sliding and locking knot while being simple to master and reproducible to perform.
Tabulating knot polynomials for arborescent knots
Mironov, A.; Morozov, A.; Morozov, A.; Ramadevi, P.; Singh, Vivek Kumar; Sleptsov, A.
2017-02-01
Arborescent knots are those which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present knowledge is sufficient for lifting topological description to the level of effective analytical formulas. The paper describes the origin and structure of the new tables of colored knot polynomials, which will be posted at the dedicated site (http://knotebook.org). Even if formal expressions are known in terms of modular transformation matrices, the computation in finite time requires additional ideas. We use the ‘family’ approach, suggested in Mironov and Morozov (2015 Nucl. Phys. B 899 395–413), and apply it to arborescent knots in the Rolfsen table by developing a Feynman diagram technique, associated with an auxiliary matrix model field theory. Gauge invariance in this theory helps to provide meaning to Racah matrices in the case of non-trivial multiplicities and explains the need for peculiar sign prescriptions in the calculation of [21]-colored HOMFLY-PT polynomials.
Combinatorial Maps with Normalized Knot
Zeps, Dainis
2010-01-01
We consider combinatorial maps with fixed combinatorial knot numbered with augmenting numeration called normalized knot. We show that knot's normalization doesn't affect combinatorial map what concerns its generality. Knot's normalization leads to more concise numeration of corners in maps, e.g., odd or even corners allow easy to follow distinguished cycles in map caused by the fixation of the knot. Knot's normalization may be applied to edge structuring knot too. If both are normalized then one is fully and other partially normalized mutually.
Banagl, Markus
2011-01-01
The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested
Self-assembly of knots and links
Orlandini, Enzo; Polles, Guido; Marenduzzo, Davide; Micheletti, Cristian
2017-03-01
Guiding the self-assembly of identical building blocks towards complex three-dimensional structures with a set of desired properties is a major goal in material science, chemistry and physics. A particularly challenging problem, especially explored in synthetic chemistry, is that of self-assembling closed structures with a target topology starting by simple geometrical templates. Here we overview and revisit recent advancements, based on stochastic simulations, where the geometry of rigid helical templates with functionalised sticky ends has been designed for self-assembling efficiently and reproducibly into a wide range of three-dimensional closed structures. Notably, these include non trivial topologies of links and knots, including the 819 knot that we had predicted to be highly encodable and that has only recently been obtained experimentally. By appropriately tuning the parameters that define the template shape, we show that, for fixed concentration of templates, the assembly process can be directed towards the formation of specific knotted and linked structures such as the trefoils, pentafoil knots, Hopf and Solomon links. More exotic and unexpected knots and links are also found. Our results should be relevant to the design of new protocols that can both increase and broaden the population of synthetise molecular knots and catenanes.
Millett, Kenneth C; Rawdon, Eric J; Stasiak, Andrzej; Physical and Numerical Models in Knot theory: including Applications to the Life Sciences; Conference on Knots, Random Walks and Biomolecules
2005-01-01
The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year. This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knot...
Nawata, Satoshi
2015-01-01
We provide various formulations of knot homology that are predicted by string dualities. In addition, we also explain the rich algebraic structure of knot homology which can be understood in terms of geometric representation theory in these formulations. These notes are based on lectures in the workshop "Physics and Mathematics of Link Homology" at Centre de Recherches Math\\'ematiques, Universit\\'e de Montr\\'eal.
Aneziris, Charilaos N
1999-01-01
One of the most significant unsolved problems in mathematics is the complete classification of knots. The main purpose of this book is to introduce the reader to the use of computer programming to obtain the table of knots. The author presents this problem as clearly and methodically as possible, starting from the very basics. Mathematical ideas and concepts are extensively discussed, and no advanced background is required.
Studying uniform thickness II: Transversely nonsimple iterated torus knots
LaFountain, Douglas
2011-01-01
We prove that an iterated torus knot type in the standard contact 3-sphere fails the uniform thickness property (UTP) if and only if it is formed from repeated positive cablings, which is precisely when an iterated torus knot supports the standard contact structure. This is the first complete UTP...
Evolution of the 1919 Ejecta of V605 Aquilae
Clayton, Geoffrey C; Long, Lindsey A; Meyer, Paul I; Sugerman, Ben E K; Montiel, Edward; Sparks, William B; Meakes, M G; Chesneau, O; De Marco, O
2013-01-01
New imaging of V605 Aql, was obtained in 2009 with HST/WFPC2, which had a nova-like outburst in 1919, and is located at the center of the planetary nebula (PN), Abell 58. This event has long been ascribed to a final helium shell flash, but it has been suggested recently that it may instead have been an ONe nova. The new images provide an 18 year baseline for the expansion of the ejecta from the 1919 event. In addition, the central star has been directly detected in the visible for the first time since 1923, when it faded from sight due to obscuration by dust. The expansion of the ejecta has a velocity of ~200 km/s, and an angular expansion rate of ~10 mas/yr, consistent with a 1919 ejection. This implies a geometric distance of 4.6 kpc for V605 Aql, consistent with previous estimates. The gas mass in the central knot of ejecta was previously estimated to be 5 x 10^-5 M(Sun). It is estimated that warm dust associated with this gas has a mass of ~10^-5 M(Sun). There is also evidence for a significant amount, 10...
The Three-Dimensional Motions of the Ejecta of Tycho's Supernova Remnant
Williams, Brian J.; Coyle, Nina; Yamaguchi, Hiroya; DePasquale, Joseph M.; Hewitt, John W.; Blondin, John M.; Borkowski, Kazimierz J.; Ghavamian, Parviz; Petre, Robert; Reynolds, Stephen P.
2017-01-01
We present the first three-dimensional measurements of the velocity of various ejecta knots in Tycho's supernova remnant, the remains of SN 1572, known to be a Type Ia explosion. When the ejecta knots pass through the reverse shock, they become heated to X-ray emitting temperatures, and Chandra's unmatched spatial resolution combined with the small age of this remnant allows us to watch it expand on measurable timescales. By combining a new epoch of 2015 Chandra X-ray observations with a previous 2003 epoch, we have a 12-year baseline over which we can measure proper motions from nearly 60 "tufts" of Si-rich ejecta, giving us the velocity in the plane of the sky. For the line of sight velocity, we use two different methods: a non-equilibrium ionization model fit to the strong Si and S lines in the 1.2-2.8 keV regime, and a fit consisting of a series of Gaussian lines. These methods give consistent results, and allow us to determine the red or blue shift of each of the knots, and thus, the third dimension of the velocity vector. Assuming a distance of 3.5 kpc, we find total velocities that range from roughly 2400 to 6600 km/s, with mean and median values of 4429 and 4450 km/s, respectively. In the plane of the sky, we find several regions where the ejecta knots have overtaken the forward shock. These regions have proper motions in excess of 6000 km/s. Some Type Ia supernova explosion models predict a velocity asymmetry in the ejecta, where the ejecta on one side of the remnant is moving faster than another side. We find no such velocity asymmetries in Tycho, and discuss our findings in light of various explosion models. Our previous work has shown an asymmetry in the velocity of the forward shock, with speeds in the southwest being significantly higher than those in the northeast. We have attributed this to a measured density gradient in the ISM, and not an asymmetry in the explosion. We compare our measurements with hydrodynamic simulations to show how the forward
Ejecta emplacement: from distal to proximal
Artemieva, N.
2008-09-01
liquid with specific properties, i.e. finite-difference equations are the same as in standard hydrodynamics [6-8]. Another approach is based on solving equations of motion for representative particles [9]. Each of these markers describes the motion of a large number of real particles with similar sizes, velocities, and trajectories. Equation of motion (gravity, viscosity, and drag) is solved for every marker and then exchange of momentum, heat and energy with surrounding vaporair mixture is taken into account. This approach is used in the SOVA code [10] and allows to vary particle sizes within a broad range (from a few m to a few microns). Implicit procedure of velocity update allows a larger time step. The substantial advantage of the model is its three-dimensional geometry, allowing modeling of asymmetric deposits of oblique impact ejecta. Turbulent diffusion is taken into account in a simplified manner [6]. Fragments size-frequency distribution (SFD) may be of crucial importance: while large fragments move ballistically, the smallest ones are passively involved in gas motion. Ejected material is usually transformed into particles under tension. The initial particle velocity is given by the hydrodynamic velocity, but the object's initial position within the cell is randomly defined. The SFD of solid fragments in high velocity impacts has been studied experimentally [2,11], numerically [12,13], and has been derived from the lunar and terrestrial crater observations [14,15]. Various approaches may be used to implement fragment size in a dynamic model: in Grady-Kipp model the average fragment size is defined by strain rate [12]; alternatively, average ejection velocity [16] or maximum shock compression [17] may be used. All methods may be verified through comparison with known data. Volcanic direct blast. Numerical modeling of pyroclastic flows, checked against recent observations and young deposits, may be then a useful instrument for reconstruction of terrestrial
Extended knots and the space of states of quantum gravity
Griego, J R
1996-01-01
In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions has been traditionally based upon geometric (in contrast to analytic) properties of the loops. The reason for this preferred way is twofold: for one hand the inherent difficulties associated with the analytic loop calculus, and on the other our limited knowledge about the analytic properties of knots invariants. Extended loops provide a way to overcome the difficulties at both levels. For one hand, a systematic method to construct analytic expressions of diffeomorphism invariants (the extended knots) in terms of the Chern-Simons propagators can be developed. Extended knots are simply related to ordinary knots (at least formally). The analytic expressions of knot invariants could be produced then in a generic way. On the other hand, the evaluation of the Hamiltonian over ex...
Chicxulub Impact Ejecta in Belize
Ocampo, A.; Pope, K.; Fischer, A.; Alvarez, W.; Fouke, B.; Asaro, F.; Webster, C., Jr.; Vega, F.; Smith, J.; Fritsche, A. E.
1997-01-01
Chicxulub ejecta deposits in Belize provide the closest exposures of ejecta to the crater and the only exposures of proximal ejecta deposited in a terrestrial environment. A quarry on Albion Island in northern Belize exposes Late Cretaceous, possibly Maastrichtian, carbonate platform sediments that were folded, eroded, and subaerially weathered prior to the deposition of coarse ejecta from Chicxulub. These ejecta deposits are composed of a basal, about 1-m-thick clay and dolomite Spheroid Bed overlain by a about 15-m-thick coarse Diamictite Bed. Many and perhaps most of the clay spheroids are altered glass. Many dolomite spheroids have concentric layers and angular cores are probably of accretionary lapilli origin. A slight Ir concentration (111-152 ppt) was detected in the base of the Spheroid Bed. The Diamictite Bed contains about 10% altered glass, rare shocked quartz, 3-8 m diameter boulders and striated and polished cobbles, one with a penetrating rock chip that plastically deformed the cobble. Ejecta deposits extend to the surface at Albion and the maximum thickness in this area is not known. Ejecta deposits are exposed in several roadside quarries in the Cayo District of central Belize. The Late Cretaceous here is also represented by carbonate platform sediments. The upper surface of the carbonate platform is a highly irregular and extensively recrystallized horizon possibly representing deep karst weathering. Approximately 30 in of diamictite overlies this horizon with a texture similar to the Diamictite Bed at the Albion quarry, but with a more diverse lithology. In three locations the Cayo diamictites, contain red clay layers with abundant polished and striated limestone pebbles and cobbles called Pook's Pebbles, several of which have penetrating rock chips and ablated surfaces. We interpret the Albion Spheroid Bed as a deposit from the impact vapor plume and the Albion and Cayo diamictites as the result of a turbulent flow that contained debris derived
Knot solitons in the AFZ model
Ren Ji-Rong; Mo Shu-Fan; Zhu Tao
2009-01-01
This paper studies the topological properties of knotted solitons in the (3 + 1)-dimensional Aratyn-Ferreira-Zimerman (AFZ) model. Topologically, these solitons are characterized by the Hopf invariant I, which is an integral class in the homotopy group π3(S3)= Z. By making use of the decomposition of U(1) gauge potential theory and Duan's topological current theory, it is shown that the invariant is just the total sum of all the self-linking and linking numbers of the knot family while only linking numbers are considered in other papers. Furthermore, it is pointed out that this invariant is preserved in the branch processes (splitting, merging and intersection) of these knot vortex lines.
Rational-slice Knots via Strongly Negative-amphicheiral Knots
KAWAUCHI AKIO
2009-01-01
We show that certain satellite knots of every strongly negative-amphicheiral rational knot are rational-slice knots. This proof also shows that the 0-surgery man-ifold of a certain strongly negative amphicheiral knot such as the figure-eight knot bounds a compact oriented smooth 4-manifold homotopy equivalent to the 2-sphere such that a second homology class of the 4-manifold is represented by a smoothly embedded 2-sphere if and only if the modulo two reduction of it is zero.
Sedimentation of Knotted Polymers
Piili, Joonas; Kaski, Kimmo; Linna, Riku
2012-01-01
We investigate the sedimentation of knotted polymers by means of the stochastic rotation dynamics, a molecular dynamics algorithm which takes hydrodynamics fully into account. We show that the sedimentation coefficient s, related to the terminal velocity of the knotted polymers, increases linearly with the average crossing number n_c of the corresponding ideal knot. To the best of our knowledge, this provides the first direct computational confirmation of this relation, postulated on the basis of experiments in "The effect of ionic conditions on the conformations of supercoiled DNA. I. sedimentation analysis" by Rybenkov et al., for the case of sedimentation. Such a relation was previously shown to hold with simulations for knot electrophoresis. We also show that there is an accurate linear dependence of s on the inverse of the radius of gyration R_g^-1, more specifically with the inverse of the R_g component that is perpendicular to the direction along which the polymer sediments. Intriguingly, the linear de...
Hamann, Fred
Eta Carinae's inner ejecta are dominated observationally by the bright Weigelt blobs and their famously rich spectra of nebular emission and absorption lines. They are dense (n e ˜ 107-108 cm- 3), warm (T e ˜ 6,000-7,000 K) and slow moving ( ˜ 40 km s- 1) condensations of mostly neutral (H0) gas. Located within 1,000 AU of the central star, they contain heavily CNO-processed material that was ejected from the star about a century ago. Outside the blobs, the inner ejecta include absorption-line clouds with similar conditions, plus emission-line gas that has generally lower densities and a wider range of speeds (reaching a few hundred km s- 1) compared to the blobs. The blobs appear to contain a negligible amount of dust and have a nearly dust-free view of the central source, but our view across the inner ejecta is severely affected by uncertain amounts of dust having a patchy distribution in the foreground. Emission lines from the inner ejecta are powered by photoionization and fluorescent processes. The variable nature of this emission, occurring in a 5.54years "event" cycle, requires specific changes to the incident flux that hold important clues to the nature of the central object.
A class of ejecta transport test problems
Hammerberg, James E [Los Alamos National Laboratory; Buttler, William T [Los Alamos National Laboratory; Oro, David M [Los Alamos National Laboratory; Rousculp, Christopher L [Los Alamos National Laboratory; Morris, Christopher [Los Alamos National Laboratory; Mariam, Fesseha G [Los Alamos National Laboratory
2011-01-31
Hydro code implementations of ejecta dynamics at shocked interfaces presume a source distribution function ofparticulate masses and velocities, f{sub 0}(m, v;t). Some of the properties of this source distribution function have been determined from extensive Taylor and supported wave experiments on shock loaded Sn interfaces of varying surface and subsurface morphology. Such experiments measure the mass moment of f{sub o} under vacuum conditions assuming weak particle-particle interaction and, usually, fully inelastic capture by piezo-electric diagnostic probes. Recently, planar Sn experiments in He, Ar, and Kr gas atmospheres have been carried out to provide transport data both for machined surfaces and for coated surfaces. A hydro code model of ejecta transport usually specifies a criterion for the instantaneous temporal appearance of ejecta with source distribution f{sub 0}(m, v;t{sub 0}). Under the further assumption of separability, f{sub 0}(m,v;t{sub 0}) = f{sub 1}(m)f{sub 2}(v), the motion of particles under the influence of gas dynamic forces is calculated. For the situation of non-interacting particulates, interacting with a gas via drag forces, with the assumption of separability and simplified approximations to the Reynolds number dependence of the drag coefficient, the dynamical equation for the time evolution of the distribution function, f(r,v,m;t), can be resolved as a one-dimensional integral which can be compared to a direct hydro simulation as a test problem. Such solutions can also be used for preliminary analysis of experimental data. We report solutions for several shape dependent drag coefficients and analyze the results of recent planar dsh experiments in Ar and Xe.
Knotted vs. unknotted proteins: evidence of knot-promoting loops.
Raffaello Potestio
Full Text Available Knotted proteins, because of their ability to fold reversibly in the same topologically entangled conformation, are the object of an increasing number of experimental and theoretical studies. The aim of the present investigation is to assess, on the basis of presently available structural data, the extent to which knotted proteins are isolated instances in sequence or structure space, and to use comparative schemes to understand whether specific protein segments can be associated to the occurrence of a knot in the native state. A significant sequence homology is found among a sizeable group of knotted and unknotted proteins. In this family, knotted members occupy a primary sub-branch of the phylogenetic tree and differ from unknotted ones only by additional loop segments. These "knot-promoting" loops, whose virtual bridging eliminates the knot, are found in various types of knotted proteins. Valuable insight into how knots form, or are encoded, in proteins could be obtained by targeting these regions in future computational studies or excision experiments.
Motion of charged particles in a knotted electromagnetic field
Arrayas, M; Trueba, J L, E-mail: joseluis.trueba@urjc.e [Area de Electromagnetismo, Universidad Rey Juan Carlos, Camino del Molino s/n, 28943 Fuenlabrada, Madrid (Spain)
2010-06-11
In this paper we consider the classical relativistic motion of charged particles in a knotted electromagnetic field. After reviewing how to construct electromagnetic knots from maps between the three-sphere and the two-sphere, we introduce a mean quadratic radius of the energy density distribution in order to study some properties of this field. We study the classical relativistic motion of electrons in the electromagnetic field of the Hopf map, and compute their trajectories. It is observed that these electrons initially at rest are strongly accelerated by the electromagnetic force, becoming ultrarelativistic in a period of time that depends on the knot energy and size.
Determining Knots by Minimizing Energy
Cai-Ming Zhang; Hui-Jian Han; Fuhua Frank Cheng
2006-01-01
A new method for determining knots to construct polynomial curves is presented. At each data point, a quadric curve which passes three consecutive points is constructed. The knots for constructing the quadric curve are determined by minimizing the internal strain energy, which can be regarded as a function of the angle. The function of the angle is expanded as a Taylor series with two terms, then the two knot intervals between the three consecutive points are defined by linear expression. Between the two consecutive points, there are two knot intervals, and the combination of the two knot intervals is used to define the final knot interval. A comparison of the new method with several existing methods is included.
Knot probabilities in random diagrams
Cantarella, Jason; Chapman, Harrison; Mastin, Matt
2016-10-01
We consider a natural model of random knotting—choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to compute exact probabilities for knots in this model. As expected, most diagrams with 10 and fewer crossings are unknots (about 78% of the roughly 1.6 billion 10 crossing diagrams). For these crossing numbers, the unknot fraction is mostly explained by the prevalence of ‘tree-like’ diagrams which are unknots for any assignment of over/under information at crossings. The data shows a roughly linear relationship between the log of knot type probability and the log of the frequency rank of the knot type, analogous to Zipf’s law for word frequency. The complete tabulation and all knot frequencies are included as supplementary data.
Constructing a polynomial whose nodal set is the three-twist knot 52
Dennis, Mark R.; Bode, Benjamin
2017-06-01
We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot 52. The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as the nodal set of a certain complex polynomial which depends on an additional parameter. For sufficiently small values of this parameter, the nodal lines form the three-twist knot. Further mathematical properties of this map are explored, including the relationship of the phase critical points with the Morse-Novikov number, which is nonzero as this knot is not fibred. We also find analogous functions for other simple knots and links. The particular function we find, and the general procedure, should be useful for designing knotted fields of particular knot types in various physical systems.
Untangling of knotted urethral catheters
Sambrook, Andrew J. [Aberdeen Royal Infirmary, Department of Radiology, Aberdeen (United Kingdom); Todd, Alistair [Raigmore Hospital, Inverness (United Kingdom)
2007-04-15
Intravesical catheter knotting during micturating cystourethrography is a rare but recognized complication of the procedure. We were able to untangle a knot utilizing a fluoroscopically guided vascular guidewire. Following this success, a small study was performed using a model. Various types of guidewires and techniques were tested for different diameters of knots in order to predict the likelihood of success in this type of situation. (orig.)
Untangling of knotted urethral catheters.
Sambrook, Andrew J; Todd, Alistair
2007-04-01
Intravesical catheter knotting during micturating cystourethrography is a rare but recognized complication of the procedure. We were able to untangle a knot utilizing a fluoroscopically guided vascular guidewire. Following this success, a small study was performed using a model. Various types of guidewires and techniques were tested for different diameters of knots in order to predict the likelihood of success in this type of situation.
Naughty knot: a case of nasogastric tube knotting.
Ravind, Rahul; Prameela, Chelakkot G; Gurram, Bharath Chandra; Dinesh, Makuny
2015-10-13
Nasogastric intubation is a common procedure for enteral nutritional support in medical practice. Random spontaneous true knot formation in the tube is rarely encountered and is a cause of unanticipated trauma. This is a case of a true knot formation diagnosed with fluoroscopy and managed without untoward trauma.
How superfluid vortex knots untie
Kleckner, Dustin; Kauffman, Louis H.; Irvine, William T. M.
2016-07-01
Knots and links often occur in physical systems, including shaken strands of rope and DNA (ref. ), as well as the more subtle structure of vortices in fluids and magnetic fields in plasmas. Theories of fluid flows without dissipation predict these tangled structures persist, constraining the evolution of the flow much like a knot tied in a shoelace. This constraint gives rise to a conserved quantity known as helicity, offering both fundamental insights and enticing possibilities for controlling complex flows. However, even small amounts of dissipation allow knots to untie by means of `cut-and-splice’ operations known as reconnections. Despite the potentially fundamental role of these reconnections in understanding helicity--and the stability of knotted fields more generally--their effect is known only for a handful of simple knots. Here we study the evolution of 322 elemental knots and links in the Gross-Pitaevskii model for a superfluid, and find that they universally untie. We observe that the centreline helicity is partially preserved even as the knots untie, a remnant of the perfect helicity conservation predicted for idealized fluids. Moreover, we find that the topological pathways of untying knots have simple descriptions in terms of minimal two-dimensional knot diagrams, and tend to concentrate in states which are twisted in only one direction. These results have direct analogies to previous studies of simple knots in several systems, including DNA recombination and classical fluids. This similarity in the geometric and topological evolution suggests there are universal aspects in the behaviour of knots in dissipative fields.
On knots in overtwisted contact structures
Etnyre, John B
2010-01-01
We prove that each overtwisted contact structure has knot types that are represented by infinitely many distinct transverse knots all with the same self-linking number. In some cases, we can even classify all such knots. We also show similar results for Legendrian knots and prove a "folk" result concerning loose transverse and Legendrian knots (that is knots with overtwisted complements) which says that such knots are determined by their classical invariants (up to contactomorphism). Finally we discuss how these results partially fill in our understanding of the "geography" and "botany"' problems for Legendrian knots in overtwisted contact structures, as well as many open questions regarding these problems.
Zhao, Xin
2013-05-01
Elastic rods have been studied intensively since the 18th century. Even now the theory of elastic rods is still developing and enjoying popularity in computer graphics and physical-based simulation. Elastic rods also draw attention from architects. Architectural structures, NODUS, were constructed by elastic rods as a new method of form-finding. We study discrete models of elastic rods and NODUS structures. We also develop computational tools to find the equilibria of elastic rods and the shape of NODUS. Applications of elastic rods in forming torus knot and closing Bishop frame are included in this thesis.
Arrayás, M.; Bouwmeester, D.; Trueba, J. L.
2017-01-01
Maxwell equations in vacuum allow for solutions with a non-trivial topology in the electric and magnetic field line configurations at any given moment in time. One example is a space filling congruence of electric and magnetic field lines forming circles lying on the surfaces of nested tori. In this example the electric, magnetic and Poynting vector fields are orthogonal everywhere. As time evolves the electric and magnetic fields expand and deform without changing the topology and energy, while the Poynting vector structure remains unchanged while propagating with the speed of light. The topology is characterized by the concept of helicity of the field configuration. Helicity is an important fundamental concept and for massless fields it is a conserved quantity under conformal transformations. We will review several methods by which linked and knotted electromagnetic (spin-1) fields can be derived. A first method, introduced by A. Rañada, uses the formulation of the Maxwell equations in terms of differential forms combined with the Hopf map from the three-sphere S3 to the two-sphere S2. A second method is based on spinor and twistor theory developed by R. Penrose in which elementary twistor functions correspond to the family of electromagnetic torus knots. A third method uses the Bateman construction of generating null solutions from complex Euler potentials. And a fourth method uses special conformal transformations, in particular conformal inversion, to generate new linked and knotted field configurations from existing ones. This fourth method is often accompanied by shifting singularities in the field to complex space-time points. Of course the various methods must be closely related to one another although they have been developed largely independently and they suggest different directions in which to expand the study of topologically non-trivial field configurations. It will be shown how the twistor formulation allows for a direct extension to massless
The beauty of knots at the molecular level.
Sauvage, Jean-Pierre; Amabilino, David B
2012-01-01
What makes a given object look beautiful to the observer, be it in the macroscopic world or at the molecular level? This very general question will be briefly addressed at the beginning of this essay, in relation to contemporary molecular chemistry and biology, leading to the general statement that, most of the time, beauty is tightly connected to function as well as to the cultural background of the observer. The main topic of the present article will be that of topologically non-trivial molecules or molecular ensembles and the fascination that such species have exerted on molecular or solid state chemists. Molecules with a graph identical to Kuratowski's K₅ or K₃,₃ graphs are indeed highly attractive from an aesthetical viewpoint, but perhaps even more fascinating and beautiful are molecular knots. A general discussion will be devoted to these compounds, which are still considered as exotic species because of the very limited number of efficient synthetic strategies leading to their preparation. Particularly efficient are templated approaches based either on transition metals such as copper(I) or on organic groups able to form hydrogen bonds or acceptor-donor stacks. A particularly noteworthy property of knots, and in particular of the trefoil knot, is their topological chirality. The isolation of both enantiomers of the trefoil knot (3₁) could be achieved and showed that such species have fascinating chiroptical properties. Finally, various routes to more complex and beautiful knots than the trefoil knot, which is the simplest non-trivial knot, will be discussed in line with the remarkable ability of transition metals to gather and orient in a very precise fashion several organic components in their coordination spheres, thus leading to synthetic precursors displaying geometries which are perfectly well adapted to the preparation of the desired knots or links.
Energy of knots and conformal geometry
O'Hara, Jun
2003-01-01
Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a "canonical configuration" of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments. Contents: In Search of the "Optima
Finkelstein, Robert J.
It is shown that the four quantum trefoil solitons that are described by the irreducible representations { D}3/2mm' of the quantum algebra SLq(2) [and that may be identified with the four families of elementary fermions (e, μ, τ νeνμντd, s, b; u, c, t)] may be built out of three preons, chosen from two charged preons with charges (1/3, -1/3) and two neutral preons. These preons are fermions and are described by the { D}1/2mm' representation of SLq(2). There are also four bosonic preons described by the { D}1mm^' and { D}000 representations of SLq(2). The knotted standard theory may be replicated at the preon level and the conjectured particles are in principle indirectly observable.
Erosion of ejecta at Meteor Crater, Arizona
Grant, John A.; Schultz, Peter H.
1993-01-01
New methods for estimating erosion at Meteor Crater, Arizona, indicate that continuous ejecta deposits beyond 1/4-1/2 crater radii from the rim have been lowered less than 1 m on the average. This conclusion is based on the results of two approaches: coarsening of unweathered ejecta into surface lag deposits and calculation of the sediment budget within a drainage basin on the ejecta. Preserved ejecta morphologies beneath thin alluvium revealed by ground-penetrating radar provide qualitative support for the derived estimates. Although slightly greater erosion of less resistant ejecta locally has occurred, such deposits were limited in extent, particularly beyond 0.25R-0.5R from the present rim. Subtle but preserved primary ejecta features further support our estimate of minimal erosion of ejecta since the crater formed about 50,000 years ago. Unconsolidated deposits formed during other sudden extreme events exhibit similarly low erosion over the same time frame; the common factor is the presence of large fragments or large fragments in a matrix of finer debris. At Meteor Crater, fluvial and eolian processes remove surrounding fines leaving behind a surface lag of coarse-grained ejecta fragments that armor surfaces and slow vertical lowering.
Knot invariants from Virasoro related representation and pretzel knots
Galakhov, D; Mironov, A; Morozov, A
2015-01-01
We remind the method to calculate colored Jones polynomials for the plat representations of knot diagrams from the knowledge of modular transformation (monodromies) of Virasoro conformal blocks with insertions of degenerate fields. As an illustration we use a rich family of pretzel knots, lying on a surface of arbitrary genus g, which was recently analyzed by the evolution method. Further generalizations can be to generic Virasoro modular transformations, provided by integral kernels, which can lead to the Hikami invariants.
Cosmetic crossings of genus one knots
Balm, Cheryl
2011-01-01
We show that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove the nugatory crossing conjecture for the negatively twisted, positive Whitehead doubles of all knots. We also verify the conjecture for several families of pretzel knots and all genus one knots with up to 10 crossings.
Riley, Pete; Gosling, J. T.; McComas, D. J.; Forsyth, R. J.
2001-01-01
In this paper, magnetic and plasma measurements are used to analyze 17 interplanetary coronal mass ejections (CMEs) identified by Ulysses during its in-ecliptic passage to Jupiter. We focus on the expansion characteristics of these CMEs (as inferred from the time rate of change of the velocity profiles through the CMEs) and the properties of 14 forward shocks unambiguously associated with these CMEs. We highlight radial trends from 1 to 5.4 AU. Our results indicate that the CMEs are generally expanding at all heliocentric distances. With regard to the shocks preceding these ejecta, we note the following: (1) There is a clear tendency for the shock speed (in the upstream frame of reference) to decrease with increasing heliocentric distance as the CMEs transfer momentum to the ambient solar wind and slow down; (2) 86% of the shock fronts are oriented in the ecliptic plane such that their normals point westward (i.e., in the direction of planetary motion about the Sun), (3) 86% of the shocks are propagating toward the heliographic equator; and (4) no clear trend was found in the strength of the shocks versus heliocentric distance. These results are interpreted using simple dynamical arguments and are supported by fluid and magnetohydrodynamic (MHD) simulations.
Saeed Najafi
2016-09-01
Full Text Available Knots appear frequently in semiflexible (biopolymers, including double-stranded DNA, and their presence can affect the polymer’s physical and functional properties. In particular, it is possible and indeed often the case that multiple knots appear on a single chain, with effects which have only come under scrutiny in the last few years. In this manuscript, we study the interaction of two knots on a stretched semiflexible polymer, expanding some recent results on the topic. Specifically, we consider an idealization of a typical optical tweezers experiment and show how the bending rigidity of the chain—And consequently its persistence length—Influences the distribution of the entanglements; possibly more importantly, we observe and report how the relative chirality of the otherwise identical knots substantially modifies their interaction. We analyze the free energy of the chain and extract the effective interactions between embedded knots, rationalizing some of their pertinent features by means of simple effective models. We believe the salient aspect of the knot–knot interactions emerging from our study will be present in a large number of semiflexible polymers under tension, with important consequences for the characterization and manipulation of these systems—Be they artificial or biologica in origin—And for their technological application.
Induction effects of torus knots and unknots
Oberti, Chiara; Ricca, Renzo L.
2017-09-01
Geometric and topological aspects associated with induction effects of field lines in the shape of torus knots/unknots are examined and discussed in detail. Knots are assumed to lie on a mathematical torus of circular cross-section and are parametrized by standard equations. The induced field is computed by direct integration of the Biot-Savart law. Field line patterns of the induced field are obtained and several properties are examined for a large family of knots/unknots up to 51 crossings. The intensity of the induced field at the origin of the reference system (center of the torus) is found to depend linearly on the number of toroidal coils and reaches maximum values near the boundary of the mathematical torus. New analytical estimates and bounds on energy and helicity are established in terms of winding number and minimum crossing number. These results find useful applications in several contexts when the source field is either vorticity, electric current or magnetic field, from vortex dynamics to astrophysics and plasma physics, where highly braided magnetic fields and currents are present.
Handbook of knotting and splicing
Hasluck, Paul N
2005-01-01
Clearly written and amply illustrated with 208 figures, this classic guide ranges from simple and useful knots to complex varieties. Additional topics include rope splicing, working cordage, hammock making, more.
Weaving knotted vector fields with tunable helicity
Kedia, Hridesh; Dennis, Mark R; Irvine, William T M
2016-01-01
We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot and its generalizations. As finite-energy physical fields they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knotted fields. The construction can be used to generate isolated knotted flux tubes, filled by knots encoded in the lines of the vector field. Lastly we give examples of manifestly knotted vector fields with vanishing helicity. Our results provide building blocks for analytical models and simulations alike.
A steered molecular dynamics study on the elastic behaviour of knotted polymer chains
Shen Yu; Zhang Lin-Xi
2008-01-01
In this paper the influence of a knot on the structure of a polymethylene (PM) strand in the tensile process is investigated by using the steered molecular dynamics (SMD) method. The gradual increasing of end-to-end distance, R,results in a tighter knot and a more stretched contour. That the break in a knotted rope almost invariably occurs at a point just outside the 'entrance' to the knot, which has been shown in a good many experiments, is further theoretically verified in this paper through the calculation of some structural and thermodynamic parameters. Moreover, it is found that the analyses on bond length, torsion angle and strain energy can facilitate to the study of the localization and the size of a knot in the tensile process. The symmetries of torsion angles, bond lengths and bond angles in the knot result in the whole symmetry of the knot in microstructure, thereby adapting itself to the strain applied. Additionally,the statistical property of the force-dependent average knot size illuminates in detail the change in size of a knot with force f, and therefore the minimum size of the knot in the restriction of the potentials considered in this work for a PM chain is deduced. At the same time, the difference in response to uniaxial strain, between a knotted PM strand and an unknotted one is also investigated. The force-extension profile is easily obtained from the simulation. As expected,for a given f, the knotted chain has an R significantly smaller than that of an unknotted polymer. However, the scaled difference becomes less pronounced for larger values of N, and the results for longer chains approach those of the unknotted chains.
Universal Racah matrices and adjoint knot polynomials: Arborescent knots
Mironov, A.; Morozov, A.
2016-04-01
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.
Phase Doppler anemometry as an ejecta diagnostic
Bell, D. J.; Chapman, D. J.
2017-01-01
When a shock wave is incident on a free surface, micron sized pieces of the material can be ejected from that surface. Phase Doppler Anemometry (PDA) is being developed to simultaneously measure the sizes and velocities of the individual shock induced ejecta particles; providing an important insight into ejecta phenomena. The results from experiments performed on the 13 mm bore light gas gun at the Institute of Shock Physics, Imperial College London are presented. Specially grooved tin targets were shocked at pressures of up to 14 GPa, below the melt on release pressure, to generate ejecta particles. These experiments are the first time that PDA has been successfully fielded on dynamic ejecta experiments. The results and current state of the art of the technique are discussed along with the future improvements required to optimise performance and increase usability.
A Precambrian proximal ejecta blanket from Scotland
Amor, Kenneth; Hesselbo, Stephen P.; Porcelli, Don; Thackrey, Scott; Parnell, John
2008-04-01
Ejecta blankets around impact craters are rarely preserved onEarth. Although impact craters are ubiquitous on solid bodiesthroughout the solar system, on Earth they are rapidly effaced,and few records exist of the processes that occur during emplacementof ejecta. The Stac Fada Member of the Precambrian Stoer Groupin Scotland has previously been described as volcanic in origin.However, shocked quartz and biotite provide evidence for high-pressureshock metamorphism, while chromium isotope values and elevatedabundances of platinum group metals and siderophile elementsindicate addition of meteoritic material. Thus, the unit isreinterpreted here as having an impact origin. The ejecta blanketreaches >20 m in thickness and contains abundant dark green,vesicular, devitrified glass fragments. Field observations suggestthat the deposit was emplaced as a single fluidized flow thatformed as a result of an impact into water-saturated sedimentarystrata. The continental geological setting and presence of groundwatermake this deposit an analogue for Martian fluidized ejecta blankets.
On ambiguity in knot polynomials for virtual knots
Morozov, A; Popolitov, A
2015-01-01
We claim that HOMFLY polynomials for virtual knots, defined with the help of the matrix-model recursion relations, contain more parameters, than just the usual $q$ and $A = q^N$. These parameters preserve topological invariance and do not show up in the case of ordinary (non-virtual) knots and links. They are most conveniently observed in the hypercube formalism: then they substitute $q$-dimensions of certain fat graphs, which are not constrained by recursion and can be chosen arbitrarily. The number of these new topological invariants seems to grow fast with the number of non-virtual crossings: 0, 1, 1, 5, 15, 91, 784, 9160, ... This number can be decreased by imposing the factorization requirement for composites, in addition to topological invariance -- still freedom remains. None of these new parameters, however, appear in HOMFLY for Kishino unknot, which thus remains unseparated from the ordinary unknots even by this enriched set of knot invariants.
On ambiguity in knot polynomials for virtual knots
Morozov, A.; Morozov, And.; Popolitov, A.
2016-06-01
We claim that HOMFLY polynomials for virtual knots, defined with the help of the matrix-model recursion relations, contain more parameters, than just the usual q and A =qN. These parameters preserve topological invariance and do not show up in the case of ordinary (non-virtual) knots and links. They are most conveniently observed in the hypercube formalism: then they substitute q-dimensions of certain fat graphs, which are not constrained by recursion and can be chosen arbitrarily. The number of these new topological invariants seems to grow fast with the number of non-virtual crossings: 0, 1, 1, 5, 15, 91, 784, 9160, ... This number can be decreased by imposing the factorization requirement for composites, in addition to topological invariance - still freedom remains. None of these new parameters, however, appears in HOMFLY for Kishino unknot, which thus remains unseparated from the ordinary unknots even by this enriched set of knot invariants.
Chicxulub Ejecta Blanket Deposits From Belize
Ocampo, A.
1995-01-01
The Chicxulub impact into a thick sequence of carbonates and sulfates released over a trillion tons of volatiles. The importance of the explosive release of such a large mass of volatiles has been greatly underestimated in studies of ejecta depositional processes. Proximal Chicxulub ejecta blanket deposits recent discovered on Albion Island in Belize provide a key to understanding the role of volatile-rich target material during large impact events.
Knot polynomial identities and quantum group coincidences
Morrison, Scott; Snyder, Noah
2010-01-01
We construct link invariants using the D_2n subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories involving the even parts of the D_2n planar algebras. We discuss the origins of these coincidences, explaining the role of SO level-rank duality, Kirby-Melvin symmetry, and properties of small Dynkin diagrams. One of these coincidences involves G_2 and does not appear to be related to level-rank duality.
Stern, S A
2008-01-01
We examine the ability of impacts by Kuiper Belt debris to cause regolith exchange between objects in the Pluto system. We find that ejecta velocities from KB impacts are too low to escape from Pluto and Charon. However, ejecta can escape Nix and Hydra, and is capable of covering one another to depths as high as 10s of meters, and Charon and Pluto, perhaps to depths up to several 10s of cm. Although Pluto's annual atmospheric frost deposition cycle will cover such imported debris on timescales faster than it is emplaced, no such masking mechanism is available on Hydra, Nix, and Charon. As a result, ejecta exchange between these bodies is expected to evolve their colors, albedos, and other photometric properties to be similar. We examined the ability of ejecta exchange to work for other Kuiper Belt binaries and found the process can be effective in many cases. This process may also operate in asteroid binary systems.
Planar and spherical stick indices of knots
Adams, Colin; Hawkins, Katherine; Sia, Charmaine; Silversmith, Rob; Tshishiku, Bena; 10.1142/S0218216511008954
2011-01-01
The stick index of a knot is the least number of line segments required to build the knot in space. We define two analogous 2-dimensional invariants, the planar stick index, which is the least number of line segments in the plane to build a projection, and the spherical stick index, which is the least number of great circle arcs to build a projection on the sphere. We find bounds on these quantities in terms of other knot invariants, and give planar stick and spherical stick constructions for torus knots and for compositions of trefoils. In particular, unlike most knot invariants,we show that the spherical stick index distinguishes between the granny and square knots, and that composing a nontrivial knot with a second nontrivial knot need not increase its spherical stick index.
Colored HOMFLY polynomials of knots presented as double fat diagrams
Mironov, A; Morozov, An; Ramadevi, P; Singh, Vivek Kumar
2015-01-01
Many knots and links in S^3 can be drawn as gluing of three manifolds with one or more four-punctured S^2 boundaries. We call these knot diagrams as double fat graphs whose invariants involve only the knowledge of the fusion and the braiding matrices of four-strand braids. Incorporating the properties of four-point conformal blocks in WZNW models, we conjecture colored HOMFLY polynomials for these double fat graphs where the color can be rectangular or non-rectangular representation. With the recent work of Gu-Jockers, the fusion matrices for the non-rectangular [21] representation, the first which involves multiplicity is known. We verify our conjecture by comparing with the [21] colored HOMFLY of many knots, obtained as closure of three braids. The conjectured form is computationally very effective leading to writing [21]-colored HOMFLY polynomials for many pretzel type knots and non-pretzel type knots. In particular, we find class of pretzel mutants which are distinguished and another class of mutants whic...
Emission knots and polarization swings of swinging jets
Lyutikov, Maxim
2016-01-01
Knots (emission features in jets of active galactic nuclei) often show non-ballistic dynamics and variable emission/polarization properties. We model these features as emission pattern propagating in a jet that carries helical magnetic field and is launched along a changing direction. The model can reproduce a wide range of phenomena observed in the motion of knots: non-ballistic motion (both smooth and occasional sudden change of direction, and/or oscillatory behavior), variable brightness, confinement of knots' motion within an overlaying envelope. The model also reproduces smooth large polarization angle swings, and at the same time allows for the seemingly random behavior of synchrotron fluxes, polarization fraction and occasional $\\pi/2$ polarization jumps.
Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
Mironov, A
2015-01-01
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SU_N) and Kauffman (SO_N) polynomials. For E_8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6x6 case. The adjoint polynomials do not distinguish between mutant...
Preflow stresses in Martian rampart ejecta blankets - A means of estimating the water content
Woronow, A.
1981-01-01
Measurements of extents of rampart ejecta deposits as a function of the size of the parent craters support models which, for craters larger than about 6 km diameter, constrain ejecta blankets to all have a similar maximum thickness regardless of the crater size. These volatile-rich ejecta blankets may have failed under their own weights, then flowed radially outward. Assuming this to be so, some of the physicomechanical properties of the ejecta deposits at the time of their emplacement can then be determined. Finite-element studies of the stress magnitudes, distributions, and directions in hypothetical Martian rampart ejecta blankets reveal that the material most likely failed when the shear stresses were less than 500 kPa and the angle of internal friction was between 26 and 36 deg. These figures imply that the ejecta has a water content between 16 and 72%. Whether the upper limit or the lower limit is more appropriate depends on the mode of failure which one presumes: namely, viscous flow of plastic deformation.
Mercurian impact ejecta: Meterorites and mantle
Gladman, B
2008-01-01
We have examined the fate of impact ejecta liberated from the surface of Mercury due to impacts by comets or asteroids, in order to study (1) meteorite transfer to Earth, and (2) re-accumulation of an expelled mantle in giant-impact scenarios seeking to explain Mercury's large core. In the context of meteorite transfer, we note that Mercury's impact ejecta leave the planet's surface much faster (on average) than other planet's in the Solar System because it is the only planet where impact speeds routinely range from 5-20 times the planet's escape speed. Thus, a large fraction of mercurian ejecta may reach heliocentric orbit with speeds sufficiently high for Earth-crossing orbits to exist immediately after impact, resulting in larger fractions of the ejecta reaching Earth as meteorites. We calculate the delivery rate to Earth on a time scale of 30 Myr and show that several percent of the high-speed ejecta reach Earth (a factor of -3 less than typical launches from Mars); this is one to two orders of magnitude ...
Orbital Evolution of Impact Ejecta from Ganymede
Alvarellos, Jose Luis; Zahnle, Kevin J.; Dobrovolskis, Anthony R.; Hamill, Patrick
2002-11-01
We have numerically computed the orbital evolution of ˜10 3 particles representing high-speed ejecta from Gilgamesh, the largest impact basin on Ganymede. The integration includes the four Galilean satellites, Jupiter (including J2 and J4), Saturn, and the Sun. The integrations last 100,000 years. The particles are ejected at a variety of speeds and directions, with the fastest particles ejected at 1.4 times the escape speed vesc≡ 2GM G/R G of Ganymede. Ejecta with speeds v0.96 vesc, most particles escape Ganymede and achieve orbits about Jupiter. Eventually most (˜71%) of the jovicentric particles hit Ganymede, with 92% of these hitting within 1000 years. The accretion rate scales as 1/ t. Their impact sites are randomly distributed, as expected for planetocentric debris. We estimate that most of the resulting impact craters are a few kilometers across and smaller. The rest of the escaping ejecta are partitioned as follows: ˜3% hit Io; ˜10% hit Europa; ˜13% hit Callisto; 2% reach heliocentric space; and less than ˜1% hit Jupiter. Only two particles survived the entire 10 5-year integration. Ejecta from large impact events do not appear to be a plausible source of large craters on the Galilean satellites; however, such ejecta may account for the majority of small craters.
Introduction to Virtual Knot Theory
Kauffman, Louis H
2011-01-01
This paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial and categorifications of the arrow polynomial. The paper is relatively self-contained and it describes virtual knot theory both combinatorially and in terms of the knot theory in thickened surfaces. The arrow polynomial (of Dye and Kauffman) is a natural generalization of the Jones polynomial, obtained by using the oriented structure of diagrams in the state sum. The paper discusses uses of parity pioneered by Vassily Manturov and uses his parity bracket polynomial to give a counterexample to a conjecture of Fenn, Kauffman and Manturov. The paper gives an exposition of the categorification of the arrow polynomial due to Dye, Kauffman and Manturov and it gives one example (from many found by Aaron Kaestner) of a pair of virtual knots that are not distinguished by Khovanov homology (mod 2), or by the arrow polynomial, bu...
In plain sight: the Chesapeake Bay crater ejecta blanket
D. L. Griscom
2012-02-01
during reentry.
An idealized calculation of the CBIS ejecta-blanket elevation profile minutes after the impact was carried out founded on well established rules for explosion and impact-generated craters. This profile is shown here to match the volume of the upland deposits ≥170 km from the crater center. Closer to the crater, much of the "postdicted" ejecta blanket has clearly been removed by erosion. Nevertheless the Shirley and fossil-free Bacons Castle Formations, located between the upland deposits and the CBIS interior and veneering the present day surface with units ∼10–20 m deep, are respectively identified as curtain- and excavation-phase ejecta. The neritic-fossil-bearing Calvert Formation external to the crater is deduced to be of Eocene age (as opposed to early Miocene as currently believed, preserved by the armoring effects of the overlying CBIS ejecta composed of the (distal upland deposits and the (proximal Bacons Castle Formation. The lithofacies of the in-crater Calvert Formation can only have resulted from inward mass wasting of the postdicted ejecta blanket, vestiges of which (i.e. the Bacons Castle and Shirley Formations still overlap the crater rim and sag into its interior, consistent with this expectation.
Because there appear to be a total of ∼10 000 km^{2} of CBIS ejecta lying on the present-day surface, future research should center the stratigraphic, lithologic, and petrologic properties of these ejecta versus both radial distance from the crater center (to identify ejecta from different ejection stages and circumferentially at fixed radial distances (to detect possible anisotropies relating the impact angle and direction of approach of the impactor.
The geological units described here may comprise the best preserved, and certainly the most accessible, ejecta blanket of a major crater on the Earth's surface and therefore promise to be a boon to the field of impact geology. As a corollary, a major
Simulating regolith ejecta due to gas impingement
Chambers, Wesley Allen; Metzger, Philip; Dove, Adrienne; Britt, Daniel
2016-10-01
Space missions operating at or near the surface of a planet or small body must consider possible gas-regolith interactions, as they can cause hazardous effects or, conversely, be employed to accomplish mission goals. They are also directly related to a body's surface properties; thus understanding these interactions could provide an additional tool to analyze mission data. The Python Regolith Interaction Calculator (PyRIC), built upon a computational technique developed in the Apollo era, was used to assess interactions between rocket exhaust and an asteroid's surface. It focused specifically on threshold conditions for causing regolith ejecta. To improve this model, and learn more about the underlying physics, we have begun ground-based experiments studying the interaction between gas impingement and regolith simulant. Compressed air, initially standing in for rocket exhaust, is directed through a rocket nozzle at a bed of simulant. We assess the qualitative behavior of various simulants when subjected to a known maximum surface pressure, both in atmosphere and in a chamber initially at vacuum. These behaviors are compared to prior computational results, and possible flow patterns are inferred. Our future work will continue these experiments in microgravity through the use of a drop tower. These will use several simulant types and various pressure levels to observe the effects gas flow can have on target surfaces. Combining this with a characterization of the surface pressure distribution, tighter bounds can be set on the cohesive threshold necessary to maintain regolith integrity. This will aid the characterization of actual regolith distributions, as well as informing the surface operation phase of mission design.
Factorization of colored knot polynomials at roots of unity
Kononov, Ya.; Morozov, A.
2015-07-01
HOMFLY polynomials are the Wilson-loop averages in Chern-Simons theory and depend on four variables: the closed line (knot) in 3d space-time, representation R of the gauge group SU (N) and exponentiated coupling constant q. From analysis of a big variety of different knots we conclude that at q, which is a 2m-th root of unity, q2m = 1, HOMFLY polynomials in symmetric representations [ r ] satisfy recursion identity: Hr+m =Hr ṡHm for any A =qN, which is a generalization of the property Hr = H1r for special polynomials at m = 1. We conjecture a further generalization to arbitrary representation R, which, however, is checked only for torus knots. Next, Kashaev polynomial, which arises from HR at q2 = e 2 πi / | R |, turns equal to the special polynomial with A substituted by A| R |, provided R is a single-hook representations (including arbitrary symmetric) - what provides a q - A dual to the similar property of Alexander polynomial. All this implies non-trivial relations for the coefficients of the differential expansions, which are believed to provide reasonable coordinates in the space of knots - existence of such universal relations means that these variables are still not unconstrained.
Factorization of colored knot polynomials at roots of unity
Ya. Kononov
2015-07-01
Full Text Available HOMFLY polynomials are the Wilson-loop averages in Chern–Simons theory and depend on four variables: the closed line (knot in 3d space–time, representation R of the gauge group SU(N and exponentiated coupling constant q. From analysis of a big variety of different knots we conclude that at q, which is a 2m-th root of unity, q2m=1, HOMFLY polynomials in symmetric representations [r] satisfy recursion identity: Hr+m=Hr⋅Hm for any A=qN, which is a generalization of the property Hr=H1r for special polynomials at m=1. We conjecture a further generalization to arbitrary representation R, which, however, is checked only for torus knots. Next, Kashaev polynomial, which arises from HR at q2=e2πi/|R|, turns equal to the special polynomial with A substituted by A|R|, provided R is a single-hook representations (including arbitrary symmetric – what provides a q−A dual to the similar property of Alexander polynomial. All this implies non-trivial relations for the coefficients of the differential expansions, which are believed to provide reasonable coordinates in the space of knots – existence of such universal relations means that these variables are still not unconstrained.
Adams operators and knot decorations
Aiston, A K
1997-01-01
We use an explicit isomorphism from the representation ring of the quantum group U_q(sl(N)) to the Homfly skein of the annulus, to determine an element of the skein which is the image of the mth Adams operator, \\psi_m, on the fundamental representation, c_1. This element is a linear combination of m very simple m-string braids. Using this skein element, we show that the Vassiliev invariant of degree n in the power series expansion of the U_q(sl(N)) quantum invariant of a knot coloured by \\psi_m(c_1) is the canonical Vassiliev invariant with weight system W_n\\psi_m^{(n)} where W_n is the weight system for the Vassiliev invariant of degree n in the expansion of the quantum invariant of the knot coloured by c_1 and \\psi_m^{(n)} is the Adams operator on n-chord diagrams defined by Bar-Natan.
Eta Carinae -- Physics of the Inner Ejecta
Hamann, Fred
2012-01-01
Eta Carinae's inner ejecta are dominated observationally by the bright Weigelt blobs and their famously rich spectra of nebular emission and absorption lines. They are dense (n_e ~ 10^7 to 10^8 cm^-3), warm (T_e ~ 6000 to 7000 K) and slow moving (~40 km/s) condensations of mostly neutral (H^0) gas. Located within 1000 AU of the central star, they contain heavily CNO-processed material that was ejected from the star about a century ago. Outside the blobs, the inner ejecta include absorption-line clouds with similar conditions, plus emission-line gas that has generally lower densities and a wider range of speeds (reaching a few hundred km/s) compared to the blobs. The blobs appear to contain a negligible amount of dust and have a nearly dust-free view of the central source, but our view across the inner ejecta is severely affected by uncertain amounts of dust having a patchy distribution in the foreground. Emission lines from the inner ejecta are powered by photoionization and fluorescent processes. The variabl...
Vortex knots in tangled quantum eigenfunctions
Taylor, Alexander J
2016-01-01
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic 3-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex 3-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose-Einstein condensates.
Endoscopic Release of Master Knot of Henry.
Lui, Tun Hing
2015-12-01
A post-traumatic partial tear of the flexor hallucis longus tendon at the master knot of Henry and the resultant fibrosis of the knot can result in pain at the medial foot arch or posteromedial ankle pain with trigger hallux. Open debridement of the master knot of Henry is indicated if the symptoms do not improve with nonoperative treatment. The open procedure requires extensive soft-tissue dissection because the master knot of Henry is a deep structure. Endoscopic release of the master knot of Henry is an alternative to the open procedure and has the advantage of less surgical trauma and potential for less chance of recurrence of fibrosis of the master knot of Henry.
Knotted solitons in nonlinear magnetic metamaterials.
Rosanov, Nikolay N; Vysotina, Nina V; Shatsev, Anatoly N; Desyatnikov, Anton S; Kivshar, Yuri S
2012-03-30
We demonstrate that nonlinear magnetic metamaterials comprised of a lattice of weakly coupled split-ring resonators driven by an external electromagnetic field may support entirely new classes of spatially localized modes--knotted solitons, which are stable self-localized dissipative structures in the form of closed knotted chains. We demonstrate different topological types of stable knots for the subcritical coupling between resonators and instability-induced breaking of the chains for the supercritical coupling.
Knowledge of knots: shapes in action
Casati, Roberto
2013-01-01
Logic is to natural language what knot theory is to natural knots. Logic is concerned with some cognitive performances; in particular, some natural language inferences are captured by various types of calculi (propositional, predicate, modal, deontic, quantum, probabilistic, etc.), which in turn may generate inferences that are arguably beyond natural logic abilities, or non-well synchronized therewith (eg. ex falso quodlibet, material implication). Mathematical knot theory accounts for some ...
Coherent band pathways between knots and links
Buck, Dorothy
2014-01-01
We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small crossing number. We demonstrate these band surgeries for knots and links with small crossing number. We apply these results to place lower bounds on the minimum number of recombinant events separating DNA configurations, restrict the recombination pathways and determine chirality and/or orientation of the resulting recombinant DNA molecules.
The mathematics and physics of knots
Kauffman, Louis H [Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045 (United States)
2005-12-01
This paper is an introduction to relationships between knot theory and theoretical physics. We give an exposition of the theory of polynomial invariants of knots and links, the Witten functional integral formulation of knot and link invariants, and the beginnings of topological quantum field theory, and show how the theory of knots is related to a number of key issues in mathematical physics, including loop quantum gravity and quantum information theory. Along with the references cited in the text below, we also recommend the following as sources of background information.
Differential and symplectic topology of knots and curves
Tabachnikov, S
1999-01-01
This book presents a collection of papers on two related topics: topology of knots and knot-like objects (such as curves on surfaces) and topology of Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory (""quantum"" knot invariants, knot invariants of finite type), in symplectic and contact topology, and in singularity theory. The interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A particularly enticing feature of the volume is
HST Images Flash Ionization of Old Ejecta by the 2011 Eruption of Recurrent Nova T Pyxidis
Shara, Michael M; Schaefer, Bradley E; Bond, Howard E; Godon, Patrick; Mac Low, Mordecai-Mark; Pagnotta, Ashley; Prialnik, Dina; Sion, Edward M; Toraskar, Jayashree; Williams, Robert E
2015-01-01
T Pyxidis is the only recurrent nova surrounded by knots of material ejected in previous outbursts. Following the eruption that began on 2011 April 14.29, we obtained seven epochs (from 4 to 383 days after eruption) of Hubble Space Telescope narrowband Ha images of T Pyx . The flash of radiation from the nova event had no effect on the ejecta until at least 55 days after the eruption began. Photoionization of hydrogen located north and south of the central star was seen 132 days after the beginning of the eruption. That hydrogen recombined in the following 51 days, allowing us to determine a hydrogen atom density of at least 7e5 cm^-3 - at least an order of magnitude denser than the previously detected, unresolved [NII] knots surrounding T Pyx. Material to the northwest and southeast was photoionized between 132 and 183 days after the eruption began. 99 days later that hydrogen had recombined. Both then (282 days after outburst) and 101 days later, we detected almost no trace of hydrogen emission around T Pyx...
Dust Formation and Survival in Supernova Ejecta
Bianchi, S
2007-01-01
The presence of dust at high redshift requires efficient condensation of grains in SN ejecta, in accordance with current theoretical models. Yet, observations of the few well studied SNe and SN remnants imply condensation efficiencies which are about two orders of magnitude smaller. Motivated by this tension, we have (i) revisited the model of Todini & Ferrara (2001) for dust formation in the ejecta of core collapse SNe and (ii) followed, for the first time, the evolution of newly condensed grains from the time of formation to their survival - through the passage of the reverse shock - in the SN remnant. We find that 0.1 - 0.6 M_sun of dust form in the ejecta of 12 - 40 M_sun stellar progenitors. Depending on the density of the surrounding ISM, between 2-20% of the initial dust mass survives the passage of the reverse shock, on time-scales of about 4-8 x 10^4 yr from the stellar explosion. Sputtering by the hot gas induces a shift of the dust size distribution towards smaller grains. The resulting dust ex...
Cosmetic surgeries on knots in $S^3$
Ni, Yi
2010-01-01
Two Dehn surgeries on a knot are called {\\it purely cosmetic}, if they yield manifolds that are homeomorphic as oriented manifolds. Using Heegaard Floer homology, we give necessary conditions for the existence of purely cosmetic surgeries on knots in $S^3$. Among other things, we show that the two surgery slopes must be the opposite of each other.
Diagnosis of true umbilical cord knot.
Guzikowski, Wojciech; Kowalczyk, Dariusz; Więcek, Jacek
2014-02-24
Many abnormalities are observed in the morphology and pathology of the umbilical cord. The aim of the study was to assess the role of 3D sonography in pathology of true umbilical cord knots. In our materials we observed 10 cases of true umbilical cord knots in a population of 2,864 deliveries. The 2-dimensional transverse scan of the umbilical cord was shown in 3- and 4-dimensional volume scan in order to get a precise image. Four knots were diagnosed prenatally, 3 knots were not diagnosed before the delivery and in the 3 remaining cases ultrasound examinations were not undertaken because the patients were in the course of delivery. In the pregnant subjects with diagnosed true umbilical cord knot once a week the Doppler blood flow indices were examined in the umbilical cord sections before and after the knot. In the three shown cases there were no signs of constriction or tightening of the knot. Four newborns were delivered spontaneously and five by caesarean section. In none of the cases was a pathological FHR trace an indication for emergency delivery. Four-dimensional and Color Doppler examination is very important to diagnose a true umbilical cord. To make a precise diagnosis a longer observation of the abnormality is necessary and its repeated confirmation by color Doppler and power Doppler. This diagnosis requires strict monitoring of fetal wellbeing during pregnancy and the delivery. Perfection of true umbilical cord knot diagnoses may reduce sudden and unforeseen fetal distress.
THE TERMINAL VELOCITY OF THE DEEP IMPACT DUST EJECTA
M. Rengel
2009-01-01
Full Text Available The collision of the projectile released from NASA Deep Impact spacecraft on the nucleus of comet 9P/Tempel 1 generated a hot plume. Afterwards ejecta were created, and material moved slowly in a form of a dust cloud, which dissipated during several days after the impact. Here we report a study about the distribution of terminal velocities of the particles ejected by the impact. This is performed by the development and application of an illconditioned inverse problem approach. We model the light-curves as seen by the Narrow Angle Camera (NAC of OSIRIS onboard the ESA spacecraft Rosetta, and we compare them with the OSIRIS observations. Terminal velocities are derived using a maximum likelihood estimator. The dust velocity distribution is well constrained, and peaks at around 220 m s-1, which is in good agreement with published estimates of the expansion velocities of the dust cloud. Measured and modeled velocity of the dust cloud suggests that the impact ejecta were quickly accelerated by the gas in the cometary coma. This analysis provides a more thorough understanding of the properties (velocity and mass of dust of the Deep Impact dust cloud.
Knot strength of nylon-band cerclage.
Kirby, B M; Wilson, J W
1989-12-01
Nylon bands of five sizes were tested to failure using a splint circular jaw mounted on a tensile testing machine. Four treatment groups of each of the five sizes were tested: as supplied by the manufacturer, ethylene oxide sterilized, autoclave sterilized, and saline-soaked. Comparisons were made between groups and to previously reported results of similar testing of stainless steel wire of three sizes. All the bands failed at the lock mechanism. Knot strength increased with increased size of nylon band. There was no difference between untreated and ethylene oxide sterilized bands, whereas bands subjected to autoclaving or saline soaking failed at less force. The knot strength of all the treatment groups in the three smaller sizes of bands was less than twist-knotted 0.8-mm wire cerclage; and when soaked in saline for 24 hours, the knot strength of the two largest size bands dropped to less than 1.2-mm twist-knotted wire.
Kenkmann, Thomas; Wulf, Gerwin; Sturm, Sebastian; Pietrek, Alexa
2015-04-01
The ejecta blankets of impact craters in volatile-rich environments often show characteristic layered ejecta morphologies. The so-called double-layer ejecta (DLE) craters are probably the most confusing crater types showing two ejecta layers with distinct morphologies. A phenomenological ejecta excavation and emplacement model for DLE craters is proposed based on a detailed case study of the Martian crater Steinheim - a textbook like, pristine DLE crater - and studies of other DLE craters [1]. The observations show that DLE craters on Mars are the result of an impact event into a rock/ice mixture that produces large amounts of shock-induced vaporization and melting of ground ice. The deposits of the ejecta curtain are wet in the distal part and dryer in composition in the proximal part. As a result, the outer ejecta layer is emplaced as medial and distal ejecta that propagate outwards in a fluid saturated debris flow mode after landing overrunning previously formed secondary craters. In contrast, the inner ejecta layer is formed by a translational slide of the proximal ejecta deposits. This slide overruns and superimposes parts of the outer ejecta layer. Basal melting of the ice components of the ejecta volumes at the transient crater rim is induced by frictional heating and the enhanced pressure at depth. The results indicate similar processes also for other planetary bodies with volatile-rich environments, such as Ganymede, Europa or the Earth. The Ries crater on Earth has a similar ejecta thickness distribution as DLE craters on Mars [2]. Here basal sliding and fluidization of the ejecta increases outward by the entrainment of locally derived Tertiary sands and clays, that are saturated with groundwater. References: [1] Wulf, G. & Kenkmann, T. (2015) Met. Planet. Sci. (in press); [2] Sturm, S., Wulf. G., Jung, D. & Kenkmann, T. (2013) Geology 41, 531-534.
The Origin of the Iron-Rich Knot in Tycho's Supernova Remnant
Yamaguchi, Hiroya; Badenes, Carles; Bravo, Eduardo; Seitenzahl, Ivo R; Martınez-Rodrıguez, Hector; Park, Sangwook; Petre, Robert
2016-01-01
X-ray observations of supernova remnants (SNRs) allow us to investigate the chemical inhomogeneity of ejecta, offering unique insight into the nucleosynthesis in supernova explosions. Here we present detailed imaging and spectroscopic studies of the "Fe knot" located along the eastern rim of the Type Ia SNR Tycho (SN 1572) using Suzaku and Chandra long-exposure data. Surprisingly, the Suzaku spectrum of this knot shows no emission from Cr, Mn, or Ni, which is unusual for the Fe-rich regions in this SNR. Within the framework of the canonical delayed-detonation models for SN Ia, the observed mass ratios M_Cr/M_Fe < 0.023, M_Mn/M_Fe < 0.012, and M_Ni/M_Fe < 0.029 (at 90% confidence) can only be achieved for a peak temperature of (5.3-5.7) x 10^9 K and a neutron excess of < 2.0 x 10^-3. These constraints rule out the deep, dense core of a Chandrasekhar-mass white dwarf as the origin of the Fe knot, and favors either incomplete Si burning or the alpha-rich freeze-out regime, probably close to their bou...
A pseudo-haptic knot diagram interface
Zhang, Hui; Weng, Jianguang; Hanson, Andrew J.
2011-01-01
To make progress in understanding knot theory, we will need to interact with the projected representations of mathematical knots which are of course continuous in 3D but significantly interrupted in the projective images. One way to achieve such a goal would be to design an interactive system that allows us to sketch 2D knot diagrams by taking advantage of a collision-sensing controller and explore their underlying smooth structures through a continuous motion. Recent advances of interaction techniques have been made that allow progress to be made in this direction. Pseudo-haptics that simulates haptic effects using pure visual feedback can be used to develop such an interactive system. This paper outlines one such pseudo-haptic knot diagram interface. Our interface derives from the familiar pencil-and-paper process of drawing 2D knot diagrams and provides haptic-like sensations to facilitate the creation and exploration of knot diagrams. A centerpiece of the interaction model simulates a "physically" reactive mouse cursor, which is exploited to resolve the apparent conflict between the continuous structure of the actual smooth knot and the visual discontinuities in the knot diagram representation. Another value in exploiting pseudo-haptics is that an acceleration (or deceleration) of the mouse cursor (or surface locator) can be used to indicate the slope of the curve (or surface) of whom the projective image is being explored. By exploiting these additional visual cues, we proceed to a full-featured extension to a pseudo-haptic 4D visualization system that simulates the continuous navigation on 4D objects and allows us to sense the bumps and holes in the fourth dimension. Preliminary tests of the software show that main features of the interface overcome some expected perceptual limitations in our interaction with 2D knot diagrams of 3D knots and 3D projective images of 4D mathematical objects.
Evolutionary signatures in complex ejecta and their driven shocks
Farrugia, C.; Berdichevsky, D.
2004-10-01
We examine interplanetary signatures of ejecta-ejecta interactions. To this end, two time intervals of inner-heliospheric (≤1AU) observations separated by 2 solar cycles are chosen where ejecta/magnetic clouds are in the process of interacting to form complex ejecta. At the Sun, both intervals are characterized by many coronal mass ejections (CMEs) and flares. In each case, a complement of observations from various instruments on two spacecraft are examined in order to bring out the in-situ signatures of ejecta-ejecta interactions and their relation to solar observations. In the first interval (April 1979), data are shown from Helios-2 and ISEE-3, separated by ~0.33AU in radial distance and 28° in heliographic longitude. In the second interval (March-April 2001), data from the SOHO and Wind probes are combined, relating effects at the Sun and their manifestations at 1AU on one of Wind's distant prograde orbits. At ~0.67AU, Helios-2 observes two individual ejecta which have merged by the time they are observed at 1AU by ISEE-3. In March 2001, two distinct Halo CMEs (H-CMEs) are observed on SOHO on 28-29 March approaching each other with a relative speed of 500kms-1 within 30 solar radii. In order to isolate signatures of ejecta-ejecta interactions, the two event intervals are compared with expectations for pristine (isolated) ejecta near the last solar minimum, extensive observations on which were given by Berdichevsky et al. (2002). The observations from these two event sequences are then intercompared. In both event sequences, coalescence/merging was accompanied by the following signatures: heating of the plasma, acceleration of the leading ejecta and deceleration of the trailing ejecta, compressed field and plasma in the leading ejecta, disappearance of shocks and the strengthening of shocks driven by the accelerated ejecta. A search for reconnection signatures at the interface between the two ejecta in the March 2001 event was inconclusive because the
Kelvin Waves and Dynamic Knots on Perturbative Helical Vortex Lines
Kou, Su-Peng
2016-01-01
Vortex lines are one-dimensional extended objects in three-dimensional superfluids. Vortex lines have many interesting properties, including Kelvin waves, exotic statistics, and possible entanglement. In this paper, an emergent "quantum world" is explored by projecting helical vortex lines. A one-dimensional quantum Fermionic model is developed to effectively describe the local fluctuations of helical vortex lines. The elementary excitations are knots with half winding-number that obey emergent quantum mechanics. The Biot-Savart equation, and its Kelvin wave solutions on helical vortex lines become Schrodinger equation, and the wave functions of probability waves for finding knots, respectively. This work shows an alternative approach to simulating quantum many-body physics based on classical systems.
SU(2)/SL(2) knot invariants and KS monodromies
Galakhov, D; Morozov, A
2015-01-01
We review the Reshetikhin-Turaev approach to construction of non-compact knot invariants involving R-matrices associated with infinite-dimensional representations, primarily those made from Faddeev's quantum dilogarithm. The corresponding formulas can be obtained from modular transformations of conformal blocks as their Kontsevich-Soibelman monodromies and are presented in the form of transcendental integrals, where the main issue is manipulation with integration contours. We discuss possibilities to extract more explicit and handy expressions which can be compared with the ordinary (compact) knot polynomials coming from finite-dimensional representations of simple Lie algebras, with their limits and properties. In particular, the quantum A-polynomials, difference equations for colored Jones polynomials should be the same, just in non-compact case the equations are homogeneous, while they have a non-trivial right-hand side for ordinary Jones polynomials.
Open knot-tying skills: residents skills assessed
van Empel, P.J.; Verdam, M.G.E.; Huirne, J.A.; Bonjer, H.J.; Meijerink, W.J.; Scheele, F.
2013-01-01
Aim: Open knot-tying and suturing skills are fundamental surgical skills, founding many alternative knot-tying techniques. It is therefore mandatory for residents to possess adequate basic open knot-tying skills. The aim of this study was to compare an objective assessment of open knot-tying skills
On the concordance orders of knots
Collins, Julia
2012-01-01
This thesis develops some general calculational techniques for finding the orders of knots in the topological concordance group C. The techniques currently available in the literature are either too theoretical, applying to only a small number of knots, or are designed to only deal with a specific knot. The thesis builds on the results of Herald, Kirk and Livingston [HKL10] and Tamulis [Tam02] to give a series of criteria, using twisted Alexander polynomials, for determining whether a knot is of infinite order in C. There are two immediate applications of these theorems. The first is to give the structure of the subgroups of the concordance group C and the algebraic concordance group G generated by the prime knots of 9 or fewer crossings. This should be of practical value to the knot-theoretic community, but more importantly it provides interesting examples of phenomena both in the algebraic and geometric concordance groups. The second application is to find the concordance orders of all prime knots with up t...
Torus knots and the rational DAHA
Gorsky, Eugene; Rasmussen, Jacob; Shende, Vivek
2012-01-01
We conjecturally extract the triply graded Khovanov-Rozansky homology of the (m, n) torus knot from the unique finite dimensional simple representation of the rational DAHA of type A, rank n - 1, and central character m/n. The conjectural differentials of Gukov, Dunfield and the third author receive an explicit algebraic expression in this picture, yielding a prescription for the doubly graded Khovanov-Rozansky homologies. We match our conjecture to previous conjectures of the first author relating knot homology to q, t-Catalan numbers, and of the last three authors relating knot homology to Hilbert schemes on singular curves.
Urethral catheter knotting: an avoidable complication
Ismail Burud
2013-03-01
Full Text Available Urethral catheterisation is a common andsafe procedure performed routinely. The small sizeof the urethra in a child necessitates the use of aninfant feeding tube (Size 5 to 8 F for catheterisation.Knotting within the bladder is a rare complication withsignificant morbidity often necessitating surgical orendoscopic removal. Insertion of an excessive lengthof tube contributes to coiling and knotting. We reportan instance of knotting of an infant feeding tube inthe proximal penile urethra of a 4 year-old male childrequiring urethrotomy to remove it. Awareness of therisk and proper technique can reduce this complication.
Knot Invariants from Classical Field Theories
Leal, L C
1999-01-01
We consider the Non-Abelian Chern-Simons term coupled to external particles, in a gauge and diffeomorphism invariant form. The classical equations of motion are perturbativelly studied, and the on-shell action is shown to produce knot-invariants associated with the sources. The first contributions are explicitly calculated, and the corresponding knot-invariants are recognized. We conclude that the interplay between Knot Theory and Topological Field Theories is manifested not only at the quantum level, but in a classical context as well.
Grid homology for knots and links
Ozsváth, Peter S; Szabó, Zoltán
2015-01-01
Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the ab
The Ejecta of Eta Carinae as Studied by STIS
Gull, Theodore R.; Oegerle, William R. (Technical Monitor)
2002-01-01
The Space Telescope Imaging Spectrograph has been used to study the emission and absorption spectra of ejecta surrounding Eta Carinae. Discussion will be presented on the overall structure of the Homunculus, the Weigelt blobs and the Strontium filament. Three visits have been accomplished with the Position Angle precisely the same and covering the Central Source and Weigelt Blobs B and D. Deep spectra have been done at several positions to obtain the overall velocity structure of the Homunculus and the disk region. Mapping has been done with the STIS medium dispersion gratings set near H beta and H alpha. We have obtained full coverage of the strontium filament from 1640 Angstroms to 10300 Angstroms. The structure and physical properties will be described.
A Partial Order in the Knot Table Ⅱ
Teruaki KITANO; Masaaki SUZUKI
2008-01-01
A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups.In the previous paper,we determined the partial order in the knot table.In this paper,we prove that 31 and 41 are minimal elements.Further,we study which surjection a pair of a periodic knot and its quotient knot induces,and which surjection a degree one map can induce.
Zeros of the Jones Polynomial for Torus Knots and 2-bridge Knots
HAN You-fa; ZHANG Rong-wei; WANG Lin-lin; MA Xiao-sha
2014-01-01
We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2 and e(2m+1)πi/4(m is a positive integer) can not be the zeros of Jones polynomial for torus knots Tp,q by the knowledge of the trigonometric function. We elicit the normal form of Jones polynomials of the 2-bridge knot C (−2, 2, · · · , (−1)r 2) by the recursive form and discuss the distribution of their zeros.
Probing Supernova Ejecta Dust with Stellar Lightbulbs: MID-IR Imaging of G54.1+0.3
Borkowski, Kazimierz
2015-10-01
Stellar explosions govern the interstellar dust lifecycle. In the early Universe, supernovae (SN) injected the first heavy elements into the interstellar medium (ISM). A significant fraction of ejecta was dust, but most of it might have been destroyed in supernova remnant's (SNR) reverse shocks. Our current understanding of both formation of dust in SNe and destruction of dust in shock waves is poor. We propose to observe young SNR G54.1+0.3 with the SOFIA telescope in order to advance our knowledge of dust formation in SNe. Progenitor of SN that produced G54.1+0.3 exploded in a stellar cluster containing a number of hot O and B stars. These stars heat ejecta dust to high temperatures, providing us with a unique opportunity to study its properties prior to arrival of a reverse shock and to shed light on formation of dust in SNe. Ejecta dust heated by the stellar ultraviolet radiation in the vicinity of hot stars emits most efficiently in the infrared spectral window accessible only to SOFIA. The proposed observations will provide spectral and spatial information crucial for understanding of ejecta dust properties such as its temperature, composition, and spatial distribution. We propose to do multi-band imaging observations with FORCAST in four filters to learn about spectral and spatial distribution of ejecta dust in the vicinity of hot stars. The high spatial resolution of SOFIA is crucial to our investigation, and only SOFIA can observe this dust at wavelengths where it emits radiation most efficiently. High-spatial resolution FORCAST images obtained in this investigation will be interpreted in the framework of radiatively-heated ejecta dust. When combined with Spitzer IRAC and MIPS images, and Herschel PACS images, we expect a dramatic advance in understanding of properties of ejecta dust that has not yet been processed by SNR shocks.
Kleckner, Dustin; Irvine, William T M
2013-01-01
The idea that the knottedness (hydrodynamic Helicity) of a fluid flow is conserved has a long history in fluid mechanics. The quintessential example of a knotted flow is a knotted vortex filament, however, owing to experimental difficulties, it has not been possible until recently to directly generate knotted vortices in real fluids. Using 3D printed hydrofoils and high-speed laser scanning tomography, we generate vortex knots and links and measure their subsequent evolution. In both cases, we find that the vortices deform and stretch until a series of vortex reconnections occurs, eventually resulting several disjoint vortex rings. This article accompanies a fluid dynamics video entered into the Gallery of Fluid Motion at the 66th Annual Meeting of the APS Division of Fluid Dynamics.
Cotranslational folding of deeply knotted proteins
Chwastyk, Mateusz
2015-01-01
Proper folding of deeply knotted proteins has a very low success rate even in structure-based models which favor formation of the native contacts but have no topological bias. By employing a structure-based model, we demonstrate that cotranslational folding on a model ribosome may enhance the odds to form trefoil knots for protein YibK without any need to introduce any non-native contacts. The ribosome is represented by a repulsive wall that keeps elongating the protein. On-ribosome folding proceeds through a a slipknot conformation. We elucidate the mechanics and energetics of its formation. We show that the knotting probability in on-ribosome folding is a function of temperature and that there is an optimal temperature for the process. Our model often leads to the establishment of the native contacts without formation of the knot.
The crossing number of composite knots
Lackenby, Marc
2008-01-01
It is a very old conjecture that the crossing number of knots is additive under connected sum. In other words, if K#K' is the connected sum of knots K and K', then does the equality c(K#K') = c(K) + c(K') hold? We prove that c(K#K') is at most c(K) + c(K') and at least (c(K) + c(K'))/152.
On rectangular HOMFLY for twist knots
Kononov, Ya
2016-01-01
As a new step in the study of rectangularly-colored knot polynomials, we reformulate the prescription of arXiv:1606.06015 for twist knots in the double-column representations $R=[rr]$ in terms of skew Schur polynomials. These, however, are mysteriously shifted from the standard topological locus, what makes further generalization to arbitrary $R=[r^s]$ not quite straightforward.
Counting Links and Knots in Complete Graphs
Abrams, Loren
2010-01-01
We investigate the minimal number of links and knots in complete partite graphs. We provide exact values or bounds on the minimal number of links for all complete partite graphs with all but 4 vertices in one partition, or with 9 vertices in total. In particular, we find that the minimal number of links for $K_{4,4,1}$ is 74. We also provide exact values or bounds on the minimal number of knots for all complete partite graphs with 8 vertices.
Twisted Alexander polynomials of hyperbolic knots
Dunfield, Nathan M; Jackson, Nicholas
2011-01-01
We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation to SL(2, C). It is an unambiguous symmetric Laurent polynomial whose coefficients lie in the trace field of the knot. It contains information about genus, fibering, and chirality, and moreover is powerful enough to sometimes detect mutation. We calculated this invariant numerically for all 313,209 hyperbolic knots in S^3 with at most 15 crossings, and found that in all cases it gave a sharp bound on the genus of the knot and determined both fibering and chirality. We also study how such twisted Alexander polynomials vary as one moves around in an irreducible component X_0 of the SL(2, C)-character variety of the knot group. We show how to understand all of these polynomials at once in terms of a polynomial whose coefficients lie in the function field of X_0. We use this to help explain some of the patterns observed for knots in S^3, and explore a potential...
Torus Knots and the Topological Vertex
Jockers, Hans; Soroush, Masoud
2012-01-01
We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S^3. The key role is played by the SL(2,Z) transformation, which generates a general torus knot from the unknot. Applying the topological vertex to the proposed A-branes, we rederive the colored HOMFLY polynomials for torus knots, in agreement with the Rosso and Jones formula. We show that our A-model construction is mirror symmetric to the B-model analysis of Brini, Eynard and Marino. Comparing to the recent proposal by Aganagic and Vafa for knots on S^3, we demonstrate that the disk amplitude of the A-brane associated to any knot is sufficient to reconstruct the entire B-model spectral curve. Finally, the construction of toric Lagrangian A-branes is generalized to other local toric Calabi-Yau geometries, which paves the road to study knots in other three-manifolds such as lens spaces.
Chicxulub High-Altitude Ballistic Ejecta from Central Belize
Pope, K. O.; Ocampo, A. C.
2000-01-01
Chicxulub ejecta are found in central Belize, 475 km southeast of the impact crater center. These deposits are ballistic ejecta launched along high-altitude trajectories above the atmosphere and deposited as a discontinuous sheet on the terminal Cretaceous land surface.
The Crater Ejecta Distribution on Ceres
Schmedemann, Nico; Neesemann, Adrian; Schulzeck, Franziska; Krohn, Katrin; Gathen, Isabel; Otto, Katharina; Jaumann, Ralf; Michael, Gregory; Raymond, Carol; Russell, Christopher
2017-04-01
Since March 6 2015 the Dawn spacecraft [1] has been in orbit around the dwarf planet Ceres. At small crater diameters Ceres appears to be peppered with secondary craters that often align in chains or form clusters. Some of such possible crater chains follow curved geometries and are not in a radial orientation with respect to possible source craters [2]. Ceres is a fast rotating body ( 9 h per revolution) with comparatively low surface gravity ( 0.27 m/s2). A substantial fraction of impact ejecta may be launched with velocities similar to Ceres' escape velocity (510 m/s), which implies that many ejected particles follow high and long trajectories. Thus, due to Ceres' fast rotation the distribution pattern of the reimpacting ejected material is heavily affected by Coriolis forces that results in a highly asymmetrical and curved pattern of secondary crater chains. In order to simulate flight trajectories and distribution of impact ejected material for individual craters on Ceres we used the scaling laws by [3] adjusted to the Cerean impact conditions [4] and the impact ejecta model by [5]. These models provide the starting conditions for tracer particles in the simulation. The trajectories of the particles are computed as n-body simulation. The simulation calculates the positions and impact velocities of each impacting tracer particle with respect to the rotating surface of Ceres, which is approximated by a two-axis ellipsoid. Initial results show a number of interesting features in the simulated deposition geometries of specific crater ejecta. These features are roughly in agreement with features that can be observed in Dawn imaging data of the Cerean surface. For example: ray systems of fresh impact craters, non-radial crater chains and global scale border lines of higher and lower color ratio areas. Acknowledgment: This work has been supported by the German Space Agency (DLR) on behalf of the Federal Ministry for Economic Affairs and Energy, Germany, grants 50 OW
Knots in homology spheres which have simple knot Floer homology are trivial
Eftekhary, Eaman
2010-01-01
We show that if K is a non-trivial knot inside a homology sphere X, the rank of the knot Floer homology group associated with K is strictly bigger than the rank of the Heegaard Floer homology group associated with X.
Capitanio, F.; Mottana, A.
1998-12-31
The Sanidine holocrystalline ejecta with intergranular texture from the central Sabatini Volcanic District contain high-T feldspars, out-of-equilibrium K- and Na- Ca-feldspar, and two pyroxene generations formed at different depths, as well as many mineral phases which indicate high f (H{sub 2}O) and/or f(O{sub 2}). A simple evolution model by fractional crystallization, in a plutonic or hypoabissal domain, has been derived from the mineralogical assemblages present in both the isotropic and intergranular type of ejecta. The intergranular type, the crystallization of which began at deeper levels than the isotropic one, underwent multiple pyroxene-liquidus re-equilibration during a quick magma ascent to shallower levels.
Legendrian and transverse cables of positive torus knots
Etnyre, John; LaFountain, Douglas; Tosun, Bülent
2012-01-01
In this paper we classify Legendrian and transverse knots in the knot types obtained from positive torus knots by cabling. This classification allows us to demonstrate several new phenomena. Specifically, we show there are knot types that have non-destabilizable Legendrian representatives whose...... Thurston-Bennequin invariant is arbitrarily far from maximal. We also exhibit Legendrian knots requiring arbitrarily many stabilizations before they become Legendrian isotopic. Similar new phenomena are observed for transverse knots. To achieve these results we define and study "partially thickenable" tori...
Origin of Metastable Knots in Single Flexible Chains
Dai, Liang; Renner, C. Benjamin; Doyle, Patrick S.
2015-01-01
Recent theoretical progress has explained the physics of knotting of semiflexible polymers, yet knotting of flexible polymers is relatively unexplored. We herein develop a new theory for the size distribution of knots on a flexible polymer and the existence of metastable knots. We show the free energy of a flexible molecule in a tube can be mapped to quantitatively reproduce the free energy distribution of a knot on a flexible chain. The size distribution of knots on flexible chains is expected to be universal and might be observed at a macroscopic scale, such as a string of hard balls.
Comparing models of Red Knot population dynamics
McGowan, Conor
2015-01-01
Predictive population modeling contributes to our basic scientific understanding of population dynamics, but can also inform management decisions by evaluating alternative actions in virtual environments. Quantitative models mathematically reflect scientific hypotheses about how a system functions. In Delaware Bay, mid-Atlantic Coast, USA, to more effectively manage horseshoe crab (Limulus polyphemus) harvests and protect Red Knot (Calidris canutus rufa) populations, models are used to compare harvest actions and predict the impacts on crab and knot populations. Management has been chiefly driven by the core hypothesis that horseshoe crab egg abundance governs the survival and reproduction of migrating Red Knots that stopover in the Bay during spring migration. However, recently, hypotheses proposing that knot dynamics are governed by cyclical lemming dynamics garnered some support in data analyses. In this paper, I present alternative models of Red Knot population dynamics to reflect alternative hypotheses. Using 2 models with different lemming population cycle lengths and 2 models with different horseshoe crab effects, I project the knot population into the future under environmental stochasticity and parametric uncertainty with each model. I then compare each model's predictions to 10 yr of population monitoring from Delaware Bay. Using Bayes' theorem and model weight updating, models can accrue weight or support for one or another hypothesis of population dynamics. With 4 models of Red Knot population dynamics and only 10 yr of data, no hypothesis clearly predicted population count data better than another. The collapsed lemming cycle model performed best, accruing ~35% of the model weight, followed closely by the horseshoe crab egg abundance model, which accrued ~30% of the weight. The models that predicted no decline or stable populations (i.e. the 4-yr lemming cycle model and the weak horseshoe crab effect model) were the most weakly supported.
Racah matrices and hidden integrability in evolution of knots
Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A.
2016-09-01
We construct a general procedure to extract the exclusive Racah matrices S and S bar from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R = [ 1 ], [2], [3] and [ 2 , 2 ]. The matrices S and S bar relate respectively the maps (R ⊗ R) ⊗ R bar ⟶ R with R ⊗ (R ⊗ R bar) ⟶ R and (R ⊗ R bar) ⊗ R ⟶ R with R ⊗ (R bar ⊗ R) ⟶ R. They are building blocks for the colored HOMFLY polynomials of arbitrary arborescent (double fat) knots. Remarkably, the calculation realizes an unexpected integrability property underlying the evolution matrices.
The inner knot of the Crab nebula
Lyutikov, Maxim; Porth, Oliver
2015-01-01
We model the inner knot of the Crab Nebula as a synchrotron emission coming from the non-spherical MHD termination shock of relativistic pulsar wind. The post-shock flow is mildly relativistic; as a result the Doppler-beaming has a strong impact on the shock appearance. The model can reproduce the knot location, size, elongation, brightness distribution, luminosity and polarization provided the effective magnetization of the section of the pulsar wind producing the knot is low, $\\sigma \\leq 1$. In the striped wind model, this implies that the striped zone is rather wide, with the magnetic inclination angle of the Crab pulsar $\\ge 45^\\circ$; this agrees with the previous model-dependent estimate based on the gamma-ray emission of the pulsar. We conclude that the tiny knot is indeed a bright spot on the surface of a quasi-stationary magnetic relativistic shock and that this shock is a site of efficient particle acceleration. On the other hand, the deduced low magnetization of the knot plasma implies that this i...
The inner knot of the Crab nebula
Lyutikov, Maxim; Komissarov, Serguei S.; Porth, Oliver
2016-02-01
We model the inner knot of the Crab nebula as a synchrotron emission coming from the non-spherical MHD termination shock of relativistic pulsar wind. The post-shock flow is mildly relativistic; as a result the Doppler beaming has a strong impact on the shock appearance. The model can reproduce the knot location, size, elongation, brightness distribution, luminosity and polarization provided the effective magnetization of the section of the pulsar wind producing the knot is low, σ ≤ 1. In the striped wind model, this implies that the striped zone is rather wide, with the magnetic inclination angle of the Crab pulsar ≥45°; this agrees with the previous model-dependent estimate based on the gamma-ray emission of the pulsar. We conclude that the tiny knot is indeed a bright spot on the surface of a quasi-stationary magnetic relativistic shock and that this shock is a site of efficient particle acceleration. On the other hand, the deduced low magnetization of the knot plasma implies that this is an unlikely site for the Crab's gamma-ray flares, if they are related to the fast relativistic magnetic reconnection events.
Symmetries in proteins: A knot theory approach
Chen, Shi-Jie; Dill, Ken A.
1996-04-01
Whereas the symmetries of small molecules are described by the methods of group theory, there is no corresponding way to describe the complex symmetries in proteins. We develop a quantitative method to define and classify symmetries in compact polymers, based on the mathematical theory of graphs and knots. We represent different chain folds by their ``polymer graphs,'' equivalent to contact maps. We transform those graphs into mathematical knots to give a parsing of different possible chain folds into conformational taxonomies. We use Alexander-Conway knot polynomials to characterize the knots. We find that different protein structures with the same tertiary fold, e.g., a βαβ motif with different lengths of α helix and β sheet, can be described in terms of the different powers of the propagation matrices of the knot polynomial. This identifies a fundamental type of topological length invariance in proteins, ``elongatable'' symmetries. For example, ``helix,'' ``sheet,'' ``helix-turn-helix,'' and other secondary, supersecondary, and tertiary structures define structures of any chain length. Possibly the nine superfolds identified by Thornton et al. have elongatable symmetries.
The recurrent true umbilical cord knots: a case report
I Naghi
2012-11-01
Full Text Available Background: True umbilical cord knot is one of the abnormalities of the umbilical cord. Active fetal movements create cord knotting. True umbilical cord knots are rare but may be associated with fetal distress and stillbirth. True umbilical cord knots are capable of impeding blood flow to the fetus.Case presentation: A 26-year old primigravid woman was first treated for genital herpes simplex virus (HSV type 2 at 36 weeks of gestational age. She received oral acyclovir (400 mg three times daily for 10 days. At the gestational age of 38 weeks and 5 days, fetal activity decreased and NST was nonreactive. She was delivered by cesarean section and a true umbilical cord knot was found. Four years later, in her second pregnancy, another true knot was seen.Conclusion: Excessively long umbilical cords are more likely to be associated with true knots. Genetics has an important role in determining cord length and occurrence of true knots.
Representations of Knot Groups and Twisted Alexander Polynomials
Xiao Song LIN
2001-01-01
We present a twisted version of the Alexander polynomial associated with a matrix representation of the knot group. Examples of two knots with the same Alexander module but differenttwisted Alexander polynomials are given.
Nonlinear electrodynamics is skilled with knots
Goulart, E.
2016-07-01
The aim of this letter is threefold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the specific Lagrangian density, at least if the latter gives rise to a well-posed theory. Second, is to describe the interaction between probe waves and knotted background configurations. We show that the qualitative behaviour of this interaction may be described in terms of Robinson congruences, which appear explicitly in the causal structure of the theory. Finally, we argue that optical arrangements endowed with intense background fields could be the natural place to look for the knots experimentally.
Nonlinear electrodynamics is skilled with knots
Goulart, E
2016-01-01
The aims of this letter are three-fold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the specific Lagrangian density, at least if the latter gives rise to a well-posed theory. Second is to describe the interaction between probe waves and knotted background configurations. We show that the qualitative behaviour of this interaction may be described in terms of Robinson congruences, which appear explicitly in the causal structure of the theory. Finally, we argue that optical arrangements endowed with intense background fields could be the natural place to look for the knots experimentally.
Evolutionary signatures in complex ejecta and their driven shocks
C. J. Farrugia
2004-11-01
Full Text Available We examine interplanetary signatures of ejecta-ejecta interactions. To this end, two time intervals of inner-heliospheric (≤1AU observations separated by 2 solar cycles are chosen where ejecta/magnetic clouds are in the process of interacting to form complex ejecta. At the Sun, both intervals are characterized by many coronal mass ejections (CMEs and flares. In each case, a complement of observations from various instruments on two spacecraft are examined in order to bring out the in-situ signatures of ejecta-ejecta interactions and their relation to solar observations. In the first interval (April 1979, data are shown from Helios-2 and ISEE-3, separated by ~0.33AU in radial distance and 28° in heliographic longitude. In the second interval (March-April 2001, data from the SOHO and Wind probes are combined, relating effects at the Sun and their manifestations at 1AU on one of Wind's distant prograde orbits. At ~0.67AU, Helios-2 observes two individual ejecta which have merged by the time they are observed at 1AU by ISEE-3. In March 2001, two distinct Halo CMEs (H-CMEs are observed on SOHO on 28-29 March approaching each other with a relative speed of 500kms^{-1} within 30 solar radii. In order to isolate signatures of ejecta-ejecta interactions, the two event intervals are compared with expectations for pristine (isolated ejecta near the last solar minimum, extensive observations on which were given by Berdichevsky et al. (2002. The observations from these two event sequences are then intercompared. In both event sequences, coalescence/merging was accompanied by the following signatures: heating of the plasma, acceleration of the leading ejecta and deceleration of the trailing ejecta, compressed field and plasma in the leading ejecta, disappearance of shocks and the strengthening of shocks driven by the accelerated ejecta. A search for reconnection signatures at the interface between the two ejecta in the March 2001 event was
On the concordance genus of topologically slice knots
Hom, Jennifer
2012-01-01
The concordance genus of a knot K is the minimum Seifert genus of all knots smoothly concordant to K. Concordance genus is bounded below by the 4-ball genus and above by the Seifert genus. We give a lower bound for the concordance genus of K coming from the knot Floer complex of K. As an application, we prove that there are topologically slice knots with 4-ball genus equal to one and arbitrarily large concordance genus.
Knot invariants and higher representation theory II: the categorification of quantum knot invariants
Webster, Ben
2010-01-01
We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for sl_2 and sl_3 and by Mazorchuk-Stroppel and Sussan for sl_n. We also suggest an approach to showing that these knot homologies are functorial. Our technique uses categorifications of the tensor products of integrable representations of Kac-Moody algebras and quantum groups, constructed a prequel to this paper. In particular, we construct functors on these categorifying the action of the braiding and duality of quantum group representations. These categories are based on the pictorial approach of Khovanov and Lauda.
A principle for ideal torus knots
Olsen, Kasper Wibeck; Bohr, Jakob
2013-01-01
Using bent-helix embeddings, we investigate simple and knotted torus windings that are made of tubes of finite thickness. Knots which have the shortest rope length are often denoted as ideal structures. Conventionally, the ideal structures are found by rope shortening routines. It is shown...... that alternatively they can be directly determined as maximally twisted structures. In many cases these structures are also structures with zero strain-twist coupling, i.e. structures that neither rotate one or the other way under strain. We use this principle to implement rapid numerical calculations of the ideal...
On Chebyshev polynomials and torus knots
Gavrilik, A. M.; Pavlyuk, A. M.
2009-01-01
In this work we demonstrate that the q-numbers and their two-parameter generalization, the q,p-numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely connected with the Chebyshev polynomials, can also be related with the Alexander polynomials for the class T(s,2) of torus knots, s being an odd integer, and used for finding the corresponding skein relation. Then, we develop this procedure in order to obtain, wit...
Knotted strings and leptonic flavor structure
Kephart, Thomas W; Päs, Heinrich
2011-01-01
Tight knots and links arising in the infrared limit of string theories may provide an interesting alternative to flavor symmetries for explaining the observed flavor patterns in the leptonic sector. As an example we consider a type I seesaw model where the Majorana mass structure is based on the discrete length spectrum of tight knots and links. It is shown that such a model is able to provide an excellent fit to current neutrino data and that it predicts a normal neutrino mass hierarchy as well as a small mixing angle $\\theta_{13}$.
Universal Form of Renormalizable Knots in Symbolic Dynamics
GAO Wen; PENG Shou-Li
2005-01-01
@@ The knot structure of three-dimensional flow has been constructed based on minimal braid assumption [Chin. Phys. Lett. 20 (2003) 1444]. Here we provide a new universal form of renormalizable knots. From this universal form an arbitrary renormalizable knot can be decomposed into a unique set of elementary templates.
Knotcraft the practical and entertaining art of tying knots
Macfarlan, Allan and Paulette
1983-01-01
Comprehensive reference work explains how to tie hundreds of practical (and decorative) knots in clear illustrations and precisely worded written instructions. Ideal for boaters and campers. Also covers knots in history, knot mystery and magic, and games, stunts and tricks with rope. Introduction. Index. 166 black-and-white illustrations.
On slope genera of knotted tori in the 4-space
Liu, Yi; Sun, Hongbin; Wang, Shicheng
2011-01-01
In this note, we investigate genera for the slopes of a knotted torus in the 4-sphere analogous to the genus of a classical knot. We compare various formulations of this notion, and use this notion to study the extendable subgroup of the mapping class group of the knotted torus.
(U) An Analytic Study of Piezoelectric Ejecta Mass Measurements
Tregillis, Ian Lee [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-02-16
We consider the piezoelectric measurement of the areal mass of an ejecta cloud, for the specific case where ejecta are created by a single shock at the free surface and fly ballistically through vacuum to the sensor. To do so, we define time- and velocity-dependent ejecta “areal mass functions” at the source and sensor in terms of typically unknown distribution functions for the ejecta particles. Next, we derive an equation governing the relationship between the areal mass function at the source (which resides in the rest frame of the free surface) and at the sensor (which resides in the laboratory frame). We also derive expressions for the analytic (“true”) accumulated ejecta mass at the sensor and the measured (“inferred”) value obtained via the standard method for analyzing piezoelectric voltage traces. This approach enables us to derive an exact expression for the error imposed upon a piezoelectric ejecta mass measurement (in a perfect system) by the assumption of instantaneous creation. We verify that when the ejecta are created instantaneously (i.e., when the time dependence is a delta function), the piezoelectric inference method exactly reproduces the correct result. When creation is not instantaneous, the standard piezo analysis will always overestimate the true mass. However, the error is generally quite small (less than several percent) for most reasonable velocity and time dependences. In some cases, errors exceeding 10-15% may require velocity distributions or ejecta production timescales inconsistent with experimental observations. These results are demonstrated rigorously with numerous analytic test problems.
Fates of satellite ejecta in the Saturn system, II
Alvarellos, José Luis; Dobrovolskis, Anthony R.; Zahnle, Kevin J.; Hamill, Patrick; Dones, Luke; Robbins, Stuart
2017-03-01
We assess the fates of ejecta from the large craters Aeneas on Dione and Ali Baba on Enceladus (161 and 39 km in diameter, respectively), as well as that from Herschel (130 km in diameter) on Mimas. The ejecta are treated either as 'spalls' launched from hard surfaces, or as 'rubble' launched from a weak rubble pile regolith. Once in orbit we consider the ejecta as massless test particles subject to the gravity of Saturn and its classical satellites. The great majority of escaped ejecta get swept up by the source moons. The best fit to the ejecta population decay is a stretched exponential with exponent near 1/2 (Dobrovolskis et al., Icarus 188, 481-505, 2007). We bracket the characteristic ejecta sizes corresponding to Grady-Kipp fragments and spalls. Based on this and computed impact velocities and incidence angles, the resulting sesquinary craters, if they exist, should have diameters on the order of a few meters to a few km. The observed longitude distribution of small craters on Mimas along with the findings of Bierhaus et al. that small moons should not have a secondary crater population (Icarus 218, 602-621, 2012) suggest that the most likely place to find sesquinary craters in the Saturn system is the antapex of Mimas.
Refined large N duality for torus knots
Nawata, Satoshi; Kameyama, Masaya
We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S³. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate...
Four-manifolds, geometries and knots
Hillman, Jonathan A
2007-01-01
The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruc...
Kontsevich integral for knots and Vassiliev invariants
Dunin-Barkowski, P.; Sleptsov, A.; Smirnov, A.
2013-01-01
We review quantum field theory approach to the knot theory. Using holomorphic gauge, we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental
The constrictor knot is the best ligature.
Taylor, H; Grogono, A W
2014-03-01
An ideal ligature should tighten readily and remain tight. Ligature failure can be a critical complication of invasive procedures in human and veterinary surgical practice. Previous studies have tested various knots but not the constrictor knot. A new test bench was employed to compare six ligatures using four suture materials. As tension in a ligature is not readily measured, the study employed a surrogate measurement: the force required to slide a ligature along a rod. Benchmark values tested each suture material wrapped around the rod to establish the ratio between this force and the ligature tension for each material. Each ligature was tested first during tightening and then again afterwards. The benchmark ratios were employed to calculate the tensions to evaluate which ligature and which suture material retained tension best. The model provided consistent linear relationships between the tension in the suture and the force required to pull the ligature along the rod. The constrictor knot retained tension in the ligature best (55-107% better than the next best ligature). Among the suture materials, polydioxanone had the greatest ability to retain the tension in a ligature and polyglactin the least. The constrictor knot showed superior characteristics for use as a ligature, and should be introduced into teaching and clinical practice for human and veterinary surgery. The new test bench is recommended for future testing of ligatures as well as objective comparison of suture materials.
Refined large N duality for torus knots
Nawata, Satoshi; Kameyama, Masaya
We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S³. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate...
A preliminary design of a knot undulator.
Xi, Fuchun; Shi, Tan; Fan, Qingyan; Prestemon, Soren; Wan, Weishi; An, Zhenghua; Qiao, S
2013-01-01
The magnetic field configuration of the previously proposed knot undulator [Qiao et al. (2009). Rev. Sci. Instrum. 80, 085108] is realised in the design of a hybridized elliptically polarized undulator, which is presented. Although the details of the field distribution are not the same as those in the theoretical proposal, it is demonstrated that the practical knot undulator could work perfectly. In order to understand the minor discrepancies of the two, mathematical formulae of the synchrotron radiation are derived based on the Fourier transform of the magnetic field. From the results of calculations by simulation program, the discrepancies could be well interpreted by the corresponding formulae. The results show the importance of optimization of the end sections of the knot undulator to suppress the on-axis heat load. Furthermore, a study of the impact of the undulator on beam dynamics of the storage ring was conducted using the Shanghai Synchrotron Radiation Facility as an example and the results show that the knot undulator has little effect on the beam.
Colored HOMFLY polynomials can distinguish mutant knots
Nawata, Satoshi; Singh, Vivek Kumar
2015-01-01
We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMFLY polynomials with multiplicity structure can detect mutations. As an example, we explicitly evaluate the (2,1)-colored HOMFLY polynomials that distinguish a famous mutant pair, Kinoshita-Terasaka and Conway knot.
Searching for Biosignatures in Exoplanetary Impact Ejecta
Cataldi, Gianni; Brandeker, Alexis; Thébault, Philippe; Singer, Kelsi; Ahmed, Engy; de Vries, Bernard L.; Neubeck, Anna; Olofsson, Göran
2017-08-01
With the number of confirmed rocky exoplanets increasing steadily, their characterization and the search for exoplanetary biospheres are becoming increasingly urgent issues in astrobiology. To date, most efforts have concentrated on the study of exoplanetary atmospheres. Instead, we aim to investigate the possibility of characterizing an exoplanet (in terms of habitability, geology, presence of life, etc.) by studying material ejected from the surface during an impact event. For a number of impact scenarios, we estimate the escaping mass and assess its subsequent collisional evolution in a circumstellar orbit, assuming a Sun-like host star. We calculate the fractional luminosity of the dust as a function of time after the impact event and study its detectability with current and future instrumentation. We consider the possibility to constrain the dust composition, giving information on the geology or the presence of a biosphere. As examples, we investigate whether calcite, silica, or ejected microorganisms could be detected. For a 20 km diameter impactor, we find that the dust mass escaping the exoplanet is roughly comparable to the zodiacal dust, depending on the exoplanet's size. The collisional evolution is best modeled by considering two independent dust populations, a spalled population consisting of nonmelted ejecta evolving on timescales of millions of years, and dust recondensed from melt or vapor evolving on much shorter timescales. While the presence of dust can potentially be inferred with current telescopes, studying its composition requires advanced instrumentation not yet available. The direct detection of biological matter turns out to be extremely challenging. Despite considerable difficulties (small dust masses, noise such as exozodiacal dust, etc.), studying dusty material ejected from an exoplanetary surface might become an interesting complement to atmospheric studies in the future.
Long-term dynamical evolution of dusty ejecta from Deimos
Makuch, Martin; Krivov, Alexander V.; Spahn, Frank
2005-04-01
We re-assess expected properties of the presumed dust belt of Mars formed by impact ejecta from Deimos. Previous studies have shown that dynamics of Deimos particles are dominated by two perturbing forces: radiation pressure (RP) and Mars' oblateness (J2). At the same time, they have demonstrated that lifetimes of particles, especially of grains about ten of micrometers in size, may reach more than 104 years. On such timescales, the Poynting-Robertson drag (PR) becomes important. Here we provide a study of the dynamics under the combined action of all three perturbing forces. We show that a PR decay of the semimajor axes leads to an adiabatic decrease of amplitudes and periods of oscillations in orbital inclinations predicted in the framework of the underlying RP+J2 problem. Furthermore, we show that smallest of the long-lived Deimos grains (radius≈5- 10μm) may reach a chaotic regime, resulting in unpredictable and abrupt changes of their dynamics. The particles just above that size ( ≈10- 15μm) should be the most abundant in the Deimos torus. Our dynamical analysis, combined with a more accurate study of the particle lifetimes, provides corrections to earlier predictions about the dimensions and geometry of the Deimos torus. In addition to a population, appreciably inclined and shifted towards the Sun, the torus should contain a more contracted, less asymmetric, and less tilted component between the orbits of Phobos and Deimos.
Planet formation from the ejecta of common envelopes
Schleicher, Dominik R G
2013-01-01
The close binary system NN Serpentis must have gone through a common envelope phase before the formation of its white dwarf. During this phase, a substantial amount of mass was lost from the envelope. The recently detected orbits of circumbinary planets were suggested to be inconsistent with planet formation before the mass loss. We explore whether new planets may have formed from the ejecta of the common envelope, and derive the expected planetary mass as a function of radius. We employ the model of \\citet{Kashi11} to estimate the amount of mass that is retained during the ejection event, and infer the properties of the resulting disk from the conservation of mass and angular momentum. The resulting planetary masses are estimated from models with and without radiative feedback. We show that the observed planetary masses can be reproduced for appropriate model parameters. Photoheating can stabilize the disks in the interior, potentially explaining the observed planetary orbits on scales of a few AU. We compar...
Thackrey, S.; Lee, P.; Mason, C. E.; Parnell, J.
2008-03-01
We report the discovery of a well preserved, proximal multi-layered ejecta deposit on the NW sector of the Haughton impact crater. The deposit provides evidence that subsurface volatiles plays a vital role in the emplacement of layered ejecta.
Radio continuum emission from knots in the DG Tau jet
Rodriguez, L F; Raga, A C; Canto, J; Riera, A; Loinard, L; Dzib, S A; Zapata, L A
2011-01-01
Context: HH 158, the jet from the young star DG Tau, is one of the few sources of its type where jet knots have been detected at optical and X-ray wavelengths. Aims: To search, using Very Large Array observations of this source, radio knots and if detected, compare them with the optical and X-ray knots. To model the emission from the radio knots. Methods: We analyzed archive data and also obtained new Very Large Array observations of this source, as well as an optical image, to measure the present position of the knots. We also modeled the radio emission from the knots in terms of shocks in a jet with intrinsically time-dependent ejection velocities. Results: We detected radio knots in the 1996.98 and 2009.62 VLA data. These radio knots are,within error, coincident with optical knots. We also modeled satisfactorily the observed radio flux densities as shock features from a jet with intrinsic variability. All the observed radio, optical, and X-ray knot positions can be intepreted as four successive knots, ejec...
Venusian extended ejecta deposits as time-stratigraphic markers
Izenberg, Noam R.
1992-12-01
Use of impact crater ejects at time-stratigraphic markers was established during lunar geologic mapping efforts. The basic premise is that the deposition of impact ejecta, either by itself or mixed with impact-excavated material, is superimposed on a surface. The deposit becomes an observable, mappable unit produced in a single instant in geologic time. Up to two-thirds of Venus craters exhibit extended ejecta deposits. A reconnaissance survey of 336 craters (about 40 percent of the total population) was conducted. About half the craters examined were located in and around the Beta-Atla-Themis region, and half were spread over the western hemisphere of the planet. The survey was conducted using primarily C1-MIDR images. The preliminary survey shows: (1) of the 336 craters, 223 were found to have extended ejecta deposits. This proportion is higher than that found in other Venus crater databases by up to a factor of 2. (2) 53 percent of all extended ejecta craters were unambiguously superimposed on all volcanic and tectonic units. Crater Annia Faustina's associated parabolic ejecta deposit is clearly superimposed on volcanic flows coming from Gula Mons to the west. Parabola material from Faustina has covered the lava flows, smoothing the surface and reducing its specific backscatter cross section. The stratigraphy implies that the parabola material is the youngest observable unit in the region. (3) 12 percent of extended ejecta deposits are superimposed by volcanic materials. Crater Hwangcini has extended ejecta that has been covered by volcanic flows from a dome field to the northwest, implying that the volcanic units were emplaced subsequent to the ejecta deposit and are the youngest units in the locality. (4) It is difficult to determine the stratigraphic relationships of the remaining extended ejecta deposits in SAR at C1-MIDR resolution. Examination of higher resolution images and application of the other Magellan datasets in systematic manner should resolve
Effect of knots on binding of intercalators to DNA
Medalion, Shlomi; Rabin, Yitzhak
2014-05-01
We study the effect of knots in circular dsDNA molecules on the binding of intercalating ligands. Using Monte Carlo simulations we show that depending on their handedness, the presence of knots can either suppress or enhance intercalation in supercoiled DNA. When the occupancy of intercalators on DNA is low, the effect of knots on intercalation can be captured by introducing a shift in the mean writhe of the chain that accounts for the writhe of the corresponding ideal knot. In the limit of high intercalator occupancy, the writhe distribution of different knots is strongly affected by excluded volume effects and therefore by salt concentration. Based on the finding that different knots yield well-separated probability distributions of bound intercalators, we propose a new experimental approach to determine DNA topology by monitoring the intensity of fluorescence emitted by dye molecules intercalated into knotted DNA molecules.
Characterization of the Inner Knot of the Crab: the Site of the Gamma-ray Flares?
Weisskopf, Martin C.
2015-01-01
One of the most intriguing recent discoveries has been the detection of powerful gamma-ray flares from the Crab Nebula. Such events, with a recurrence time of about once per year, can be so dramatic to make the system the brightest source in the gamma-ray sky as occurred, e.g. in April 2011. These flares challenge our understanding of how pulsar wind nebulae work and defy current astrophysical models for particle acceleration. We present here our study of the inner knot located within a fraction of an arcsecond from the pulsar with the aim of characterizing the feature and asking if this might be the site of the origin of the gamma-ray flares. We took data using Keck, HST, and Chandra obtained as part of our multi-wavelength campaign to identify the source of the enigmatic flares. We set an upper limit as to the gamma-ray flux from the knot. We also find that the dimensions, surface brightness, flux, etc. of the optical and infrared knot are all correlated with distance from the pulsar. This distance, in turn, varies with time. In addition to this most thorough characterization of the inner knot's properties, we examine the hypothesis that the knot may be the site of the flares by examining the knot separation versus the Fermi/LAT gamma-ray flux. Finally, as part of this research, we make use of a new approach employing singular value decomposition (SVD) for analyzing time series of images and compare the approach to more traditional methods. Our conclusions are only refined but not impacted by using the new approach.
Frosch, Stephan; Buchhorn, Gottfried; Hoffmann, Anja; Balcarek, Peter; Schüttrumpf, Jan Philipp; August, Florian; Stürmer, Klaus Michael; Walde, Hans Joachim; Walde, Tim Alexander
2015-05-01
In rotator cuff repair, strong and long-lasting suturing techniques that do not require additional implants are needed. This study examines the ultimate load to failure and the Young's modulus at the suture-tendon interface for a novel single-loop knot stitch and double-loop knot stitch. These values are compared to those of the modified Mason-Allen stitch. Twenty-four infraspinatus muscles with tendons were dissected from porcine shoulders (twelve Goettingen minipigs). The preparations were randomly allocated to three groups of eight samples. Load-to-failure testing of the single-loop knot stitch, the double-loop knot stitch and the mMAS were performed using a Zwick 1446 universal testing machine (Zwick-Roell AG, Ulm, Germany). The highest ultimate load to failure for the three techniques occurred with the double-loop knot stitch with a median value of 382.2 N (range 291.8-454.2 N). These values were significantly higher than those of the single-loop knot stitch, which had a median value of 259.5 N (range 139.6-366.3 N) and the modified Mason-Allen stitch, which had a median value of 309.3 N (range 84.55-382.9 N). The values of the single-loop knot stitch and the modified Mason-Allen stitch did not differ significantly. Regarding the Young's modulus, no significant differences were found between the double-loop knot stitch with a median value of 496.02 N/mm² (range 400.4-572.6 N/mm²) and the modified Mason-Allen stitch with 498.5 N/mm² (range 375.5-749.2 N/mm²) with respect to the stiffness of the suture-tendon complex. The median value for the Young's modulus of the single-loop knot stitch of 392.1 N/mm² (range 285.7-510.6 N/mm²) was significantly lower than those of the double-loop knot stitch and modified Mason-Allen stitch. This in vitro animal study demonstrated that both the single-loop knot stitch and the double-loop knot stitch have excellent ultimate load-to-failure properties when used for rotator cuff repair. The introduced single-loop knot stitch
(U) An Analytic Examination of Piezoelectric Ejecta Mass Measurements
Tregillis, Ian Lee [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-02-02
Ongoing efforts to validate a Richtmyer-Meshkov instability (RMI) based ejecta source model [1, 2, 3] in LANL ASC codes use ejecta areal masses derived from piezoelectric sensor data [4, 5, 6]. However, the standard technique for inferring masses from sensor voltages implicitly assumes instantaneous ejecta creation [7], which is not a feature of the RMI source model. To investigate the impact of this discrepancy, we define separate “areal mass functions” (AMFs) at the source and sensor in terms of typically unknown distribution functions for the ejecta particles, and derive an analytic relationship between them. Then, for the case of single-shock ejection into vacuum, we use the AMFs to compare the analytic (or “true”) accumulated mass at the sensor with the value that would be inferred from piezoelectric voltage measurements. We confirm the inferred mass is correct when creation is instantaneous, and furthermore prove that when creation is not instantaneous, the inferred values will always overestimate the true mass. Finally, we derive an upper bound for the error imposed on a perfect system by the assumption of instantaneous ejecta creation. When applied to shots in the published literature, this bound is frequently less than several percent. Errors exceeding 15% may require velocities or timescales at odds with experimental observations.
Surface-knots in 4-space an introduction
Kamada, Seiichi
2017-01-01
This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field. Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval. Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surf...
On Chebyshev polynomials and torus knots
Gavrilik, A M
2009-01-01
In this work we demonstrate that the q-numbers and their two-parameter generalization, the q,p-numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely connected with the Chebyshev polynomials, can also be related with the Alexander polynomials for the class T(s,2) of torus knots, s being an odd integer, and used for finding the corresponding skein relation. Then, we develop this procedure in order to obtain, with the help of q,p-numbers, the generalized two-variable Alexander polynomials, and prove their direct connection with the HOMFLY polynomials and the skein relation of the latter.
Towards effective topological field theory for knots
Mironov, A
2015-01-01
Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371 corresponds to the case m=2, and our generalizations sheds additional light on the structure of those mysterious formulas. Explicit expressions are now combined from Racah matrices of the type $R\\otimes R\\otimes\\bar R\\longrightarrow \\bar R$ and mixing matrices in the sectors $R^{\\otimes 3}\\longrightarrow Q$. Further extension is provided by composition rules, allowing to glue two blocks, connected by an m-strand braid (they generalize the product formula for ordinary composite knots with m=1).
Modelling circumplanetary ejecta clouds at low altitudes: a probabilistic approach
Christou, Apostolos A
2014-01-01
A model is presented of a ballistic, collisionless, steady state population of ejecta launched at randomly distributed times and velocities and moving under constant gravity above the surface of an airless planetary body. Within a probabilistic framework, closed form solutions are derived for the probability density functions of the altitude distribution of particles, the distribution of their speeds in a rest frame both at the surface and at altitude and with respect to a moving platform such as an orbiting spacecraft. These expressions are validated against numerically-generated synthetic populations of ejecta under lunar surface gravity. The model is applied to the cases where the ejection speed distribution is (a) uniform (b) a power law. For the latter law, it is found that the effective scale height of the ejecta envelope directly depends on the exponent of the power law and increases with altitude. The same holds for the speed distribution of particles near the surface. Ejection model parameters can, t...
Ejecta model development at pRad (u)
Buttler, William T [Los Alamos National Laboratory; Oro, David M [Los Alamos National Laboratory; Dimonte, Guy [Los Alamos National Laboratory; Terrones, Guillermo [Los Alamos National Laboratory; Morris, Christopher [Los Alamos National Laboratory; Bainbridge, J R [Los Alamos National Laboratory; Hogan, Gary E. [Los Alamos National Laboratory; Hollander, Brian J. [Los Alamos National Laboratory; Holtkamp, David B. [Los Alamos National Laboratory; Kwiathowski, Kris [Los Alamos National Laboratory; Marr-Lyon, Mark [Los Alamos National Laboratory; Mariam, Fesseha G. [Los Alamos National Laboratory; Merrill, Frank E [Los Alamos National Laboratory; Nedrow, Paul [Los Alamos National Laboratory; Saunders, Alexander [Los Alamos National Laboratory; Schwartz, C L [Los Alamos National Laboratory; Stone, B [Los Alamos National Laboratory; Tupa, Dale [Los Alamos National Laboratory; Vogan-McNeil, Wendy S [Los Alamos National Laboratory
2010-02-09
In July 2009 we fielded three explosively (HE) driven Richtmyer-Meshkov instability experiments at the LANSCE Proton Radiography Facility (pRad), and in August of 2009 we fielded one flyer plate experiment on the pRad 40 mm powder gun. One HE experiment was done in vacuum, and the other two within four atmospheres of noble gasses: Xe and Ne. These two gases were chosen to study the viscous effects on ejecta formation. It is unexpected, but the viscosity {eta} of Ne is twice that of Xe, and, due to the atomic mass difference between the two, the kinematic viscosity ({eta}/{rho}) of Ne is about ten times that of Xe. The results showed that ejecta formation is sensitively linked to the gas density, which implies that the Weber number is more important in ejecta formation than the Reynolds number.
Hydrodynamical interaction of mildly relativistic ejecta with an ambient medium
Suzuki, Akihiro; Shigeyama, Toshikazu
2016-01-01
Hydrodynamical interaction of spherical ejecta freely expanding at mildly relativistic speeds into an ambient cold medium is studied in semi-analytical and numerical ways to investigate how ejecta produced in energetic stellar explosions dissipate their kinetic energy through the interaction with the surrounding medium. We especially focus on the case in which the circumstellar medium is well represented by a steady wind at a constant mass-loss rate having been ejected from the stellar surface prior to the explosion. As a result of the hydrodynamical interaction, the ejecta and circumstellar medium are swept by the reverse and forward shocks, leading to the formation of a geometrically thin shell. We present a semi-analytical model describing the dynamical evolution of the shell and compare the results with numerical simulations. The shell can give rise to bright emission as it gradually becomes transparent to photons. while it is optically thick. We develop an emission model for the expected emission from th...
Chicxulub Ejecta Impact Trenches And Terminal Impact
Page, R. L.
2013-05-01
DISCOVERY During a Pacific voyage from E. Australia to the US on a small sailing research vessel what appears to be two Chicxulub impact trenches were discovered in the ocean floor at depths of 4,627m and 3,519m. DESCRIPTION Trench A begins at a depth of 4,627m, 704km from the Chicxulub impact and is 18km long, 5km wide and 225m deep. Trench B begins at a depth of 3,519m, 732km from the Chixculub impact and is 23km long, 7 km wide and 400m deep. At the end of Trench B is what appears to be a debris deposit 5km long. Their relationship to the Chicxulub impact seems confirmed by their central axis, which when extended intersect at the Chicxulub impact at N Lat 21.33, W Long 89.5. Down range 286km from the end of Trench B is what appears to be the terminal impact of the object that created the two trenches. This is in the form of several large boulders, small seamounts, and islands in shallower depths indicating breakup of the object 1040km from the Chicxulub impact. The trenches are in an area of the Caribbean where currents prevented them from being silted in, preserving their physical form on the ocean floor. The object that created the trenches could have been large ejecta from the impact or possibly part of the asteroid that separated before impact or upon impact and carried on 1000km down range. The trajectory of both trenches is an upward angle of about 3 degrees. This indicates that the trajectory of the object was at a low angle, very high velocity and was deflected slightly upward upon impact with the ocean floor 4,627 below sea level. RESEARCH The first two phases of 10 phases consisting of mapping, exploration, research, and documentation of the impacts have been completed. Phase 1 consisted of assembling available sea floor data of the area of the impacts. Phase 2 consisted of selecting aerial and under water images from Google Earth, preparing bathymetric mapping from a GEBCO_08. BODC raster analysis with 50m contour intervals of the impact area
Modeling the Effects of Knots in Structural Timber
Foley, Christina
was established, which describes variations of radial growth direction and fiber orientation related to knots in timber. The adaptability of the paradigm allows practically any softwood knot and its effect on surrounding wood material to be modeled with an accuracy that is limited only by input data. The knot......The main purpose of the pursued research presented in this thesis is to increase knowledge of the effects of knots in structural timber so that characteristics of weaker timber may be determined and applied to improve current grading techniques. In the process, a three-dimensional fiber paradigm...... are given to Shigo's knot formation theory, and thus predicts two separate patterns of fiber direction within annual growth layers related to live knots. In order to determine the possibility to practically and non destructively predict local material directions in structural timber with the three...
Factorization of differential expansion for antiparallel double-braid knots
Morozov, A
2016-01-01
Continuing the quest for exclusive Racah matrices, which are needed for evaluation of colored arborescent-knot polynomials in Chern-Simons theory, we suggest to extract them from a new kind of a double-evolution -- that of the antiparallel double-braids, which is a simple two-parametric family of two-bridge knots, generalizing the one-parametric family of twist knots. In the case of rectangular representations $R=[r^s]$ we found an evidence that the corresponding differential expansion miraculously factorizes and can be obtained from that for the twist knots. This reduces the problem of rectangular exclusive Racah to constructing the answers for just a few twist knots. We develop a recent conjecture on the structure of differential expansion for the simplest members of this family -- the trefoil and the figure-eight knot,-- but manage to guess the full answer only for contributions of single-floor pyramids. One step still remains to be done.
Hin-mediated DNA knotting and recombining promote replicon dysfunction and mutation
Mann Jennifer K
2007-05-01
Full Text Available Abstract Background The genetic code imposes a dilemma for cells. The DNA must be long enough to encode for the complexity of an organism, yet thin and flexible enough to fit within the cell. The combination of these properties greatly favors DNA collisions, which can knot and drive recombination of the DNA. Despite the well-accepted propensity of cellular DNA to collide and react with itself, it has not been established what the physiological consequences are. Results Here we analyze the effects of recombined and knotted plasmids in E. coli using the Hin site-specific recombination system. We show that Hin-mediated DNA knotting and recombination (i promote replicon loss by blocking DNA replication; (ii block gene transcription; and (iii cause genetic rearrangements at a rate three to four orders of magnitude higher than the rate for an unknotted, unrecombined plasmid. Conclusion These results show that DNA reactivity leading to recombined and knotted DNA is potentially toxic and may help drive genetic evolution.
Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices
2002-01-01
The theory of quandle (co)homology and cocycle knot invariants is rapidly being developed. We begin with a summary of these recent advances. One such advance is the notion of a dynamical cocycle. We show how dynamical cocycles can be used to color knotted surfaces that are obtained from classical knots by twist-spinning. We also demonstrate relations between cocycle invariants and Alexander matrices.
Large N duality, lagrangian cycles, and algebraic knots
Diaconescu, D -E; Vafa, C
2011-01-01
We consider knot invariants in the context of large $N$ transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicity constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.
Large N Duality, Lagrangian Cycles, and Algebraic Knots
Diaconescu, D.-E.; Shende, V.; Vafa, C.
2013-05-01
We consider knot invariants in the context of large N transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicitly constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.
Classical invariants of Legendrian knots in the 3-dimensional torus
SJ, Paul A. Schweitzer; Souza, Fábio S.
2014-01-01
All knots in $R^3$ possess Seifert surfaces, and so the classical Thurston-Bennequin and rotation (or Maslov) invariants for Legendrian knots in a contact structure on $R^3$ can be defined. The definitions extend easily to null-homologous knots in any $3$-manifold $M$ endowed with a contact structure $\\xi$. We generalize the definition of Seifert surfaces and use them to define these invariants for all Legendrian knots, including those that are not null-homologous, in a contact structure on t...
Disciplinary Knots and Learning Problems in Waves Physics
Di Renzone, Simone; Montalbano, Vera
2012-01-01
An investigation on student understanding of waves is performed during an optional laboratory realized in informal extracurricular way with few, interested and talented pupils. The background and smart intuitions of students rendered the learning path very dynamic and ambitious. The activities started by investigating the basic properties of waves by means of a Shive wave machine. In order to make quantitative observed phenomena, the students used a camcorder and series of measures were obtained from the captured images. By checking the resulting data, it arose some learning difficulties especially in activities related to the laboratory. This experience was the starting point for a further analysis on disciplinary knots and learning problems in the physics of waves in order to elaborate a teaching-learning proposal on this topic.
Rectangular superpolynomials for the figure-eight knot
Kononov, Ya
2016-01-01
We rewrite the recently proposed differential expansion formula for HOMFLY polynomials of the knot $4_1$ in arbitrary rectangular representation $R=[r^s]$ as a sum over all Young sub-diagrams $\\lambda$ of $R$ with extraordinary simple coefficients $D_{\\lambda^{tr}}(r)\\cdot D_\\lambda(s)$ in front of the $Z$-factors. Somewhat miraculously, these coefficients are made from quantum dimensions of symmetric representations of the groups $SL(r)$ and $SL(s)$ and restrict summation to diagrams with no more than $s$ rows and $r$ columns. They possess a natural $\\beta$-deformation to Macdonald dimensions and produces positive Laurent polynomials, which can be considered as plausible candidates for the role of the rectangular superpolynomials. Both polynomiality and positivity are non-evident properties of arising expressions, still they are true. This extends the previous suggestions for symmetric and antisymmetric representations (when $s=1$ or $r=1$ respectively) to arbitrary rectangular representations. As usual for ...
Racah matrices and hidden integrability in evolution of knots
Mironov, A; Morozov, An; Sleptsov, A
2016-01-01
We construct a general procedure to extract the exclusive Racah matrices S and \\bar S from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R =[1], [2], [3] and [2,2]. The matrices S and \\bar S relate respectively the maps (R\\otimes R)\\otimes \\bar R\\longrightarrow R with R\\otimes (R \\otimes \\bar R) \\longrightarrow R and (R\\otimes \\bar R) \\otimes R \\longrightarrow R with R\\otimes (\\bar R \\otimes R) \\longrightarrow R. They are building blocks for the colored HOMFLY polynomials of arbitrary arborescent (double fat) knots. Remarkably, the calculation realizes an unexpected integrability property underlying the evolution matrices.
Distal ejecta - an efficient tool to study ancient impacts?
Artemieva, N.
2011-12-01
Ejecta from impact craters received a scientific attention not too many years ago, after the revolutionary discovery of the global K-Pg layer and its Ir-anomaly. Impact ejecta are subjected to quick erosion and, hence, are not widely presented on Earth. However, globally distributed ejecta from the largest terrestial craters may be locally preserved even if the crater itself is totally obliterated. The oldest craters on Earth, Vredefort and Sudbury, are ~1.5 Gyr younger than then oldest Archean spherule layers [1-2]. These ejecta layers potentially allow to extract an important information regarding a projectile type/size, the Earth's crust and ocean. Recent numerical modeling of the K-Pg layer [3] successfully reproduced ejecta distribution around the globe including chemical composition, shock metamorphic features, and pressure-temperature history of deposited materials. It has been shown that the main components of global ejecta are projectile and sediments (the uppermost layer of the target), while materials from the crystalline basement represent the minor component and have been transported non-ballistically by atmospheric flows. These results could serve as a benchmark for the modeling of ancient impacts. As the Archean layers are much thicker and the spherules are larger, we can speculate about much larger and more frequent impacts. A few questions should be addressed via numerical modeling: 1) are these ejecta layers proximal layers of relatively small impacts or distal layers of giant impacts; 2) is there any correlation between layers at different locations;.3) why there are no any shocked minerals within these layers; 3) why the composition of spherules is mainly basaltic? In this paper the modeling results are compared with available observations (mainly on K-Pg boundary) and then are extrapolated to much larger impacts. [1] Lowe D.R., Byerly G. R., Asaro F., Kyte F. T. (1989) Science 245:959-962. [2] Simonson, B. M. and B. P. Glass (2004) Annual
Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots
Kholodenko, Arkady L., E-mail: string@clemson.edu
2016-08-15
Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang–Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric–magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada’s results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].
Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots
Kholodenko, Arkady L.
2016-08-01
Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang-Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric-magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada's results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].
Root-knot nematode resistant rootstocks for grafted watermelon
Rootstock lines of wild watermelon (Citrullus lanatus var. citroides) with resistance to root-knot nematodes (RKN) were developed by our team at the U.S. Vegetable Laboratory. Rootstock lines RKVL 301, RKVL 316, and RKVL 318 (RKVL = Root Knot Vegetable Laboratory) were compared to wild tinda (Praec...
Correspondence Between Bell Bases and Oriented Links in Knot Theory
QIAN ShangWu; GU ZhiYu
2002-01-01
From the comparison of correlation tensor in the theory of quantum network, the Alexander relation matrix in the theory of knot crystals and the identical inversion relations under the action of Pauli matrices, we show that there is a one to one correspondence between four Bell bases and four oriented links of the linkage 41 in knot theory.
Detection of Chirality and Mutations of Knots and Links
Pichai, Ramadevi
2011-01-01
In this brief presentation, we would like to present our attempts of detecting chirality and mutations from Chern-Simons gauge theory. The results show that the generalised knot invariants, obtained from Chern-Simons gauge theory, are more powerful than Jones, HOMFLYPT and Kauffman polynomials. However the classification problem of knots and links is still an open challenging problem.
Legendrian and transverse cables of positive torus knots
B. Etnyre, John; la Fountain, Douglas James; Tosun, Bulent
Thurston-Bennequin invariant is arbitrarily far from maximal. We also exhibit Legendrian knots requiring arbitrarily many stabilizations before they become Legendrian isotopic. Similar new phenomena are observed for transverse knots. To achieve these results we define and study "partially thickenable" tori...
Legendrian and transverse cables of positive torus knots
Etnyre, John; LaFountain, Douglas; Tosun, Bülent
2012-01-01
Thurston-Bennequin invariant is arbitrarily far from maximal. We also exhibit Legendrian knots requiring arbitrarily many stabilizations before they become Legendrian isotopic. Similar new phenomena are observed for transverse knots. To achieve these results we define and study "partially thickenable" tori...
Factorization of differential expansion for antiparallel double-braid knots
Morozov, A.
2016-09-01
Continuing the quest for exclusive Racah matrices, which are needed for evaluation of colored arborescent-knot polynomials in Chern-Simons theory, we suggest to extract them from a new kind of a double-evolution — that of the antiparallel double-braids, which is a simple two-parametric family of two-bridge knots, generalizing the one-parametric family of twist knots. In the case of rectangular representations R = [ r s ] we found an evidence that the corresponding differential expansion miraculously factorizes and can be obtained from that for the twist knots. This reduces the problem of rectangular exclusive Racah to constructing the answers for just a few twist knots. We develop a recent conjecture on the structure of differential expansion for the simplest members of this family (the trefoil and the figure-eight knot) and provide the exhaustive answer for the first unknown case of R = [33]. The answer includes HOMFLY of arbitrary twist and double-braid knots and Racah matrices overline{S} and S — what allows to calculate [33]-colored polynomials for arbitrary arborescent (double-fat) knots. For generic rectangular representations fully described are only the contributions of the single-floor pyramids. One step still remains to be done.
Genetic analysis of root-knot nematode resistance in potato
Draaistra, J.
2006-01-01
The development of potato varieties with resistance towards the potato cyst nematode, allowed a dramatic decrease of the use of nematicides. Subsequently the population of the free living nematodes and the root-knot nematodes ( Meloidogyne spp.) has increased. Among the root-knot nematodes, three Me
Erosion and Ejecta Reaccretion on 243 Ida and Its Moon
Geissler, Paul; Petit, Jean-Marc; Durda, Daniel D.; Greenberg, Richard; Bottke, William; Nolan, Michael; Moore, Jeffrey
1996-03-01
Galileo images of Asteroid 243 Ida and its satellite Dactyl show surfaces which are dominantly shaped by impact cratering. A number of observations suggest that ejecta from hypervelocity impacts on Ida can be distributed far and wide across the Ida system, following trajectories substantially affected by the low gravity, nonspherical shape, and rapid rotation of the asteroid. We explore the processes of reaccretion and escape of ejecta on Ida and Dactyl using three-dimensional numerical simulations which allow us to compare the theoretical effects of orbital dynamics with observations of surface morphology. The effects of rotation, launch location, and initial launch speed are first examined for the case of an ideal triaxial ellipsoid with Ida's approximate shape and density. Ejecta launched at low speeds (V≪Vesc) reimpact near the source craters, forming well-defined ejecta blankets which are asymmetric in morphology between leading and trailing rotational surfaces. The net effect of cratering at low ejecta launch velocities is to produce a thick regolith which is evenly distributed across the surface of the asteroid. In contrast, no clearly defined ejecta blankets are formed when ejecta is launched at higher initial velocities (V∼Vesc). Most of the ejecta escapes, while that which is retained is preferentially derived from the rotational trailing surfaces. These particles spend a significant time in temporary orbit around the asteroid, in comparison to the asteroid's rotation period, and tend to be swept up onto rotational leading surfaces upon reimpact. The net effect of impact cratering with high ejecta launch velocities is to produce a thinner and less uniform soil cover, with concentrations on the asteroids' rotational leading surfaces. Using a realistic model for the shape of Ida (P. Thomas, J. Veverka, B. Carcich, M. J. S. Belton, R. Sullivan, and M. Davies 1996,Icarus120, 000-000), we find that an extensive color/albedo unit which dominates the
Relative symplectic caps, 4-genus and fibered knots
Siddhartha Gadgil; Dheeraj Kulkarni
2016-05-01
We prove relative versions of the symplectic capping theorem and sufficiency of Giroux’s criterion for Stein fillability and use these to study the 4-genus of knots. More precisely, suppose we have a symplectic 4-manifold with convex boundary and a symplectic surface in such that is a transverse knot in . In this paper, we prove that there is a closed symplectic 4-manifold with a closed symplectic surface such that (, ) embeds into (, ) symplectically. As a consequence we obtain a relative version of the symplectic Thom conjecture. We also prove a relative version of the sufficiency part of Giroux’s criterion for Stein fillability, namely, we show that a fibered knot whose mondoromy is a product of positive Dehn twists bounds a symplectic surface in a Stein filling. We use this to study 4-genus of fibered knots in $\\mathbb S^3$. Further, we give a criterion for quasipositive fibered knots to be strongly quasipositive.
Knot Solitons in Spinor Bose-Einstein Condensates
Hall, David; Ray, Michael; Tiurev, Konstantin; Ruokokoski, Emmi; Gheorghe, Andrei Horia; Möttönen, Mikko
2016-05-01
Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics and science. Following a lengthy period of theoretical investigation and development, they have recently attracted great experimental interest in classical contexts ranging from knotted DNA and nanostructures to vortex knots in fluids. We demonstrate here the controlled creation and detection of knot solitons in the quantum-mechanical order parameter of a spinor Bose-Einstein condensate. Images of the superfluid reveal the circular shape of the soliton core and its associated linked rings. Our observations of the knot soliton establish an experimental foundation for future studies of their stability, dynamics and applications within quantum systems. Supported in part by NSF Grant PHY-1205822.
Knot polynomials in the first non-symmetric representation
Anokhina, A.; Mironov, A.; Morozov, A.; Morozov, And.
2014-05-01
We describe the explicit form and the hidden structure of the answer for the HOMFLY polynomial for the figure-8 and some other 3-strand knots in representation [21]. This is the first result for non-torus knots beyond (anti)symmetric representations, and its evaluation is far more complicated. We provide a whole variety of different arguments, allowing one to guess the answer for the figure-8 knot, which can be also partly used in more complicated situations. Finally we report the result of exact calculation for figure-8 and some other 3-strand knots based on the previously developed sophisticated technique of multi-strand calculations. We also discuss a formula for the superpolynomial in representation [21] for the figure-8 knot, which heavily relies on the conjectural form of superpolynomial expansion nearby the special polynomial point. Generalizations and details will be presented elsewhere.
Colored knot polynomials. HOMFLY in representation [2,1
Mironov, A; Morozov, An; Sleptsov, A
2015-01-01
This paper starts a systematic description of colored knot polynomials, beginning from the first non-(anti)symmetric representation R=[2,1]. The project involves several steps: (i) parametrization of big families of knots a la arXiv:1506.00339, (ii) evaluating Racah/mixing matrices for various numbers of strands in various representations a la arXiv:1112.2654, (iii) tabulating and collecting the results at www.knotebook.org. In this paper we discuss only representation R=[2,1] and construct all necessary ingredients that allow one to evaluate knot/links represented by three strand closed parallel braids with inserted double-fat fingers. In particular, it is used to evaluate knots from a 7-parametric family: this family contains over 80% of knots with up to 10 intersections, but does not include mutants.
The LCROSS Ejecta Plume Revealed: First Characterization from Earth-based Imaging
Miller, C.; Chanover, N.; Hermalyn, B.; Strycker, P. D.; Hamilton, R. T.; Suggs, R. M.
2012-12-01
-extracted the synthetic plume brightness profiles using the identical PCA filtering algorithm used to detect the LCROSS plume and compared results. With this method, we found that the LCROSS plume reached a peak brightness as viewed from Earth of approximately 9.8 magnitudes/arcsec^2. By varying initial particle ejection angles and velocities in our synthetic plume simulations, we were able to create a family of possible brightness profiles to compare to the detected plume. This comparison yielded constraints on the maximum initial plume particle velocities and ejection angles. We present the results of our LCROSS plume detection and discuss the range of constraints on plume initial conditions implied by our model simulations. These ground-based observations provide a unique and complementary view of the LCROSS impact ejecta compared to that provided by LCROSS S/SC and LRO, which observed the plume from above. This Earth-based data set provides a cross-sectional view and therefore provides unique information necessary to constrain initial conditions of the LCROSS ejecta and, by inference, properties of the lunar regolith on the floor of Cabeus crater.
Non-stationary Rayleigh-Taylor instability in supernovae ejecta
Ribeyre, X; Tikhonchuk, V T; Bouquet, S; Sanz, J; Ribeyre, Xavier; Hallo, Ludovic; Tikhonchuk, Vladimir; Bouquet, Serge; Sanz, Javier
2005-01-01
The Rayleigh-Taylor instability plays an important role in the dynamics of several astronomical objects, in particular, in supernovae (SN) evolution. In this paper we develop an analytical approach to study the stability analysis of spherical expansion of the SN ejecta by using a special transformation in the co-moving coordinate frame. We first study a non-stationary spherical expansion of a gas shell under the pressure of a central source. Then we analyze its stability with respect to a no radial, non spherically symmetric perturbation of the of the shell. We consider the case where the polytropic constant of the SN shell is $\\gamma=5/3$ and we examine the evolution of a arbitrary shell perturbation. The dispersion relation is derived. The growth rate of the perturbation is found and its temporal and spatial evolution is discussed. The stability domain depends on the ejecta shell thickness, its acceleration, and the perturbation wavelength.
Rubini, F; Del Zanna, L; Bacciotti, F
2007-01-01
Elongated jets from young stellar objects typically present a nodular structure, formed by a chain of bright knots of enhanced emission with individual proper motions. Though it is generally accepted that internal shocks play an important role in the formation and dynamics of such structures, their precise origin and the mechanisms behind the observed proper motions is still a matter of debate. Our goal is to study numerically the origin, dynamics, and emission properties of such knots. Axisymmetric simulations are performed with a shock-capturing code for gas dynamics, allowing for molecular, atomic, and ionized hydrogen in non-equilibrium concentrations subject to ionization/recombination processes. Radiative losses in SII lines are computed, and the resulting synthetic emission maps are compared with observations. We show that a pattern of regularly spaced internal oblique shocks, characterized by individual proper motions, is generated by the pressure gradient between the propagating jet and the time vari...
SU(2)/ SL(2) knot invariants and Kontsevich-Soibelman monodromies
Galakhov, D. M.; Mironov, A. D.; Morozov, A. Yu.
2016-05-01
We review the Reshetikhin-Turaev approach for constructing noncompact knot invariants involving Rmatrices associated with infinite-dimensional representations, primarily those constructed from the Faddeev quantum dilogarithm. The corresponding formulas can be obtained from modular transformations of conformal blocks as their Kontsevich-Soibelman monodromies and are presented in the form of transcendental integrals, where the main issue is working with the integration contours. We discuss possibilities for extracting more explicit and convenient expressions that can be compared with the ordinary (compact) knot polynomials coming from finite-dimensional representations of simple Lie algebras, with their limits and properties. In particular, the quantum A-polynomials and difference equations for colored Jones polynomials are the same as in the compact case, but the equations in the noncompact case are homogeneous and have a nontrivial right-hand side for ordinary Jones polynomials.
DNA reshaping by MukB. Right-handed knotting, left-handed supercoiling.
Petrushenko, Zoya M; Lai, Chien-Hung; Rai, Rachna; Rybenkov, Valentin V
2006-02-24
MukB is a bacterial SMC (structural maintenance of chromosome) protein required for faithful chromosome segregation in Escherichia coli. We report here that purified MukB introduces right-handed knots into DNA in the presence of type-2 topoisomerase, indicating that the protein promotes intramolecular DNA condensation. The pattern of generated knots suggests that MukB, similar to eukaryotic condensins, stabilizes large right-handed DNA loops. In contrast to eukaryotic condensins, however, the net supercoiling stabilized by MukB was negative. Furthermore, DNA reshaping by MukB did not require ATP. These data establish that bacterial condensins alter the shape of double-stranded DNA in vitro and lend support to the notions that the right-handed knotting is the most conserved biochemical property of condensins. Finally, we found that MukB can be eluted from a heparin column in two distinct forms, one of which is inert in DNA binding or reshaping. Furthermore, we find that the activity of MukB is reversibly attenuated during chromatographic separation. Thus, MukB has a unique set of topological properties, compared with other SMC proteins, and is likely to exist in two different conformations.
The Axially Symmetric Ejecta of Supernova 1987A
Wang, L; Höflich, P; Khokhlov, A; Baade, D; Branch, D; Challis, P M; Filippenko, A V; Fransson, C; Garnavich, P M; Kirshner, R P; Lundqvist, P; McCray, R; Panagia, N; Pun, C S J; Phillips, M M; Sonneborn, G; Suntzeff, N B
2002-01-01
Extensive early observations proved that the ejecta of supernova 1987A (SN 1987A) are aspherical. Fifteen years after the supernova explosion, the Hubble Space Telescope has resolved the rapidly expanding ejecta. The late-time images and spectroscopy provide a geometrical picture that is consistent with early observations and suggests a highly structured, axially symmetric geometry. We present here a new synthesis of the old and new data. We show that the Bochum event, presumably a clump of $^{56}$Ni, and the late-time image, the locus of excitation by $^{44}$Ti, are most naturally accounted for by sharing a common position angle of about 14\\degree, the same as the mystery spot and early speckle data on the ejecta, and that they are both oriented along the axis of the inner circumstellar ring at 45\\degree to the plane of the sky. We also demonstrate that the polarization represents a prolate geometry with the same position angle and axis as the early speckle data and the late-time image and hence that the geo...
Direct Ejecta Velocity Measurements of Tycho's Supernova Remnant
Sato, Toshiki
2016-01-01
We present the first direct ejecta velocity measurements of Tycho's supernova remnant (SNR). Chandra's high angular resolution images reveal a patchy structure of radial velocities in the ejecta that can be separated into distinct redshifted, blueshifted, and low velocity ejecta clumps or blobs. The typical velocities of the redshifted and blueshifted blobs are <~ 7,800 km/s and <~ 5,000 km/s, respectively. The highest velocity blobs are located near the center, while the low velocity ones appear near the edge as expected for a generally spherical expansion. Systematic uncertainty on the velocity measurements from gain calibration was assessed by carrying out joint fits of individual blobs with both the ACIS-I and ACIS-S detectors. We identified an annular region (~3.3'-3.5'), where the surface brightness in the Si, S, and Fe K lines reaches a peak while the line width reaches a minimum value. These minimum line widths correspond to ion temperatures of ~1 MeV for each of the three species, in excellent ...
Nucleosynthesis in the Ejecta of Neutron Star Mergers
Martin, Dirk; Arcones, Almudena; Korobkin, Oleg; Thielemann, Friedrich-Karl
2015-01-01
Heavy elements like gold, platinum or uranium are produced in the r-process, which needs neutron-rich and explosive environments. Neutron star mergers are a promising candidate for an r-process site. They exhibit three different channels for matter ejection fulfilling these conditions: dynamic ejecta due to tidal torques, neutrino-driven winds and evaporating matter from the accretion disk. We present a first study of the integrated nucleosynthesis for a neutrino-driven wind from a neutron star merger with a hyper-massive neutron star. Trajectories from a recent hydrodynamical simulation are divided into four different angle regions and post-processed with a reaction network. We find that the electron fraction varies around $Y_e \\approx 0.1 - 0.4$, but its distribution differs for every angle of ejection. Hence, the wind ejecta do not undergo a robust r-process, but rather possess distinct nucleosynthesis yields depending on the angle range. Compared to the dynamic ejecta, a smaller amount of neutron-rich mat...
Dynamics of Enceladus South Pole Ejecta
Makuch, Martin; Schmidt, J.; Spahn, F.
2007-10-01
The Saturnian moon Enceladus was recently found to be a potent source of gas and dust particles. There was an active region observed on the south pole of Enceladus with jets spraying material in the space. The ejected dust particles are considered to be the main source of the faint E ring. In our work we investigate the long-term dynamics of icy particles ejected from the south pole of Enceladus. The motion of the ejected grains, being subject to many perturbation forces, strongly depends on particle properties (e.g. size, charge etc.). We study the resulting spatial distribution of particles in the E ring. Primarily we focus on the structure of the ring in the vicinity of Enceladus. In our study we also concentrated on processes limiting particle lifetime. These are mainly collisions with Enceladus and other Saturnian satellites or main ring, as well as the sputtering of particles by plasma ions bombardment. Modeling the equilibrium between particle sources and sinks we found the size distribution which is expected to be observed in the E ring.
Solving Infinite Kolam in Knot Theory
Ishimoto, Yukitaka
2007-01-01
In south India, there are traditional patterns of line-drawings encircling dots, called ``Kolam'', among which one-line drawings or the ``infinite Kolam'' provide very interesting questions in mathematics. For example, we address the following simple question: how many patterns of infinite Kolam can we draw for a given grid pattern of dots? The simplest way is to draw possible patterns of Kolam while judging if it is infinite Kolam. Such a search problem seems to be NP complete. However, it is certainly not. In this paper, we focus on diamond-shaped grid patterns of dots, (1-3-5-3-1) and (1-3-5-7-5-3-1) in particular. By using the knot-theory description of the infinite Kolam, we show how to find the solution, which inevitably gives a sketch of the proof for the statement ``infinite Kolam is not NP complete.'' Its further discussion will be given in the final section.
Decay of trefoil and other magnetic knots
Candelaresi, Simon; Brandenburg, Axel
2010-01-01
Two setups with interlocked magnetic flux tubes are used to study the evolution of magnetic energy and helicity on magnetohydrodynamical (MHD) systems like plasmas. In one setup the initial helicity is zero while in the other it is finite. To see if it is the actual linking or merely the helicity content that influences the dynamics of the system we also consider a setup with unlinked field lines as well as a field configuration in the shape of a trefoil knot. For helical systems the decay of magnetic energy is slowed down by the helicity which decays slowly. It turns out that it is the helicity content, rather than the actual linking, that is significant for the dynamics.
Teaching and Learning of Knot Theory in School Mathematics
Kawauchi, Akio
2012-01-01
This book is the result of a joint venture between Professor Akio Kawauchi, Osaka City University, well-known for his research in knot theory, and the Osaka study group of mathematics education, founded by Professor Hirokazu Okamori and now chaired by his successor Professor Tomoko Yanagimoto, Osaka Kyoiku University. The seven chapters address the teaching and learning of knot theory from several perspectives. Readers will find an extremely clear and concise introduction to the fundamentals of knot theory, an overview of curricular developments in Japan, and in particular a series of teaching
Intraoperative wide bore nasogastric tube knotting: A rare incidence.
Lamba, Sangeeta; Sethi, Surendra K; Khare, Arvind; Saini, Sudheendra
2016-01-01
Nasogastric tubes are commonly used in anesthetic practice for gastric decompression in surgical patients intraoperatively. The indications for its use are associated with a number of potential complications. Knotting of small-bore nasogastric tubes is usually common both during insertion and removal as compared to wide bore nasogastric tubes. Knotting of wide bore nasogastric tube is a rare complication and if occurs usually seen in long standing cases. We hereby report a case of incidental knotting of wide bore nasogastric tube that occurred intraoperatively.
Pinus pinaster Knot: A Source of Polyphenols against Plasmopara viticola.
Gabaston, Julien; Richard, Tristan; Cluzet, Stéphanie; Palos Pinto, Antonio; Dufour, Marie-Cécile; Corio-Costet, Marie-France; Mérillon, Jean-Michel
2017-09-29
Pine knot extract from Pinus pinaster byproducts was characterized by UHPLC-DAD-MS and NMR. Fourteen polyphenols divided into four classes were identified as follows: lignans (nortrachelogenin, pinoresinol, matairesinol, isolariciresinol, secoisolariciresinol), flavonoids (pinocembrin, pinobanksin, dihydrokaempferol, taxifolin), stilbenes (pinosylvin, pinosylvin monomethyl ether, pterostilbene), and phenolic acids (caffeic acid, ferulic acid). The antifungal potential of pine knot extract, as well as the main compounds, was tested in vitro against Plasmopara viticola. The ethanolic extract showed a strong antimildew activity. In addition, pinosylvins and pinocembrin demonstrated significant inhibition of zoospore mobility and mildew development. These findings strongly suggest that pine knot is a potential biomass that could be used as a natural antifungal product.
Topological Structure of Knotted Vortex Lines in Liquid Crystals
DUAN Yi-Shi; ZHAO Li; ZHANG Xin-Hui
2007-01-01
In this paper, a novel decomposition expression for the U(1) gauge field in liquid crystals (LCs) is derived.Using this decomposition expression and the φ-mapping topological current theory,.we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons (CS) action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.
Foucart, F.; Desai, D.; Brege, W.; Duez, M. D.; Kasen, D.; Hemberger, D. A.; Kidder, L. E.; Pfeiffer, H. P.; Scheel, M. A.
2017-02-01
Neutron star-black hole binaries are among the strongest sources of gravitational waves detectable by current observatories. They can also power bright electromagnetic signals (gamma-ray bursts, kilonovae), and may be a significant source of production of r-process nuclei. A misalignment of the black hole spin with respect to the orbital angular momentum leads to precession of that spin and of the orbital plane, and has a significant effect on the properties of the post-merger remnant and of the material ejected by the merger. We present a first set of simulations of precessing neutron star-black hole mergers using a hot, composition dependent, nuclear-theory based equation of state (DD2). We show that the mass of the remnant and of the dynamical ejecta are broadly consistent with the result of simulations using simpler equations of state, while differences arise when considering the dynamics of the merger and the velocity of the ejecta. We show that the latter can easily be understood from assumptions about the composition of low-density, cold material in the different equations of state, and propose an updated estimate for the ejecta velocity which takes those effects into account. We also present an updated mesh-refinement algorithm which allows us to improve the numerical resolution used to evolve neutron star-black hole mergers.
Knots, splices and rope-work an illustrated handbook
Verrill, A Hyatt
2006-01-01
This treasury of practical and ornamental knots ranges from easy half-hitches and bow-lines to intricate rope-work projects, such as rope buckles and cask slings. Detailed instructions accompany the 148 drawings.
Linked and knotted chimera filaments in oscillatory systems.
Lau, Hon Wai; Davidsen, Jörn
2016-07-01
While the existence of stable knotted and linked vortex lines has been established in many experimental and theoretical systems, their existence in oscillatory systems and systems with nonlocal coupling has remained elusive. Here, we present strong numerical evidence that stable knots and links such as trefoils and Hopf links do exist in simple, complex, and chaotic oscillatory systems if the coupling between the oscillators is neither too short ranged nor too long ranged. In this case, effective repulsive forces between vortex lines in knotted and linked structures stabilize curvature-driven shrinkage observed for single vortex rings. In contrast to real fluids and excitable media, the vortex lines correspond to scroll wave chimeras [synchronized scroll waves with spatially extended (tubelike) unsynchronized filaments], a prime example of spontaneous synchrony breaking in systems of identical oscillators. In the case of complex oscillatory systems, this leads to a topological superstructure combining knotted filaments and synchronization defect sheets.
Topological Aspect of Knotted Vortex Filaments in Excitable Media
REN Ji-Rong; ZHU Tao; DUAN Yi-Shi
2008-01-01
Scroll waves exist ubiquitously in three-dimensional excitable media.The rotation centre can be regarded as a topological object called the vortex filament.In three-dimensional space,the vortex filaments usually form closed loops,and can be even linked and knotted.We give a rigorous topological description of knotted vortex filaments.By using the Φ-mapping topological current theory,we rewrite the topological current form of the charge density of vortex filaments,and using this topological current we reveal that the Hopf invariant of vortex filaments is just the sum of the linking and self-linking numbers of the knotted vortex filaments.We think that the precise expression of the Hopf invariant may imply a new topological constraint on knotted vortex filaments.
Tilton, Buck
2008-01-01
Untie the mystery of knot-making with this clever and handy guide. This new compendium presents all the knots you need to know, with brightly colored photographs enabling you to easily follow the instructions. In addition, the book includes copious information on using knots in most popular activities. With its clear step-by-step instructions and friendly tone, this is the one volume you can count on to guide you toward quick success in knot-making.
Chern-Simons Invariants of Torus Knots and Links
Stevan, Sébastien
2010-01-01
We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.
SOME APPLICATIONS OF PLANAR GRAPH IN KNOT THEORY
Cheng Zhiyun; Gao Hongzhu
2012-01-01
The relationship between a link diagram and its corresponding planar graph is briefly reviewed.A necessary and sufficient condition is given to detect when a planar graph corresponds to a knot.The relationship between planar graph and almost planar Seifert surface is discussed.Using planar graph,we construct an alternating amphicheiral prime knot with crossing number n for any even number n ≥ 4.This gives an affirmative answer to problem 1.66(B) on Kirby's problem list.
Exact computation of the n-loop invariants of knots
Garoufalidis, Stavros; Scott, Shane
2015-01-01
The loop invariants of Dimofte-Garoufalidis is a formal power series with arithmetically interesting coefficients that conjecturally appears in the asymptotics of the Kashaev invariant of a knot to all orders in $1/N$. We develop methods implemented in SnapPy that compute the first 6 coefficients of the formal power series of a knot. We give examples that illustrate our method and its results.
Many-knot spline technique for approximation of data
齐东旭; 李华山
1999-01-01
A class of new fundamental functions with compact support called many-knot spline is introduced. The two-scale relation for the fundamental functions is investigated, and the higher order accuracy spline approximation scheme is constructed by using the available degrees of freedom which come from additional knots. The technique has been efficiently applied to the problems such as time-frequency analysis, computer aided geometric design, and digital signal processing.
Shunt insufficiency due to knot formation in the peritoneal catheter.
Fekete, Gábor; Nagy, Andrea; Pataki, István; Bognar, László; Novák, László
2013-07-30
The authors report a rare case of the peripheral obstruction of a ventriculoperitoneal shunt. Premature baby was operated on hydrocephalus due to germinal matrix bleeding. After two months of implantation of venticuloperitoneal shunt peripheral insufficiency of the system was emerged. During the shunt revision extensive knot formation became visible. We simply cut the catheter above the knot and the working shunt was replaced into the abdominal cavity. The postoperative course was uneventful and the baby was free of complaints for more than one year. The pathomechanism of knot formation is not clear thus the discovery of the problem during the operation is an unexpected event. In our opinion tight knot cannot be spontaneously formed intraabdominally. Loose knots can be developed and can reduce the capacity of liquor flow. We think that the knot tightens during pulling out. Longer peritoneal catheters can precipitate multiple looping and/or axial torquations and increase the peripheral resistance of the shunt. In such cases when the pulling out is challenged conversion to laparotomy is suggested.
Knots in the Helix Nebula found in H2
Matsuura, M; McHunu, B M; Tanaka, I; Wright, N J; Smith, M D; Zijlstra, A A; Viti, S; Wesson, R
2009-01-01
We present a deep and wide field-of-view (4'x 7') image of the planetary nebula (PN) NGC 7293 (the Helix Nebula) in the 2.12 micron H2 v=1-0 S(1) line. The excellent seeing (0.4'') at the Subaru Telescope, allows the details of cometary knots to be examined. The knots are found at distances of 2.2'-6.4' from the central star (CS). At the inner edge and in the inner ring (up to 4.5' fromthe CS), the knot often show a `tadpole' shape, an elliptical head with a bright crescent inside and a long tail opposite to the CS. In detail, there are variations in the tadpole shapes, such as narrowing tails, widening tails, meandering tails, or multi-peaks within a tail. In the outer ring (4.5'-6.4' from the CS), the shapes are more fractured, and the tails do not collimate into a single direction. The transition in knot morphology from the inner edge to the outer ring is clearly seen. The number density of knots governs the H2 surface brightness in the inner ring: H2 exists only within the knots. Possible mechanisms which...
Neutron star kicks and their relationship to supernovae ejecta mass
Bray, J. C.; Eldridge, J. J.
2016-10-01
We propose a simple model to explain the velocity of young neutron stars. We attempt to confirm a relationship between the amount of mass ejected in the formation of the neutron star and the `kick' velocity imparted to the compact remnant resulting from the process. We assume that the velocity is given by vkick = α (Mejecta/Mremnant) + β . To test this simple relationship, we use the BPASS (Binary Population and Spectral Synthesis) code to create stellar population models from both single and binary star evolutionary pathways. We then use our Remnant Ejecta and Progenitor Explosion Relationship (REAPER) code to apply different α and β values, and three different `kick' orientations then record the resulting velocity probability distributions. We find that while a single star population provides a poor fit to the observational data, the binary population provides an excellent fit. Values of α = 70 km s-1 and β = 110 km s-1 reproduce the Hobbs et al. observed two-dimensional velocities, and α = 70 km s-1 and β = 120 km s-1 reproduce their inferred three-dimensional velocity distribution for nearby single neutron stars with ages less than 3 Myr. After testing isotropic, spin-axis aligned and orthogonal to spin-axis `kick' orientations, we find no statistical preference for a `kick' orientation. While ejecta mass cannot be the only factor that determines the velocity of supernova compact remnants, we suggest that it is a significant contributor and that the ejecta-based `kick' should replace the Maxwell-Boltzmann velocity distribution currently used in many population synthesis codes.
Lateral Translation of Explosion Crater Ejecta: A Working Model Based Upon Pellet Experiments
1975-08-19
empiric-al ejecta studies to a variety of, telds and ,eologic-al settings, and (2) characteri-ing * the relative threat the total ejecta eavironment...inmqict cratering protesi . C-urrent thenrwie.s ies•t-•,. the cratering of impart crater frwmationt arn basedt primartly upon (1) small -cale imnpact expe...ial thrown farther travels faster so that the total ejecta deposit can reflect , variety of depositional processes ranging from the low velocity
Spatial Distribution of Mg-rich Ejecta in LMC Supernova Remnant N49B
Park, Sangwook; Bhalerao, Jayant
2017-01-01
The supernova remnant (SNR) N49B in the Large Magellanic Cloud is a peculiar example of a core-collapse SNR that shows the shocked metal-rich ejecta enriched only in Mg without evidence for a similar overabundance in O and Ne. Based on archival Chandra data, we present results from our extensive spatially resolved spectral analysis of N49B. We find that the Mg-rich ejecta gas extends from the central regions of the SNR out to the southeastern outermost boundary of the SNR. This elongated feature shows an overabundance for Mg similar to that of the main ejecta region at the SNR center, and its electron temperature appears to be higher than the central main ejecta gas. We estimate that the Mg mass in this southeastern elongated ejecta feature is ∼10% of the total Mg ejecta mass. Our estimated lower limit of >0.1 M⊙ on the total mass of the Mg-rich ejecta confirms the previously suggested large mass for the progenitor star (M ≳ 25 M⊙). We entertain scenarios of an SNR expanding into a nonuniform medium and an energetic jet-driven supernova in an attempt to interpret these results. However, with the current results, the origins of the extended Mg-rich ejecta and the Mg-only-rich nature of the overall metal-rich ejecta in this SNR remain elusive.
Eloy Caballo-Ponce
2017-06-01
Full Text Available The study of the molecular basis of tree diseases is lately receiving a renewed attention, especially with the emerging perception that pathogens require specific pathogenicity and virulence factors to successfully colonize woody hosts. Pathosystems involving woody plants are notoriously difficult to study, although the use of model bacterial strains together with genetically homogeneous micropropagated plant material is providing a significant impetus to our understanding of the molecular determinants leading to disease. The gammaproteobacterium Pseudomonas savastanoi belongs to the intensively studied Pseudomonas syringae complex, and includes three pathogenic lineages causing tumorous overgrowths (knots in diverse economically relevant trees and shrubs. As it occurs with many other bacteria, pathogenicity of P. savastanoi is dependent on a type III secretion system, which is accompanied by a core set of at least 20 effector genes shared among strains isolated from olive, oleander, and ash. The induction of knots of wild-type size requires that the pathogen maintains adequate levels of diverse metabolites, including the phytohormones indole-3-acetic acid and cytokinins, as well as cyclic-di-GMP, some of which can also regulate the expression of other pathogenicity and virulence genes and participate in bacterial competitiveness. In a remarkable example of social networking, quorum sensing molecules allow for the communication among P. savastanoi and other members of the knot microbiome, while at the same time are essential for tumor formation. Additionally, a distinguishing feature of bacteria from the P. syringae complex isolated from woody organs is the possession of a 15 kb genomic island (WHOP carrying four operons and three other genes involved in degradation of phenolic compounds. Two of these operons mediate the catabolism of anthranilate and catechol and, together with another operon, are required for the induction of full-size tumors
Tsujido, S.; Arakawa, M.; Suzuki, A. I.; Yasui, M.
2014-07-01
Introduction: Regolith formation on asteroids is caused by successive impacts of small bodies. The ejecta velocity distribution during the crater formation process is one of the most important physical properties related to the surface-evolution process, and the distribution is also necessary to reconstruct the planetary-accretion process among planetesimals. The surface of small bodies, such as asteroids and planetesimals in the solar system, could have varying porosity, strength, and density, and the impact velocity could vary across a wide range from a few tens of m/s to several km/s. Therefore, it is necessary to conduct impact experiments by changing the physical properties of the target and the projectile in a wide velocity range in order to constrain the crater-formation process applicable to the small bodies in the solar system. Housen and Holsapple (2011) compiled the data of ejecta velocity distribution with various impact velocities, porosities, grain sizes, grain shapes, and strengths of the targets, and they improved their ejecta scaling law. But the ejecta velocity data is not enough for varying projectile densities and for impact velocities less than 1 km/s. In this study, to investigate the projectile density dependence of the ejecta velocity distribution at a low velocity region, we conducted impact experiments with projectile densities from 1.1 to 11.3 g/cm^3. Then, we try to determine the effect of projectile density on the ejecta velocity distribution by means of the observation of each individual ejecta grain. Experimental methods: We made impact cratering experiments by using a vertical-type one-stage light-gas gun (V-LGG) set at Kobe University. Targets were quartz sand (irregular shape) and glass beads (spherical shape) with the grain size of 500 μ m (porosity 44.7 %). The target container with the size of 30 cm was set in a large vacuum chamber with air pressure less than 10^3 Pa. The projectile materials that we used were lead, copper
Formation of Dust in the Ejecta of Type Ia Supernovae
Nozawa, Takaya; Kozasa, Takashi; Tanaka, Masaomi; Nomoto, Ken'ichi; Umeda, Hideyuki
2011-01-01
We investigate the formation of dust grains in the ejecta of Type Ia supernovae (SNe Ia), adopting the carbon-deflagration W7 model. In the calculations of dust formation, we apply the nucleation and grain growth theory and consider the two cases with and without formation of CO and SiO molecules. The results of the calculations show that for the sticking probability of alpha_j=1, C, silicate, Si, and FeS grains can condense at early times of ~100--300 days after the explosion, whereas Fe and SiC grains cannot form substantially. Due to the low gas density in SNe Ia with no H-envelope, the average radii of the newly formed grains are generally below 0.01 micron, being much smaller than those in Type II-P SNe. This supports our previous conclusion that the radius of dust formed in the ejecta is smaller in SNe with less massive envelopes. The total dust mass ranges from 3x10^{-4} M_sun to 0.2 M_sun for alpha_j=0.1--1, depending on whether or not CO and SiO molecules are formed. We also estimate the optical dept...
Neutron Star Kicks and their Relationship to Supernovae Ejecta Mass
Bray, J C
2016-01-01
We propose a simple model to explain the velocity of young neutron stars. We attempt to confirm a relationship between the amount of mass ejected in the formation of the neutron star and the `kick' velocity imparted to the compact remnant resulting from the process. We assume the velocity is given by $v_{\\rm kick}=\\alpha\\,(M_{\\rm ejecta} / M_{\\rm remnant}) + \\beta\\,$. To test this simple relationship we use the BPASS (Binary Population and Spectral Synthesis) code to create stellar population models from both single and binary star evolutionary pathways. We then use our Remnant Ejecta and Progenitor Explosion Relationship (REAPER) code to apply different $\\alpha$ and $\\beta$ values and three different `kick' orientations then record the resulting velocity probability distributions. We find that while a single star population provides a poor fit to the observational data, the binary population provides an excellent fit. Values of $\\alpha=70\\, {\\rm km\\,s^{-1}}$ and $\\beta=110\\,{\\rm km\\,s^{-1}}$ reproduce the \\c...
Optical knots and contact geometry II. From Hopf links to transverse and cosmetic knots
Kholodenko, Arkady L
2014-01-01
In 1985 Moffatt conjectured that in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. Using methods of contact geometry Etnyre and Ghrist in 2000 developed the existence-type proof of the Moffatt conjecture. The alternative proof, also of existence-type, was proposed by Enciso and Peralta -Salas in 2012. In all three papers the Beltrami equation was used as point of departure. However, only work by Etnyre and Ghrist takes full advantage of contact-geometric nature of the Beltrami equation. In this work we propose the constructive proof of the Moffatt conjecture based on ideas and methods of contact geometry. We discuss in sufficient detail various physical processes generating such knotted structures. By employing the correspondence between ideal hydrodynamics and electrodynamics discussed in part I, the Moffatt conjecture is proved for Maxwellian electrodynamics. The potential relevance of the obtained results for source-free Yang-Mills and gravity fields is also br...
Indications of a Si-rich bilateral jet of ejecta in the Vela SNR observed with XMM-Newton
García, F.; Suárez, A. E.; Miceli, M.; Bocchino, F.; Combi, J. A.; Orlando, S.; Sasaki, M.
2017-08-01
Context. The Vela supernova remnant displays several ejecta, which are fragment-like features protruding beyond the front of its primary blast shock wave. They appear to be "shrapnel", bowshock-shaped relics of the supernova explosion. One of these pieces of shrapnel (A), located in the northeastern edge of the remnant, is peculiar because its X-ray spectrum exhibits a high Si abundance, in contrast to the other observed ejecta fragments, which show enhanced O, Ne, and Mg abundances. Aims: In this Letter we present the analysis of another ejecta fragment located opposite to shrapnel A with respect to the center of the shell, in the southwestern boundary of the remnant, named shrapnel G. We aim to fully characterize its X-ray emission to gather new information about the core-collapse supernova explosion mechanism. Methods: We thoroughly analyzed a dedicated XMM-Newton observation of shrapnel G by producing background-subtracted and exposure-corrected maps in different energy ranges, which we complemented with a spatially resolved spectral analysis of the X-ray emission. Results: The fragment presents a bowshock-like shape with its anti-apex pointing to the center of the remnant. Its X-ray spectrum is best fit by a thermal plasma out of equilibrium of ionization with low O and Fe, roughly solar Ne and Mg, and a significantly high Si abundance, which is required to fit a very clear Si line at 1.85 keV. Its chemical composition and spectral properties are compatible with those of shrapnel A, which is located on the opposite side of the remnant. Conclusions: As a consequence of the nucleosynthesis, pieces of Si-rich shrapnel are expected to originate in deeper layers of the progenitor star compared to ejecta with lower-Z elements. A high velocity and density contrast with respect to the surrounding ejecta are necessary to make shrapnel A and G overtake the forward shock. The line connecting shrapnel A and G crosses almost exactly the expansion center of the remnant
Knot Invariants from Topological Recursion on Augmentation Varieties
Gu, Jie; Klemm, Albrecht; Soroush, Masoud
2014-01-01
Using the duality between Wilson loop expectation values of SU(N) Chern-Simons theory on $S^3$ and topological open-string amplitudes on the local mirror of the resolved conifold, we study knots on $S^3$ and their invariants encoded in colored HOMFLY polynomials by means of topological recursion. In the context of the local mirror Calabi-Yau threefold of the resolved conifold, we generalize the topological recursion of the remodelled B-model in order to study branes beyond the class of toric Harvey-Lawson special Lagrangians -- as required for analyzing non-trivial knots on $S^3$. The basic ingredients for the proposed recursion are the spectral curve, given by the augmentation variety of the knot, and the calibrated annulus kernel, encoding the topological annulus amplitudes associated to the knot. We present an explicit construction of the calibrated annulus kernel for torus knots and demonstrate the validity of the topological recursion. We further argue that -- if an explicit form of the calibrated annulu...
Decay of helical and non-helical magnetic knots
Candelaresi, Simon
2011-01-01
We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call $n$-foil knots of which the trefoil knot is the most primitive member. We also consider two non-helical knots, namely the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and non-helical triple ring configurations. For the $n$-foil knots the decay is described by power laws that range form $t^{-2/3}$ to $t^{-1/3}$, which can be as slow as the $t^{-1/3}$ behavior for helical triple-ring structures that was seen in earlier work. The two non-helical configurations decay like $t^{-1}$, which is somewhat slower than the previously obtained $t^{-3/2}$ behavior in the decay of interlocked ...
Analysis of Regolith Simulant Ejecta Distributions from Normal Incident Hypervelocity Impact
Edwards, David L.; Cooke, William; Suggs, Rob; Moser, Danielle E.
2008-01-01
The National Aeronautics and Space Administration (NASA) has established the Constellation Program. The Constellation Program has defined one of its many goals as long-term lunar habitation. Critical to the design of a lunar habitat is an understanding of the lunar surface environment; of specific importance is the primary meteoroid and subsequent ejecta environment. The document, NASA SP-8013 'Meteoroid Environment Model Near Earth to Lunar Surface', was developed for the Apollo program in 1969 and contains the latest definition of the lunar ejecta environment. There is concern that NASA SP-8013 may over-estimate the lunar ejecta environment. NASA's Meteoroid Environment Office (MEO) has initiated several tasks to improve the accuracy of our understanding of the lunar surface ejecta environment. This paper reports the results of experiments on projectile impact into powdered pumice and unconsolidated JSC-1A Lunar Mare Regolith simulant targets. Projectiles were accelerated to velocities between 2.45 and 5.18 km/s at normal incidence using the Ames Vertical Gun Range (AVGR). The ejected particles were detected by thin aluminum foil targets strategically placed around the impact site and angular ejecta distributions were determined. Assumptions were made to support the analysis which include; assuming ejecta spherical symmetry resulting from normal impact and all ejecta particles were of mean target particle size. This analysis produces a hemispherical flux density distribution of ejecta with sufficient velocity to penetrate the aluminum foil detectors.
Ejecta Production in Microgravity from Low Velocity Impacts in Regolith
Colwell, J. E.; Dove, A.; Brisset, J.; Rascon, A. N.; Brightwell, K.
2015-12-01
We report on the results of the third PRIME (Physics of Regolith Impacts in Microgravity Experiment) campaign on-board the NASA C-9 airplane in August 2014. The objective of PRIME is to study low-velocity impacts of cm-scale particles into planetary regolith under reduced gravity and microgravity conditions, measuring how dust on the surfaces of planetary ring particles, planetesimals and asteroids dissipates energy in the collision and the mass-velocity distribution of any ejecta produced in the impact. PRIME can perform impacts into granular materials at speeds of ~5-50 cm/s in microgravity. Impacts are performed in vacuum and projectiles are spherical particles launched by a spring designed to provide the desired impact energy. The target materials studied are quartz sand and JSC-1 lunar regolith simulant, filled to a depth of 2 cm in the target tray. Projectile materials are quartz, brass, and stainless steel to provide a range of impact energies at constant impact velocity. Impacts are performed in isolated chambers and up to 8 experiments can be performed per flight. The data collected consists of video recordings of the impacts, taken with a high resolution video camera at 120 frames per second. The impacts observed during the PRIME-3 campaign resulted in 9 marble rebounds and 15 impacts with ejecta. Seven of these 15 were at accelerations of ~0.05 g while the remaining impacts were performed in free fall. For each rebound observed, the coefficient of restitution of the impact was measured and for each collision that produced ejecta, the ejected particles were tracked to determine their initial velocities. The PRIME-3 campaign successfully extended the region of the parameter field explored by investigating impacts at velocities lower than observed during previous campaigns while collecting new data on impacts at asteroid gravity levels. We present our new results and combine them with results from previous similar experiments and discuss applications to
Dust in the Early Universe: Dust Formation in the Ejecta of Population III Supernovae
Nozawa, T; Umeda, H; Maeda, K; Nomoto, K; Nozawa, Takaya; Kozasa, Takashi; Umeda, Hideyuki; Maeda, Keiichi; Nomoto, Ken'ichi
2003-01-01
We investigate the formation of dust grains in the ejecta of population III supernovae including pair--instability supernovae, applying a theory of non-- steady state nucleation and grain growth. In the calculations, the time evolution of gas temperature in theejecta, which strongly affects the number density and size of newly formed grains, is calculated by solving the radiative transfer equation taking account of the energy deposition of radio active elements. Two extreme cases are considered for the mixing of elements in the ejecta; unmixed and uniformly mixed cases within the He--core. The results of calculations are summarized as the followings; in the unmixed ejecta, a variety of grain species condense, reflecting the difference of the elemental composition at the formation site in the ejecta, otherwise only oxide grains condense in the uniformly mixed ejecta. The average size of newly formed grains spans the range of three orders of magnitude, depending on the grain species and the formation condition,...
Tsujido, Sayaka; Arakawa, Masahiko; Suzuki, Ayako I.; Yasui, Minami
2015-12-01
In order to clarify the effects of projectile density on ejecta velocity distributions for a granular target, impact cratering experiments on a quartz sand target were conducted by using eight types of projectiles with different densities ranging from 11 g cm-3 to 1.1 g cm-3, which were launched at about 200 m s-1 from a vertical gas gun at Kobe University. The scaling law of crater size, the ejection angle of ejecta grains, and the angle of the ejecta curtain were also investigated. The ejecta velocity distribution obtained from each projectile was well described by the π-scaling theory of v0/√{gR} =k2(x0/R)-1/μ, where v0, g, R and x0 are the ejection velocity, gravitational acceleration, crater radius and ejection position, respectively, and k2 and μ are constants mostly depending on target material properties (Housen, K.R., Holsapple, K.A. [2011]. Icarus 211, 856-875). The value of k2 was found to be almost constant at 0.7 for all projectiles except for the nylon projectile, while μ increased with the projectile density, from 0.43 for the low-density projectile to 0.6-0.7 for the high-density projectile. On the other hand, the π-scaling theory for crater size gave a μ value of 0.57, which was close to the average of the μ values obtained from ejecta velocity distributions. The ejection angle, θ, of each grain decreased slightly with distance, from higher than 45° near the impact point to 30-40° at 0.6 R. The ejecta curtain angle is controlled by the two elementary processes of ejecta velocity distribution and ejection angle; it gradually increased from 52° to 63° with the increase of the projectile density. The comparison of our experimental results with the theoretical model of the crater excavation flow known as the Z-model revealed that the relationship between μ and θ obtained by our experiments could not be described by the Z-model (Maxwell, D.E. [1977]. In: Roddy, D.J., Pepin, R.O., Merrill, R.B. (Eds.), Impact and Explosion Cratering
The reionization of unshocked ejecta in SN 1006
Hamilton, Andrew J. S.; Fesen, Robert A.
1988-01-01
The validity of carbon-deflagration models white dwarf models for type Ia supernovae is investigated by examining whether most of the iron in the center of SN 1006 exists in forms other than Fe II, such as iron grains or other ionic stages of iron, as the models require. The possible ways in which iron can be hidden in SN 1006 are reviewed, and an argument on observational grounds is made against any appreciable fraction of iron in grains or Fe I. Various mechanisms for ionizing unshocked iron beyond Fe II are discussed; the most probable mechanism for ionizing the iron appears to be photoionization by UV and X-ray emission from reverse-shocked ejecta. A detailed model for this reverse-shcok photoionization mechanism is described.
Is the Ejecta of ETA Carinae Overabundant or Overexcited
Gull, Theodore; Davidson, Kris; Johansson, Sveneric; Damineli, Augusto; Ishibashi, Kaxunori; Corcoran, Michael; Hartman, Henrick; Viera, Gladys; Nielsen, Krister
2003-01-01
The ejecta of Eta Carinae, revealed by HST/STIS, are in a large range of physical conditions. As Eta Carinae undergoes a 5.52 period, changes occur in nebular emission and nebular absorption. "Warm" neutral regions, partially ionized regions, and fully ionized regions undergo significant changes. Over 2000 emission lines, most of Fe-like elements, have been indentified in the Weigelt blobs B and D. Over 500 emission lines have been indentified in the Strontium Filament. An ionized Little Homunculus is nestled within the neutral-shelled Homunculus. In line of sight, over 500 nebular absorption lines have been identified with up to twenty velocity components. STIS is following changes in many nebular emission and absorption lines as Eta Carinae approaches the minimum, predicted to be in June/July 2003, during the General Assembly. Coordinated observations with HST, CHANDRA, RXTE, FUSE, UVES/VLT, Gemini and other observatories are following this minimum.
Is the Ejecta of Eta Carinae Overabundant or Overexcited?
Gull, Theodore; Davidson, Kris; Johansson, Sveneric; Damineli, Augusto; Ishibashi, Kazunori; Corcoran, Michael; Hartman, Henrick; Viera, Gladys; Nielsen, Krister; Eta Carinae Teams
The ejecta of Eta Carinae revealed by HST/STIS are in a large range of physical conditions. As Eta Carinae undergoes a 5.52 period changes occur in nebular emission and nebular absorption. ""Warm"" neutral regions partially ionized regions and fully ionized regions undergo significant changes. Over 2000 emission lines most of Fe-like elements have been indentified in the Weigelt blobs B and D. Over 500 emission lines have been identifed in the Strontium Filament. An ionized Little Homunculus is nestled within the neutral-shelled Homunculus. In line of sight over 500 nebular absorption lines have been identified with up to twenty velocity components. STIS is following changes in many nebular emission and absorption lines as Eta Carinae approaches the minimum predicted to be in June/July 2003 during the General Assembly. Coordinated observations with HST CHANDRA RXTE FUSE UVES/VLT Gemini and other observatories are following this minimum.
On the evolution of ejecta fragments in compact supernova remnants
Cid-Fernandes, R; Rózyczka, M; Franco, J; Terlevich, R J; Tenorio-Tagle, G; Miller, W
1996-01-01
We examine the evolution of inhomogeneities (fragments) of supernova ejecta in compact supernova remnants by means of hydrodynamical modeling and simplified analytical calculations. Under the influence of intense post-shock cooling the fragments become strongly compressed as they traverse the hot shocked region between the reverse and outer shocks of the remnant. We find that the most likely outcome of the interaction of fragments with the reverse shock and the hot shocked region is their disruption resulting in generation of secondary fragments. Secondary fragments arriving at the thin and dense outer shell of the remnant give rise to brief X-ray flashes. Under suitable conditions the primary fragments may traverse the hot shocked region without being completely destroyed, to eventually reach the outer shell as dense, elongated structures. Collisions of such fragments with the shell are likely to give rise to powerful X-ray flares.
Ham, J.-Y.; Lee, J.
2016-09-01
We calculate the Chern-Simons invariants of twist-knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of twist knot cone-manifold structures. Following the general instruction of Hilden, Lozano, and Montesinos-Amilibia, we here present concrete formulae and calculations. We use the Pythagorean Theorem, which was used by Ham, Mednykh and Petrov, to relate the complex length of the longitude and the complex distance between the two axes fixed by two generators. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic twist-knot orbifolds. We also derive some interesting results. The explicit formulae of the A-polynomials of twist knots are obtained from the complex distance polynomials. Hence the edge polynomials corresponding to the edges of the Newton polygons of the A-polynomials of twist knots can be obtained. In particular, the number of boundary components of every incompressible surface corresponding to slope -4n+2 turns out to be 2. Bibliography: 39 titles.
Differential expansion and rectangular HOMFLY for the figure eight knot
A. Morozov
2016-10-01
Full Text Available Differential expansion (DE for a Wilson loop average in representation R is built to respect degenerations of representations for small groups. At the same time it behaves nicely under some changes of the loop, e.g. of some knots in the case of 3d Chern–Simons theory. Especially simple is the relation between the DE for the trefoil 31 and for the figure eight knot 41. Since arbitrary colored HOMFLY for the trefoil are known from the Rosso–Jones formula, it is therefore enough to find their DE in order to make a conjecture for the figure eight. We fulfill this program for all rectangular representation R=[rs], i.e. make a plausible conjecture for the rectangularly colored HOMFLY of the figure eight knot, which generalizes the old result for totally symmetric and antisymmetric representations.
Untangling knots via reaction-diffusion dynamics of vortex strings
Maucher, Fabian
2016-01-01
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.
Differential expansion and rectangular HOMFLY for the figure eight knot
Morozov, A
2016-01-01
Differential expansion (DE) for a Wilson loop average in representation $R$ is built to respect degenerations of representations for small groups. At the same time it behaves nicely under some changes of the loop, e.g. of some knots in the case of $3d$ Chern-Simons theory. Especially simple is the relation between the DE for the trefoil $3_1$ and for the figure eight knot $4_1$. Since arbitrary colored HOMFLY for the trefoil are known from the Rosso-Jones formula, it is therefore enough to find their DE in order to make a conjecture for the figure eight. We fulfil this program for all rectangular representation $R=[r^s]$, i.e. make a plausible conjecture for the rectangularly colored HOMFLY of the figure eight knot, which generalizes the old result for totally symmetric and antisymmetric representations.
Differential expansion and rectangular HOMFLY for the figure eight knot
Morozov, A.
2016-10-01
Differential expansion (DE) for a Wilson loop average in representation R is built to respect degenerations of representations for small groups. At the same time it behaves nicely under some changes of the loop, e.g. of some knots in the case of 3d Chern-Simons theory. Especially simple is the relation between the DE for the trefoil 31 and for the figure eight knot 41. Since arbitrary colored HOMFLY for the trefoil are known from the Rosso-Jones formula, it is therefore enough to find their DE in order to make a conjecture for the figure eight. We fulfill this program for all rectangular representation R = [rs ], i.e. make a plausible conjecture for the rectangularly colored HOMFLY of the figure eight knot, which generalizes the old result for totally symmetric and antisymmetric representations.
Untangling Knots Via Reaction-Diffusion Dynamics of Vortex Strings
Maucher, Fabian; Sutcliffe, Paul
2016-04-01
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.
Classification of knotted tori in 2-metastable dimension
Cencelj, Matija
2012-11-30
This paper is devoted to the classical Knotting Problem: for a given manifold N and number m describe the set of isotopy classes of embeddings N → Sm. We study the specific case of knotted tori, that is, the embeddings Sp × Sq → Sm. The classification of knotted tori up to isotopy in the metastable dimension range m > p + 3 2 q + 2, p 6 q, was given by Haefliger, Zeeman and A. Skopenkov. We consider the dimensions below the metastable range and give an explicit criterion for the finiteness of this set of isotopy classes in the 2-metastable dimension: Theorem. Assume that p+ 4 3 q +2 < mp+ 3 2 q +2 and m > 2p+q +2. Then the set of isotopy classes of smooth embeddings Sp × Sq → Sm is infinite if and only if either q + 1 or p + q + 1 is divisible by 4. © 2012 RAS(DoM) and LMS.
Distal ejecta from lunar impacts: Extensive regions of rocky deposits
Bandfield, Joshua L.; Cahill, Joshua T. S.; Carter, Lynn M.; Neish, Catherine D.; Patterson, G. Wesley; Williams, Jean-Pierre; Paige, David A.
2017-02-01
Lunar Reconnaissance Orbiter (LRO) Diviner Radiometer, Mini-RF, and LRO Camera data were used to identify and characterize rocky lunar deposits that appear well separated from any potential source crater. Two regions are described: 1) A ∼18,000 km2 area with elevated rock abundance and extensive melt ponds and veneers near the antipode of Tycho crater (167.5°E, 42.5°N). This region has been identified previously, using radar and imaging data. 2) A much larger and more diffuse region, covering ∼730,000 km2, centered near 310°E, 35°S, containing elevated rock abundance and numerous granular flow deposits on crater walls. The rock distributions in both regions favor certain slope azimuths over others, indicating a directional component to the formation of these deposits. The spatial distribution of rocks is consistent with the arrival of ejecta from the west and northwest at low angles (∼10-30°) above the horizon in both regions. The derived age and slope orientations of the deposits indicate that the deposits likely originated as ejecta from the Tycho impact event. Despite their similar origin, the deposits in the two regions show significant differences in the datasets. The Tycho crater antipode deposit covers a smaller area, but the deposits are pervasive and appear to be dominated by impact melts. By contrast, the nearside deposits cover a much larger area and numerous granular flows were triggered. However, the features in this region are less prominent with no evidence for the presence of impact melts. The two regions appear to be surface expressions of a distant impact event that can modify surfaces across wide regions, resulting in a variety of surface morphologies. The Tycho impact event may only be the most recent manifestation of these processes, which likely have played a role in the development of the regolith throughout lunar history.
Modeling the human intestinal mucin (MUC2) C-terminal cystine knot dimer.
Sadasivan, Vatsala D; Narpala, Sandeep R; Budil, David E; Sacco, Albert; Carrier, Rebecca L
2011-11-01
Intestinal mucus, a viscous secretion that lines the mucosa, is believed to be a barrier to absorption of many therapeutic compounds and carriers, and is known to play an important physiological role in controlling pathogen invasion. Nevertheless, there is as yet no clear understanding of the barrier properties of mucus, such as the nature of the molecular interactions between drug molecules and mucus components as well as those that govern gel formation. Secretory mucins, large and complex glycoprotein molecules, are the principal determinants of the viscoelastic properties of intestinal mucus. Despite the important role that mucins play in controlling transport and in diseases such as cystic fibrosis, their structures remain poorly characterized. The major intestinal secretory mucin gene, MUC2, has been identified and fully sequenced. The present study was undertaken to determine a detailed structure of the cysteine-rich region within the C-terminal end of human intestinal mucin (MUC2) via homology modeling, and explore possible configurations of a dimer of this cysteine-rich region, which may play an important role in governing mucus gel formation. Based on sequence-structure alignments and three-dimensional modeling, a cystine knot tertiary structure homologous to that of human chorionic gonadotropin (HCG) is predicted at the C-terminus of MUC2. Dimers of this C-terminal cystine knot (CTCK) were modeled using sequence alignment based on HCG and TGF-beta, followed by molecular dynamics and simulated annealing. Results support the formation of a cystine knot dimer with a structure analogous to that of HCG.
Knots and physics: Old wine in new bottles
Hirshfeld, Allen C.
1998-12-01
The history of the interplay between physics and mathematics in the theory of knots is briefly reviewed. In particular, Gauss' original definition of the linking number in the context of electromagnetism is presented, along with analytical, algebraical, and geometrical derivations. In a modern context, the linking number appears in the first-order term in the perturbation expansion of a Wilson loop in Chern-Simons quantum field theory. New knot invariants, the Vassiliev numbers, arise in higher-order terms of the expansion, and can be written in a form which shows them to be generalizations of the linking number.
Excitation of knotted vortex lines in matter waves
Maucher, F.; Gardiner, S. A.; Hughes, I. G.
2016-06-01
We study the creation of knotted ultracold matter waves in Bose-Einstein condensates via coherent two-photon Raman transitions with a Λ level configuration. The Raman transition allows an indirect transfer of atoms from the internal state | a> to the target state | b> via an excited state | e> , that would be otherwise dipole-forbidden. This setup enables us to imprint three-dimensional knotted vortex lines embedded in the probe field to the density in the target state. We elaborate on experimental feasibility as well as on subsequent dynamics of the matter wave.
Root - knot nematodes on summer vegetables in North Tunisia
Moens, M.
1985-01-01
Full Text Available The influence of different factors on the root-knot nematode infestation and on the yield of tomato have been examined : date of planting, cultivar choice, rotation scheme and soil disinfestation. It was found that the earliest planting date gave the highest yield but also the most severe root galling on susceptible tomato cultivars. A cropping sequence where wheat is alternated with tomatoes was not sufficient for reducing root-knot nematode population to a level permitting the cropping of a susceptible tomato cultivar. Long rotations with non host crops should be used. Soil treatment with certain nematicides significantly reduced the root galling and improved the yield.
Successful Treatment of Stent Knot in the Proximal Ureter Using Ureteroscopy and Holmium Laser
Masters M. Richards
2011-01-01
Full Text Available Knotted ureteral stent is rare yet tedious complication that might represent a treatment challenge to the endourologist. Only twelve cases of knotted stent have been reported. Different management options have been reported, including simple traction, ureteroscopy, percutaneous removal, and open surgery. In this paper, we present the successful untying of the knot using ureteroscopy with holmium laser.
The Mental Manipulation of 2-D Representations of Knots as Deformable Structures.
McLeay, Heather; Piggins, David
1996-01-01
Spatial tests involving the comparison of diagrams of interlaced ropes or knots at varying orientations were given to (n=21) subjects, mostly English college undergraduates, to determine an ordering in terms of complexity of tasks involving the mental manipulation of the knots. Certain knot shapes were processed faster than others and greater…
邓宇晨; 顾嘉伟; 聂菲; 肖良
2016-01-01
胱氨酸结（cystine knot ，CK）模体是由两对二硫键及其相连的肽链骨架形成的一个内部环以及从环中穿过的第三对二硫键组成的球形结构，广泛存在于真菌、植物、海洋软体动物、昆虫以及蜘蛛等生物的毒素多肽和蛋白质中。CK多肽结构非常稳定、生物活性多样，是一类在药物设计和分子工程研究中的理想模型分子。本文综述了抑制剂胱氨酸结（inhibitor cystine knot ，ICK）多肽和环形胱氨酸结（cyclic cystine knot ，CCK）多肽两类主要CK毒素的氨基酸序列、拓扑结构、排列组合、人工合成以及空间折叠等特征，并进一步阐述了其在药物设计与分子工程中的应用前景。%The cystine knot (CK) motif comprises an internal ring formed by two disulfide bonds and their connecting backbone segments which is threaded by a third disulfide bond .It is present in peptides and proteins of a variety of species ,in-cluding fungi ,plants ,marine molluscs ,insects and spiders .CK polypeptide is one of the ideal model molecules for drug design and molecular engineering research because of its stable structure and variety of bioactivities .Here we summarized the main structural features of both inhibitor cystine knot (ICK) peptide and cyclic cystine knot (CCK) peptide ,including primary se-quence ,topology ,permutation ,synthesis and folding characteristics ,as well as its applications on drug design and molecular engineering .
Fe K and ejecta emission in SNR G15.9+0.2 with XMM-Newton
Maggi, Pierre
2016-01-01
Aims: We present a study of the Galactic supernova remnant SNR G15.9+0.2 with archival XMM-Newton observations. Methods: EPIC data are used to investigate the morphological and spectral properties of the remnant, searching in particular for supernova ejecta and Fe K line emission. By comparing the SNR's X-ray absorption column density with the atomic and molecular gas distribution along the line of sight, we attempt to constrain the distance to the SNR. Results: Prominent line features reveal the presence of ejecta. Abundance ratios of Mg, Si, S, Ar, and Ca strongly suggest that the progenitor of SNR G15.9+0.2 was a massive star with a main sequence mass likely in the range 20-25 $M_{\\odot}$, strengthening the physical association with a candidate central compact object detected with Chandra. Using EPIC's collective power, Fe K line emission from SNR G15.9+0.2 is detected for the first time. We measure the line properties and find evidence for spatial variations. We discuss how the source fits within the samp...
Goriely, S.; Bauswein, A.; Just, O.; Pllumbi, E.; Janka, H.-Th.
2015-10-01
We investigate β-interactions of free nucleons and their impact on the electron fraction (Ye) and r-process nucleosynthesis in ejecta characteristic of binary neutron star mergers (BNSMs). For that we employ trajectories from a relativistic BNSM model to represent the density-temperature evolutions in our parametric study. In the high-density environment, positron captures decrease the neutron richness at the high temperatures predicted by the hydrodynamic simulation. Circumventing the complexities of modelling three-dimensional neutrino transport, (anti)neutrino captures are parametrized in terms of prescribed neutrino luminosities and mean energies, guided by published results and assumed as constant in time. Depending sensitively on the adopted νe-bar{ν }_e luminosity ratio, neutrino processes increase Ye to values between 0.25 and 0.40, still allowing for a successful r-process compatible with the observed solar abundance distribution and a significant fraction of the ejecta consisting of r-process nuclei. If the νe luminosities and mean energies are relatively large compared to the bar{ν }_e properties, the mean Ye might reach values >0.40 so that neutrino captures seriously compromise the success of the r-process. In this case, the r-abundances remain compatible with the solar distribution, but the total amount of ejected r-material is reduced to a few per cent, because the production of iron-peak elements is favoured. Proper neutrino physics, in particular also neutrino absorption, have to be included in BNSM simulations before final conclusions can be drawn concerning r-processing in this environment and concerning observational consequences like kilonovae, whose peak brightness and colour temperature are sensitive to the composition-dependent opacity of the ejecta.
A possible formation mechanism of rampart-like ejecta pattern in a laboratory
Suzuki, A.; Kadono, T.; Nakamura, A. M.; Arakawa, M.; Wada, K.; Yamamoto, S.
2011-12-01
The ejecta morphologies around impact craters represent highly diverse appearance on the surface of solid bodies in our Solar System. It is considered that the varied ejecta morphologies result from the environments such as the atmospheric pressure, the volatile content in the subsurface, because they affect the emplacement process of the ejecta. Clarifying the relationships between the ejecta morphologies and the formation processes and environments could constrain the ancient surface environment and the evolution of the planets. We have investigated the ejecta patterns around the impact craters which formed on a glass beads layer in a laboratory, and found that the patterns depend on impact velocity, atmospheric pressure, and initial state of packing of the target [Suzuki et al., 2010, JpGU abstract]. Now, we focus on one of the ejecta patterns which has a petal-like (or sometimes concentric) ridges on the distal edge of the continuous ejecta. This ejecta pattern looks very similar to the rampart ejecta morphology observed around Martian impact craters [e.g. Barlow et al., 2000]. The experiments are conducted with the small light gas gun placed in Kobe University, Japan. The projectile is a cylinder with a diameter of 10 mm and a height of 10 mm, and is made of aluminum, nylon, or stainless. The target is a layer of glass beads (nearly uniform diameter) in a tub with ~28 cm in diameter. The bulk density is about 1.7 g/cm^3. The following three parameters are varied: 1) the diameter of the target glass beads (50, 100, 420 microns), 2) the ambient atmospheric pressure in the chamber (from ~500 Pa to atmospheric pressure), 3) the impact velocity of the projectile (from a few to ~120 m/s). In our experiments, the rampart-like ridged patterns are observed within the following conditions: 1) the diameter of the target glass beads is 50 and 100 microns, 2) the ambient pressure in the chamber is higher than ~10^4 Pa, and 3) the impact velocity is higher than 16 m
Spontaneous knot; a rare cause of ventriculoperitoneal shunt blockage.
Mohammed, Wail
2012-02-01
A 14-year old X linked congenital hydrocephalus presented with unexplained headaches and vomiting. He had external ventricular drain and intracranial pressure monitoring (ICP). Subsequently, he underwent exploration and removal of previously inserted ventriculoperitoneal (VP) shunts. On retrieval of peritoneal catheters a double knot was noted between his two distal catheters. This case illustrates a rare cause of ventriculoperitoneal shunt malfunction.
Integrated management of root-knot nematode (Meloidogyne ...
(p<0.05) the nematode egg hatching as well as juvenile motility over the untreated control. Higher ... the pot house experiment. .... and placed to a drop of glycerine on a clean glass slide with ... knot nematode for subsequent experiments in the.
Knot energy in unstretching ergodic magnetic flux tubes
de Andrade, Garcia
2009-01-01
Recently Titov et al [ApJ \\textbf{693},(2009) and ApJ (2007)] have made use of a covariant model to investigate magnetic reconnection of astrophysical plasmas. Earlier R Ricca [Phys Rev A (1991)] has used another covariant formalism, to investigated vortex filaments and solitons. This formalism, called Ricci rotation coefficients (RRC), is applied here, to the Chui and Moffatt [PRSA (1995)] knotted magnetic flux tube (MFT) Riemann metric in the case of vanishing stretch. It is shown that, the vanishing of some components of the (RRC) leads to unstretching knotted tubes. Computing of magnetic knot energy in terms of the RCC, shows that, uniform, unstretching and constant cross-section tubes leads to a marginal dynamo action over magnetic surfaces. Recent investigation on the role of stretching in plasma dynamo action showed that in diffusive media [Phys Plasma \\textbf{14} (2008)], unstretching unknotted tubes would not support fast dynamo action. This result was generalized here to much more general knotted MF...
Spontaneous knot; a rare cause of ventriculoperitoneal shunt blockage.
Mohammed, Wail
2011-02-01
A 14-year old X linked congenital hydrocephalus presented with unexplained headaches and vomiting. He had external ventricular drain and intracranial pressure monitoring (ICP). Subsequently, he underwent exploration and removal of previously inserted ventriculoperitoneal (VP) shunts. On retrieval of peritoneal catheters a double knot was noted between his two distal catheters. This case illustrates a rare cause of ventriculoperitoneal shunt malfunction.
The unique cysteine knot regulates the pleotropic hormone leptin.
Ellinor Haglund
Full Text Available Leptin plays a key role in regulating energy intake/expenditure, metabolism and hypertension. It folds into a four-helix bundle that binds to the extracellular receptor to initiate signaling. Our work on leptin revealed a hidden complexity in the formation of a previously un-described, cysteine-knotted topology in leptin. We hypothesized that this unique topology could offer new mechanisms in regulating the protein activity. A combination of in silico simulation and in vitro experiments was used to probe the role of the knotted topology introduced by the disulphide-bridge on leptin folding and function. Our results surprisingly show that the free energy landscape is conserved between knotted and unknotted protein, however the additional complexity added by the knot formation is structurally important. Native state analyses led to the discovery that the disulphide-bond plays an important role in receptor binding and thus mediate biological activity by local motions on distal receptor-binding sites, far removed from the disulphide-bridge. Thus, the disulphide-bridge appears to function as a point of tension that allows dissipation of stress at a distance in leptin.
True Umbilical Cord Knot Leading to Fetal Demise
She had onset of labor at a GA of 40 weeks and 5 days following cervical ripening ... the baby. We have reported a case of true umbilical cord knot in Nnewi, South‑East Nigeria. .... Besides, other possible reasons for the fetal demise could not.
Polynomial Invariants of Torus Knots and (p,q)-Calculus
Pavlyuk, Anatoliy M.
2016-01-01
We introduce the deformed fermionic numbers, corresponding to the skein relations, the main characteristics of knots and links. These fermionic numbers allow one to restore the skein relations. For the Alexander (Jones) skein relation we introduce corresponding Alexander (Jones) fermionic q-numbers, and for the HOMFLY skein relation - the HOMFLY deformed (p,q)-numbers with one fermionic parameter.
A 3D Kinematic Study of the Northern Ejecta "Jet" of the Crab Nebula
Black, Christine S
2014-01-01
We present [O III] 4959,5007 emission line spectra (FWHM = 40 km/s) of the Crab Nebula's northern ejecta `jet'. These data, along with a recent [O III] image of the Crab, are used to build 3-dimensional models of the jet and adjacent remnant nebulosity to better understand the jet's properties and possible formation. We find that the jet's radial velocities range from -190 to +480 km/s with transverse velocities from 1600 to 2650 km/s from base to tip. The jet appears virtually hollow in [O III] emission with the exception of some material at the jet's base where the it connects with the remnant. Our 3D reconstructions indicate that the jet is elliptical in shape and slightly funnel-like rather than a straight cylindrical tube as previously thought. At the base of the jet we find evidence for a significant opening or "channel" in the Crab's main nebula shell. Our analysis of the jet's expansion properties and location supports the theory that the jet may simply represent the highest velocity component of the ...
Overview of the Chicxulub impactite and proximal ejecta
Claeys, Ph
2003-04-01
Several types of impactites have now been recovered from the various wells drilled in the Chicxulub crater in Yucatan. The old Pemex wells (Yucatan 6 and Chicxulub 1) contain a highly heterogeneous and stratified suevite, which upper unit is unusually rich in carbonates, impact breccia and a possibly an impact melt at the very bottom of C1. They are located towards the crater center (C1), on the flank of the peak ring (Y6). The thickness of impactite in this zone exceeds 250 m. The UNAM wells just outside the crater rim reveal sedimentary breccia and a fall-out suevite richer in silicate melt and basement fragments, than its crater equivalent. There, the thickness of the impactite was probably several hundred meters, considering that its top might have been eroded. It can also be speculated that a cover of fall-back suevite extended over the ejecta blanket in Yucatan, all the way to Belize and perhaps even to the region of Tabasco, in Southern Mexico. The recently drilled Yaxcopoil contains about 100 m of impactites, which is currently under study. Preliminary data seem to show less variability than the material recovered from Y6. As in the UNAM well, the impactite is dominated by basement material, and shows alternating severely altered and better preserved horizons.
X-Ray Heating of the Ejecta of Supernova 1987A
Sonneborn, George; Larsson, Josefin; Fransson, Claes; Kirshner, Robert; Challis, Peter; McCray, Richard
2012-01-01
Analysis of Hubble Space Telescope Band R band images from 1994 to 2009 show that the optical luminosity of SN 1987A has transitioned from being powered by radioactive decay of Ti-44 to energy deposited by X-rays produced as the ejecta interacts with the surrounding material (Larsson et al. 2011, Nature, 474, 484). The B and R band flux from the densest, central parts of the ejecta followed the expected exponential decline until 2001 (about day 5000) when the flux in these bands started increasing, more than doubling by the end of 2009. This increase is the result of heat deposited by X-rays from the shock interaction of the fast-moving outer ejecta with the inner circumstellar ring. In time, the X-rays will penetrate farther into the ejecta, enabling us to analyze the structure and chemistry of the vanished star.
Durda, Daniel D.; Kring, David A.; Pierazzo, Elisabetta; Melosh, H. J.
1997-03-01
The origin of the K/T boundary sequence of impact ejecta of the Chicxulub impact crater has been reexamined by constructing a computer simulation of the launch and deposition of both low- and high-energy ejecta. The distribution of low- and high-energy ejecta following a vertical impact is illustrated based on 20,000 tracer particles. The distribution is also shown for a 25 deg oblique impact from the southeast. Most of the high-energy ejecta stays within 50,000 km of Earth, with several percent reaching 100,000 km or more before reentering the atmosphere. About 25 percent of the material reaccretes within 2 hrs, about 50 percent within 8 hrs, and about 75 percent within about 72 hrs. At least 20-30 percent of the ejected material escapes the Earth. The implications of these findings for the postimpact environment are considered.
Simulated meteorite impacts and volcanic explosions: Ejecta analyses and planetary implications
Gratz, A. J.; Nellis, W. J.
1992-01-01
Past cratering studies have focused primarily on crater morphology. However, important questions remain about the nature of crater deposits. Phenomena that need to be studied include the distribution of shock effects in crater deposits and crater walls; the origin of mono- and polymict breccia; differences between local and distal ejecta; deformation induced by explosive volcanism; and the production of unshocked, high-speed ejecta that could form the lunar and martian meteorites found on the Earth. To study these phenomena, one must characterize ejecta and crater wall materials from impacts produced under controlled conditions. New efforts at LLNL simulate impacts and volcanism and study resultant deformation. All experiments use the two-stage light-gas gun facility at LLNL to accelerate projectiles to velocities of 0.2 to 4.3 km/s, including shock pressures of 0.9 to 50 GPa. We use granite targets and novel experimental geometries to unravel cratering processes in crystalline rocks. We have thus far conducted three types of simulations: soft recovery of ejecta, 'frozen crater' experiments, and an 'artificial volcano. Our ejecta recovery experiments produced a useful separation of impactites. Material originally below the projectile remained trapped there, embedded in the soft metal of the flyer plate. In contrast, material directly adjacent to the projectile was jetted away from the impact, producing an ejecta cone that was trapped in the foam recovery fixture. We find that a significant component of crater ejecta shows no signs of strong shock; this material comes from the near-surface 'interference zone' surrounding the impact site. This phenomenon explains the existence of unshocked meteorites on the Earth of lunar and martian origin. Impact of a large bolide on neighboring planets will produce high-speed, weakly shocked ejecta, which may be trapped by the Earth's gravitational field. 'Frozen crater' experiments show that the interference zone is highly
Investigating the retention of bright and dark ejecta from small rayed craters on mars
Calef, Fred J., III
2010-12-01
Impact cratering is one of the principal geologic processes operating throughout the solar system. On Mars, small rayed impact craters (SRC) form continuously and randomly on the surface. Ejecta retention, the timespan and ability of excavated ejecta to remain in place around a crater rim, records a lineage of recent surface processes. However, the timescales under which small rayed craters are produced and their origin, whether terrestrial or cosmic, plays an important role in further investigating surface processes and possible recent climate variations. By examining thousands of randomly chosen panchromatic images from the Mars Orbiter Camera Narrow Angle (MOCNA) camera, a population of 630 SRC was catalogued across three equatorial and two polar regions on Mars. The survey of MOCNA images also revealed intriguing Enigmatic Linear Features (ELFs) in the northern hemisphere of Mars, which a short side study revealed to be a unique form of dust-devil track. From statistically examining several physical parameters, dust deposition and periglacial erosion were found to be the major factors affecting ejecta retention for the SRC. SRC morphology revealed ejecta retention sequences that followed four stages of ejecta retention from the initial impact to eventual erasure from the surface. By reconstructing the current cratering rate from estimates of atmospheric filtering, it was possible to calculate the ejecta retention age across Mars. In general, SRC ejecta are retained on the surface for <100 ka. Based on ejecta morphology and retention age estimates, a possible shift from depositional to erosional processes just south of the Martian equator is suspected to have occurred within this timeframe.
The effects of red supergiant mass loss on supernova ejecta and the circumburst medium
van Loon, Jacco Th
2009-01-01
Massive stars becoming red supergiants lose a significant amount of their mass during that brief evolutionary phase. They then either explode as a hydrogen-rich supernova (SN Type II), or continue to evolve as a hotter supergiant (before exploding). The slow, dusty ejecta of the red supergiant will be over-run by the hot star wind and/or SN ejecta. I will present estimates of the conditions for this interaction and discuss some of the implications.
VLBI Imagings of Kilo-parsec Knot in 3C 380
Koyama, Shoko; Nagai, Hiroshi; Hada, Kazuhiro; Kameno, Seiji; Kobayashi, Hideyuki
2012-01-01
We investigate observational properties of a kilo-parsec scale knot in radio-loud quasar 3C 380 by using two epoch archival data obtained by Very Long Baseline Interferometry (VLBI) at 5 GHz on 1998 July and 2001 April. We succeed in obtaining the highest spatial resolution image of the bright knot K1 located at 732 milliarcseconds, or more than 20 kpc de-projected, downstream from the nucleus three times better than previously obtained highest resolution image by Papageorgiou et al. (2006). Our images reveal, with new clarity, "inverted bow-shock" structure in K1 facing the nucleus and its morphology resembles a conical shock wave. By comparing the two epoch images directly, we explore the kinematics of K1 and obtain the upper limit of apparent velocity, 0.25 mas/yr or 9.8 c of K1 for the first time. The upper limit of apparent velocity is marginally smaller than superluminal motions seen in the core region. Further new epoch VLBI observations are necessary to measure the proper motion at K1.
Foucart, Francois; Brege, Wyatt; Duez, Matthew D; Kasen, Daniel; Hemberger, Daniel A; Kidder, Lawrence E; Pfeiffer, Harald P; Scheel, Mark A
2016-01-01
Neutron star-black hole binaries are among the strongest sources of gravitational waves detectable by current observatories. They can also power bright electromagnetic signals (gamma-ray bursts, kilonovae), and may be a significant source of production of r-process nuclei. A misalignment of the black hole spin with respect to the orbital angular momentum leads to precession of that spin and of the orbital plane, and has a significant effect on the properties of the post-merger remnant and of the material ejected by the merger. We present a first set of simulations of precessing neutron star-black hole mergers using a hot, composition dependent, nuclear-theory based equation of state (DD2). We show that the mass of the remnant and of the dynamical ejecta are broadly consistent with the result of simulations using simpler equations of state, while differences arise when considering the dynamics of the merger and the velocity of the ejecta. We show that the latter can easily be understood from assumptions about ...
Edwards, David L.; Cooke, William; Scruggs, Rob; Moser, Danielle E.
2008-01-01
The National Aeronautics and Space Administration (NASA) is progressing toward long-term lunar habitation. Critical to the design of a lunar habitat is an understanding of the lunar surface environment; of specific importance is the primary meteoroid and subsequent ejecta environment. The document, NASA SP-8013, was developed for the Apollo program and is the latest definition of the ejecta environment. There is concern that NASA SP-8013 may over-estimate the lunar ejecta environment. NASA's Meteoroid Environment Office (MEO) has initiated several tasks to improve the accuracy of our understanding of the lunar surface ejecta environment. This paper reports the results of experiments on projectile impact into powered pumice and unconsolidated JSC-1A Lunar Mare Regolith stimulant (JSC-1A) targets. The Ames Vertical Gun Range (AVGR) was used to accelerate projectiles to velocities in excess of 5 km/s and impact the targets at normal incidence. The ejected particles were detected by thin aluminum foil targets placed around the impact site and angular distributions were determined for ejecta. Comparison of ejecta angular distribution with previous works will be presented. A simplistic technique to characterize the ejected particles was formulated and improvements to this technique will be discussed for implementation in future tests.
Borot, Gaëtan
2012-01-01
We propose a conjecture to compute the all-order asymptotic expansion of the colored Jones polynomial of the complement of a hyperbolic knot, J_N(q = exp(2u/N)) when N goes to infinity. Our conjecture claims that the asymptotic expansion of the colored Jones polynomial is a the formal wave function of an integrable system whose semiclassical spectral curve S would be the SL_2(C) character variety of the knot (the A-polynomial), and is formulated in the framework of the topological recursion. It takes as starting point the proposal made recently by Dijkgraaf, Fuji and Manabe (who kept only the perturbative part of the wave function, and found some discrepancies), but it also contains the non-perturbative parts, and solves the discrepancy problem. These non-perturbative corrections are derivatives of Theta functions associated to S, but the expansion is still in powers of 1/N due to the special properties of A-polynomials. We provide a detailed check for the figure-eight knot and the once-punctured torus bundle...
Direct observation of DNA knots using a solid-state nanopore
Plesa, Calin; Verschueren, Daniel; Pud, Sergii; van der Torre, Jaco; Ruitenberg, Justus W.; Witteveen, Menno J.; Jonsson, Magnus P.; Grosberg, Alexander Y.; Rabin, Yitzhak; Dekker, Cees
2016-12-01
Long DNA molecules can self-entangle into knots. Experimental techniques for observing such DNA knots (primarily gel electrophoresis) are limited to bulk methods and circular molecules below 10 kilobase pairs in length. Here, we show that solid-state nanopores can be used to directly observe individual knots in both linear and circular single DNA molecules of arbitrary length. The DNA knots are observed as short spikes in the nanopore current traces of the traversing DNA molecules and their detection is dependent on a sufficiently high measurement resolution, which can be achieved using high-concentration LiCl buffers. We study the percentage of molecules with knots for DNA molecules of up to 166 kilobase pairs in length and find that the knotting occurrence rises with the length of the DNA molecule, consistent with a constant knotting probability per unit length. Our experimental data compare favourably with previous simulation-based predictions for long polymers. From the translocation time of the knot through the nanopore, we estimate that the majority of the DNA knots are tight, with remarkably small sizes below 100 nm. In the case of linear molecules, we also observe that knots are able to slide out on application of high driving forces (voltage).
Suzuki, Akihiro; Maeda, Keiichi
2017-04-01
The hydrodynamical interaction between freely expanding supernova ejecta and a relativistic wind injected from the central region is studied in analytic and numerical ways. As a result of the collision between the ejecta and the wind, a geometrically thin shell surrounding a hot bubble forms and expands in the ejecta. We use a self-similar solution to describe the early dynamical evolution of the shell and carry out a two-dimensional special relativistic hydrodynamic simulation to follow further evolution. The Rayleigh-Taylor instability inevitably develops at the contact surface separating the shocked wind and ejecta, leading to the complete destruction of the shell and the leakage of hot gas from the hot bubble. The leaking hot materials immediately catch up with the outermost layer of the supernova ejecta and thus different layers of the ejecta are mixed. We present the spatial profiles of hydrodynamical variables and the kinetic energy distributions of the ejecta. We stop the energy injection when a total energy of 1052 erg, which is 10 times larger than the initial kinetic energy of the supernova ejecta, is deposited into the ejecta and follow the subsequent evolution. From the results of our simulations, we consider expected emission from supernova ejecta powered by the energy injection at the centre and discuss the possibility that superluminous supernovae and broad-lined Ic supernovae could be produced by similar mechanisms.
NOx production and rainout from Chicxulub impact ejecta reentry
Parkos, Devon; Alexeenko, Alina; Kulakhmetov, Marat; Johnson, Brandon C.; Melosh, H. Jay
2015-12-01
The Chicxulub impact 66.0 Ma ago initiated the second biggest extinction in the Phanerozoic Eon. The cause of the concurrent oceanic nitrogen isotopic anomaly, however, remains elusive. The Chicxulub impactor struck the Yucatán peninsula, ejecting 2 × 1015 kg of molten and vaporized rock that reentered globally as approximately 1023 microscopic spherules. Here we report that modern techniques indicate that this ejecta generates 1.5 × 1014 moles of NOx, which is enough to cause the observed nitrogen enrichment of the basal layer. Additionally, reentry-based NO production would explain the anomalously heavy isotopic composition of the observed nitrogen. We include N, O, N2, O2, and NO species in simulations of nonequilibrium chemically reacting flow around a reentering spherule. We then determine the net production of NO from all the spherules and use turbulence models to determine how quickly this yield diffuses through the atmosphere. Upon reaching the stratosphere and troposphere, cloud moisture absorbs the NOx and forms nitric acid. We model this process and determine the acidity of the resulting precipitation, which peaks about 1 year after the impact. The precipitation ultimately reaches the upper ocean, where we assume that the well-mixed surface layer is 100 m deep. We then model the naturally occurring carbonate/bicarbonate buffer and determine the net pH. We find that insufficient NOx reaches the ocean to directly cause the observed end-Cretaceous oceanic extinction via acidification and buffer removal. However, the resulting nitrates are sufficient to explain the concurrent nitrogen isotopic anomaly and facilitate an end-Cretaceous algae bloom.
BPS counting for knots and combinatorics on words
Kucharski, Piotr; Sułkowski, Piotr
2016-11-01
We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating functions (Hilbert-Poincaré series) are solutions to those equations and reproduce generating series that encode BPS invariants. Furthermore, BPS invariants in question are expressed in terms of Lyndon words in an appropriate language, thereby relating counting of BPS states to the branch of mathematics referred to as combinatorics on words. We illustrate these results in the framework of colored extremal knot polynomials: among others we determine dual quantum extremal A-polynomials for various knots, present associated combinatorial models, find corresponding BPS invariants (extremal Labastida-Mariño-Ooguri-Vafa invariants) and discuss their integrality.
Mutation on Knots and Whitney's 2-Isomorphism Theorem
Zhi Yun CHENG; Hong Zhu GAO
2013-01-01
Whitney's 2-switching theorem states that any two embeddings of a 2-connected planar graph in S2 can be connected via a sequence of simple operations,named 2-switching.In this paper,we obtain two operations on planar graphs from the view point of knot theory,which we will term "twisting" and "2-switching" respectively.With the twisting operation,we give a pure geometrical proof of Whitney's 2-switching theorem.As an application,we obtain some relationships between two knots which correspond to the same signed planar graph.Besides,we also give a necessary and sufficient condition to test whether a pair of reduced alternating diagrams are mutants of each other by their signed planar graphs.
The Faddeev knots as stable solitons:Existence theorems
LIN; Fanghua; YANG; Yisong
2004-01-01
The problem of existence of knot-like solitons as the energy-minimizing configurations in the Faddeev model, topologically characterized by an Hopf invariant, Q, is considered. It is proved that, in the full space situation, there exists an infinite set S of integers so that for any m ∈ S, the Faddeev energy, E, has a minimizer among the class Q = m; in the bounded domain situation, the same existence theorem holds when S is the set of all integers. One of the important technical results is that E and Q satisfy the sublinear inequality E ≤ C|Q|3/4, where C ＞0 is a universal constant, which explains why knotted (clustered soliton) configurations are preferred over widely separated unknotted (multisoliton) configurations when |Q| is sufficiently large.
Towards U(N|M) knot invariant from ABJM theory
Eynard, Bertrand
2014-01-01
We study U(N|M) character expectation value with the supermatrix Chern-Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives U(N|M) character expectation values in terms of U(1|1) averages for a particular type of character representations. This means that the U(1|1) character expectation value is a building block for all the U(N|M) averages, and in particular, by an appropriate limit, for the U(N) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern-Simons matrix model. We obtain the Rosso-Jones-type formula and the spectral curve for this case.
Design and performance of the APPLE-Knot undulator
Ji, Fuhao [Department of Physics, State Key Laboratory of Surface Physics, and Laboratory of Advanced Materials, Fudan University, 2005 Songhu Road, Shanghai 200438, People’s Republic of (China); Chang, Rui [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, People’s Republic of (China); Zhou, Qiaogen; Zhang, Wei [Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, 239 Zhangheng Road, Shanghai 201204, People’s Republic of (China); Ye, Mao [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, People’s Republic of (China); Sasaki, Shigemi [Hiroshima Synchrotron Radiation Center, Hiroshima University, 2-313 Kagamiyama, Hiroshima 739-0046 (Japan); Qiao, Shan, E-mail: qiaoshan@mail.sim.ac.cn [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, People’s Republic of (China); School of Physical Science and Technology, ShanghaiTech University, 319 Yueyang Road, Shanghai 200031, People’s Republic of (China)
2015-06-09
The design and performance of the Apple-Knot undulator which can generate photons with arbitrary polarization and low on-axis heat load are presented. Along with the development of accelerator technology, synchrotron emittance has continuously decreased. This results in increased brightness, but also causes a heavy heat load on beamline optics. Recently, optical surfaces with 0.1 nm micro-roughness and 0.05 µrad slope error (r.m.s.) have become commercially available and surface distortions due to heat load have become a key factor in determining beamline performance, and heat load has become a serious problem at modern synchrotron radiation facilities. Here, APPLE-Knot undulators which can generate photons with arbitrary polarization, with low on-axis heat load, are reported.
Toward U(N|M) knot invariant from ABJM theory
Eynard, Bertrand; Kimura, Taro
2017-02-01
We study U(N|M) character expectation value with the supermatrix Chern-Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half-BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives U(N|M) character expectation values in terms of U(1|1) averages for a particular type of character representations. This means that the U(1|1) character expectation value is a building block for the U(N|M) averages and also, by an appropriate limit, for the U(N) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern-Simons matrix model. We obtain the Rosso-Jones-type formula and the spectral curve for this case.
BPS counting for knots and combinatorics on words
Kucharski, Piotr
2016-01-01
We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating functions (Hilbert-Poincar\\'e series) are solutions to those equations and reproduce generating series that encode BPS invariants. Furthermore, BPS invariants in question are expressed in terms of Lyndon words in an appropriate language, thereby relating counting of BPS states to the branch of mathematics referred to as combinatorics on words. We illustrate these results in the framework of colored extremal knot polynomials: among others we determine dual quantum extremal A-polynomials for various knots, present associated combinatorial models, find corresponding BPS invariants (extremal Labastida-Mari\\~no-Ooguri-Vafa invariants) and discuss their integrality.
The Preon Sector of the SLq(2) (Knot) Model
Finkelstein, Robert J
2013-01-01
We describe a Lagrangian defining the preon sector of the knot model. The preons are the elements of the fundamental representation of SLq(2). They exactly agree with the preons conjectured by Harari and Shupe. The coupling constants and masses required by this Lagrangian are in principle experimentally measurable. There is an alternative formulation of the kinematics permitting possible additional isotopic partners of the quarks.
The Knot Spectrum of Confined Random Equilateral Polygons
Diao Y.
2014-01-01
Full Text Available It is well known that genomic materials (long DNA chains of living organisms are often packed compactly under extreme confining conditions using macromolecular self-assembly processes but the general DNA packing mechanism remains an unsolved problem. It has been proposed that the topology of the packed DNA may be used to study the DNA packing mechanism. For example, in the case of (mutant bacteriophage P4, DNA molecules packed inside the bacteriophage head are considered to be circular since the two sticky ends of the DNA are close to each other. The DNAs extracted from the capsid without separating the two ends can thus preserve the topology of the (circular DNAs. It turns out that the circular DNAs extracted from bacteriophage P4 are non-trivially knotted with very high probability and with a bias toward chiral knots. In order to study this problem using a systematic approach based on mathematical modeling, one needs to introduce a DNA packing model under extreme volume confinement condition and test whether such a model can produce the kind of knot spectrum observed in the experiments. In this paper we introduce and study a model of equilateral random polygons con_ned in a sphere. This model is not meant to generate polygons that model DNA packed in a virus head directly. Instead, the average topological characteristics of this model may serve as benchmark data for totally randomly packed circular DNAs. The difference between the biologically observed topological characteristics and our benchmark data might reveal the bias of DNA packed in the viral capsids and possibly lead to a better understanding of the DNA packing mechanism, at least for the bacteriophage DNA. The purpose of this paper is to provide information about the knot spectrum of equilateral random polygons under such a spherical confinement with length and confinement ratios in a range comparable to circular DNAs packed inside bacteriophage heads.
Zeros of Jones polynomials for families of knots and links
Chang, S.-C.; Shrock, R.
2001-12-01
We calculate Jones polynomials VL( t) for several families of alternating knots and links by computing the Tutte polynomials T( G, x, y) for the associated graphs G and then obtaining VL( t) as a special case of the Tutte polynomial. For each of these families we determine the zeros of the Jones polynomial, including the accumulation set in the limit of infinitely many crossings. A discussion is also given of the calculation of Jones polynomials for non-alternating links.
Shore, S N; Aquino, I De Gennaro; Augusteijn, T; Walter, F M; Starrfield, S; Sion, E M
2012-01-01
We continue our study of the physical properties of the recurrent nova T Pyx, focussing on the structure of the ejecta in the nebular stage of expansion during the 2011 outburst. The nova was observed contemporaneously with the Nordic Optical Telescope (NOT), at high resolution spectroscopic resolution (R ~ 65000) on 2011 Oct. 11 and 2012 Apr. 8 (without absolute flux calibration), and with the Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope, at high resolution (R ~ 30000) on 2011 Oct. 10 and 2012 Mar. 28 (absolute fluxes). We use standard plasma diagnostics (e.g. [O III] and [N II] line ratios and the H$\\beta$ line fluxes) to constrain electron densities and temperatures. Using Monte Carlo modeling of the ejecta, we derive the structure and filling factor from comparisons to the optical and ultraviolet line profiles. The ejecta can be modeled using an axisymmetric conical -- bipolar -- geometry with a low inclination of the axis to the line of sight, i=15+/-5 degrees, compatible...
Colored knot amplitudes and Hall-Littlewood polynomials
Shakirov, Sh
2013-01-01
The amplitudes of refined Chern-Simons (CS) theory, colored by antisymmetric (or symmetric) representations, conjecturally generate the Lambda^r- (or S^r-) colored triply graded homology of (n,m) torus knots. This paper is devoted to the generalization of Rosso-Jones formula to refined amplitudes, that involves non-trivial Gamma-factors -- expansion coefficients in the Macdonald basis. We derive from refined CS theory a linear recursion w.r.t. transformations (n,m) -> (n, n+m) and (n,m) -> (m,-n) that fully determines these factors. Applying this recursion to (n,nk+1) torus knots colored by antisymmetric representations [1^r] we prove that their amplitudes are rectangular [n^r] Hall-Littlewood polynomials under k units of framing (a.k.a. the Garsia-Haiman nabla) operator. For symmetric representations [r], we find the dual -- q-Whittaker -- polynomials. These results confirm and give a colored extension of the observation of arXiv:1201.3339 that triply graded homology of many torus knots has a strikingly simp...
Chee, Soon-Phaik
2011-09-01
A modified suture technique for precise knot placement in the Hoffman corneoscleral pocket technique of scleral fixation is described. Both loops of the polypropylene suture passing from the intraocular device through the sclera and conjunctiva are retrieved from the pocket. A loop of suture is pulled through 3 suture throws made using the second suture loop, forming a half bow. Centration of the intraocular lens (IOL)-capsular bag is checked. If the suture tension is too tight, the surgeon can easily undo the knot of the half-bow knot by pulling it free and can then retie the sliding knot. When the IOL-capsular bag is centered, the suture loop is cut and the free end removed. The second suture end is retrieved from the pocket, and knot tying is completed without further adjustment to the tension. Posterior pressure on the intraocular device centers it and settles the knot within the sclera at the fixation point.
Wulf, Gerwin; Kenkmann, Thomas
2015-02-01
The ejecta blankets of impact craters in volatile-rich environments often possess characteristic layered ejecta morphologies. The so-called double-layered ejecta (DLE) craters are characterized by two ejecta layers with distinct morphologies. The analysis of high-resolution image data, especially HiRISE and CTX, provides new insights into the formation of DLE craters. A new phenomenological excavation and ejecta emplacement model for DLE craters is proposed based on a detailed case study of the Martian crater Steinheim—a well-preserved DLE crater—and studies of other DLE craters. The observations show that the outer ejecta layer is emplaced as medial and distal ejecta that propagate outwards in a debris avalanche or (if saturated with water) a debris flow mode after landing, overrunning previously formed secondary craters. In contrast, the inner ejecta layer is formed by a translational slide of the proximal ejecta deposits during the emplacement stage that overrun and superimpose parts of the outer ejecta layer. Based on our model, DLE craters on Mars are the result of an impact event into a rock/ice mixture that produces large amounts of shock-induced vaporization and melting of ground ice, leading to high ejection angles, proximal landing positions, and an ejecta curtain with relatively wet (in terms of water in liquid form) composition in the distal part versus dryer composition in the proximal part. As a consequence, basal melting of ice components in the ejecta at the transient crater rim, which is induced by frictional heating and the enhanced pressure at depth, initiates an outwards directed collapse of crater rim material in a translational slide mode. Our results indicate that similar processes may also be applicable for other planetary bodies with volatile-rich environments, such as Ganymede, Europa, and the Earth.
KNOT POINT PLANNING FOR CARTESIAN TRAJECTORY GENERATION BASED ON INHERITANCE BISECTION ALGORITHM
Yan Bo; Yan Guozheng
2005-01-01
The computation algorithm of knot point planning for Cartesian trajectory generation of manipulator is investigated. A novel inheritance bisection algorithm (IBA) based on conventional bisection algorithm (BA) is proposed. IBA has two steps. The first step is the 1st knot point planning under lower set position accuracy; the second step is the 2nd knot point planning that inherits the results of the 1st planning under higher set position accuracy. The simulation results reveal that the number of inverse kinematical calculation (IKC) caused by IBA is decreased compared with BA. IBA is more efficient to plan knot points.
Hayashi K.
2012-08-01
Full Text Available The effect of the impact angle of projectiles on the crater shape and ejecta in thick aluminum alloy targets was investigated in hypervelocity impacts. When polycarbonate projectiles and aluminum alloy 6061-T6 target were used, the impact angle of the projectiles clearly affected the crater shape, as expected. The impact angle also affected the ejecta mass, ejecta size and scatter angle. However, the effect at 15∘ and 22.5∘ was not great. When the impact angles were 30∘ and 45∘, the effect was clearly confirmed. The impact angle clearly affected the axial ratio of ejecta fragments, c/a.
Topological patterns in two-dimensional gel electrophoresis of DNA knots.
Michieletto, Davide; Marenduzzo, Davide; Orlandini, Enzo
2015-10-06
Gel electrophoresis is a powerful experimental method to probe the topology of DNA and other biopolymers. Although there is a large body of experimental work that allows us to accurately separate different topoisomers of a molecule, a full theoretical understanding of these experiments has not yet been achieved. Here we show that the mobility of DNA knots depends crucially and subtly on the physical properties of the gel and, in particular, on the presence of dangling ends. The topological interactions between these and DNA molecules can be described in terms of an "entanglement number" and yield a nonmonotonic mobility at moderate fields. Consequently, in 2D electrophoresis, gel bands display a characteristic arc pattern; this turns into a straight line when the density of dangling ends vanishes. We also provide a novel framework to accurately predict the shape of such arcs as a function of molecule length and topological complexity, which may be used to inform future experiments.
Combinatorial Game Theory, Well-Tempered Scoring Games, and a Knot Game
Johnson, Will
2011-01-01
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate after the same number of moves. The theory of fixed-length scoring games is shown to have properties similar to the theory of loopy combinatorial games, with operations similar to onsides and offsides. We give a complete description of the structure of fixed-length scoring games in terms of the class of short partizan games. We also consider fixed-length scoring games taking values in the two-element boolean algebra, and classify these games up to indistinguishability. We then apply these results to analyze some positions in the knotting-unknotting game of Pechenik, Townsend, Henrich, MacNaughton, and Silversmith.
A new family of cystine knot peptides from the seeds of Momordica cochinchinensis.
Chan, Lai Yue; He, Wenjun; Tan, Ninghua; Zeng, Guangzhi; Craik, David J; Daly, Norelle L
2013-01-01
Momordica cochinchinensis, a Cucurbitaceae plant commonly found in Southeast Asia, has the unusual property of containing both acyclic and backbone-cyclized trypsin inhibitors with inhibitor cystine knot (ICK) motifs. In the current study we have shown that M. cochinchinensis also contains another family of acyclic ICK peptides. We recently reported two novel peptides from M. cochinchinensis but have now discovered four additional peptides (MCo-3-MCo-6) with related sequences. Together these peptides form a novel family of M. cochinchinensis ICK peptides (MCo-ICK) that do not have sequence homology with other known peptides and are not potent trypsin inhibitors. Otherwise these new peptides MCo-3 to MCo-6 were evaluated for antimalarial activity against Plasmodium falciparum, and cytotoxic activity against the cancer cell line MDA-MB-231. But these peptides were not active. Copyright © 2012 Elsevier Inc. All rights reserved.
Pearson, Amber L; Kingham, Simon; Mitchell, Peter; Apparicio, Philippe
2013-12-01
The etiology of pneumococcal pneumonia (PP) is well-known. Yet, some events may increase its incidence. Natural disasters may worsen air quality, a risk factor for PP. We investigated spatial/spatio-temporal clustering of PP pre- and post-earthquakes in Christchurch, New Zealand. The earthquakes resulted in deaths, widespread damage and liquefaction ejecta (a source of air-borne dust). We tested for clusters and associations with ejecta, using 97 cases (diagnosed 10/2008-12/2011), adjusted for age and area-level deprivation. The strongest evidence to support the potential role of ejecta in clusters of PP cases was the: (1) geographic shift in the spatio-temporal cluster after deprivation adjustment to match the post-earthquake clusters and; (2) increased relative risk in the fully-adjusted post-earthquake compared to the pre-earthquake cluster. The application of spatial statistics to study PP and ejecta are novel. Further studies to assess the long-term impacts of ejecta inhalation are recommended particularly in Christchurch, where seismic activity continues.
Exchange of ejecta between Telesto and Calypso: Tadpoles, horseshoes, and passing orbits
Dobrovolskis, Anthony R; Zahnle, Kevin J; Lissauer, Jack J
2010-01-01
We have numerically integrated the orbits of ejecta from Telesto and Calypso, the two small Trojan companions of Saturn's major satellite Tethys. Ejecta were launched with speeds comparable to or exceeding their parent's escape velocity, consistent with impacts into regolith surfaces. We find that the fates of ejecta fall into several distinct categories, depending on both the speed and direction of launch. The slowest ejecta follow sub-orbital trajectories and re-impact their source moon in less than one day. Slightly faster debris barely escape their parent's Hill sphere and are confined to tadpole orbits, librating about Tethys' triangular Lagrange points L4 (leading, near Telesto) or L5 (trailing, near Calypso) with nearly the same orbital semi-major axis as Tethys, Telesto, and Calypso. These ejecta too eventually re-impact their source moon, but with a median lifetime of a few dozen years. Those which re-impact within the first ten years or so have lifetimes near integer multiples of 348.6 days (half th...
Spall strength and ejecta production of gold under explosively driven shock wave compression
La Lone, B. M. [National Security Technologies, LLC. (NSTec), Mercury, NV (United States); Stevens, G. D. [National Security Technologies, LLC. (NSTec), Mercury, NV (United States); Turley, W. D. [National Security Technologies, LLC. (NSTec), Mercury, NV (United States); Veeser, L. R. [National Security Technologies, LLC. (NSTec), Mercury, NV (United States); Holtkamp, D. B. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2013-12-16
Explosively driven shock wave experiments were conducted to characterize the spall strength and ejecta production of high-purity cast gold samples. The samples were from 0.75 to 1.84 mm thick and 30 mm in diameter. Peak stresses up to 44 GPa in gold were generated using PBX-9501 high explosive. Sample free surface and ejecta velocities were recorded using photonic Doppler velocimetry techniques. Lithium niobate pins were used to quantify the time dependence of the ejecta density and the total ejected mass. An optical framing camera for time-resolved imaging and a single-image x-ray radiograph were used for additional characterization. Free surface velocities exhibited a range of spall strengths from 1.7 to 2.4 GPa (mean: 2.0 ±0.3 GPa). The pullback signals were faint, minimal ringing was observed in the velocity records, and the spall layer continued to decelerate after first pull back. These results suggest finite tensile strength was present for some time after the initial void formation. Ejecta were observed for every sample with a roughened free surface, and the ejecta density increased with increased surface roughness, which was different in every experiment. The total ejected mass is consistent with the missing mass model.
X-Ray Emitting Ejecta of Supernova Remnant N132D
Borkowski, Kazimierz J; Reynolds, Stephen P
2007-01-01
The brightest supernova remnant in the Magellanic Clouds, N132D, belongs to the rare class of oxygen-rich remnants, about a dozen objects that show optical emission from pure heavy-element ejecta. They originate in explosions of massive stars that produce large amounts of O, although only a tiny fraction of that O is found to emit at optical wavelengths. We report the detection of substantial amounts of O at X-ray wavelengths in a recent 100 ks Chandra ACIS observation of N132D. A comparison between subarcsecond-resolution Chandra and Hubble images reveals a good match between clumpy X-ray and optically emitting ejecta on large (but not small) scales. Ejecta spectra are dominated by strong lines of He- and H-like O; they exhibit substantial spatial variations partially caused by patchy absorption within the LMC. Because optical ejecta are concentrated in a 5 pc radius elliptical expanding shell, the detected ejecta X-ray emission also originates in this shell.
Upper Eocene tektite and impact ejecta layer on the Continental Slope off New Jersey
Glass, B. P.; Koeberl, C.; Blum, J. D.; McHugh, C. M. G.
1998-03-01
During Leg 150 of the Ocean Drilling Project (ODP) two sites (903C and 904A) were cored which have sediments of the same biostratigraphic age as the upper Eocene tektite-bearing ejecta layer at Deep Sea Drilling Project (DSDP) Site 612. Core 45X from ODP Site 904A (~ 4 km north of Site 612) contains a 5-cm-thick tektite-bearing ejecta layer and Core 56 from Site 903C (~ 8 km north-northwest of Site 904) contains a 2-cm-thick layer of impact ejecta without any tektite or impact glass. Shocked quartz and feldspar grains, with multiple sets of planar deformation features, and abundant coesite-bearing grains are present at both sites. The major oxide contents, trace element compositions, and rare earth element patterns of the Site 904 tektites are similar to those of the Site 612 tektites and to North American tektites (especially bediasites). The Sr and Nd values for one composite tektite sample from Site 904 fall within the range previously obtained for the Site 612 tektites, which defines a linear trend that, if extrapolated, would intersect the values obtained for North American tektites. The water contents of eight tektite fragments from Site 904 range from 0.017 to 0.098 wt. %, and, thus, are somewhat higher than is typical for tektites. The heavy mineral assemblages of the 63 - 125 m size fractions from the ejecta layers at Sites 612, 903, and 904 are all similar. Therefore, we conclude that the ejecta layer at all three sites are from the same impact event and that the tektites at Sites 904 and 612 belong to the North American tektite strewn field. Clinopyroxene-bearing (cpx) spherules occur below, or in the lower part of, the main ejecta layer at all three sites. At all three sites the cpx spherules have been partly or completely replaced with pyrite which preserved the original crystalline textures. Site 612, 903, and 904 cpx spherules are similar to those found in the Caribbean Sea, Gulf of Mexico, central equatorial Pacific, western equatorial Pacific, and
X-ray illumination of the ejecta of Supernova 1987A
Larsson, J; Östlin, G; Gröningsson, P; Jerkstrand, A; Kozma, C; Sollerman, J; Challis, P; Kirshner, R P; Chevalier, R A; Heng, K; McCray, R; Suntzeff, N B; Bouchet, P; Crotts, A; Danziger, J; Dwek, E; France, K; Garnavich, P M; Lawrence, S S; Leibundgut, B; Lundqvist, P; Panagia, N; Pun, C S J; Smith, N; Sonneborn, G; Wang, L; Wheeler, J C
2011-01-01
We present the late-time optical light curve of the ejecta of SN 1987A measured from HST imaging observations spanning the past 17 years. We find that the flux from the ejecta declined up to around year 2001, powered by the radioactive decay of 44Ti. Then the flux started to increase, more than doubling by the end of 2009. We show that the increase is the result of energy deposited by X-rays produced in the interaction with the circumstellar medium. We suggest that the change of the dominant energy input to the ejecta, from internal to external, marks the transition from supernova to supernova remnant. The details of the observations and the modelling are described in the accompanying supplementary information.
Mizuno, Y.; Nishikawa, K.I.; Zhang, B.; Giacomazzo, B.; Hardee, P.E.; Nagataki, S.; Hartmann, D.H.
2008-01-01
We solve the Riemann problem for the deceleration of arbitrarily magnetized relativistic ejecta injected into a static unmagnetized medium. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization s (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when s exceeds a critical value, sc, defined by the balance between the magnetic pressure in the ejecta and the thermal pressure in the forward shock. In the rarefaction wave regime, we find that the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value. This acceleration mechanism is due to the strong magnetic pressure in the ejecta.
Chromium isotope evidence in ejecta deposits for the nature of Paleoproterozoic impactors
Mougel, Bérengère; Moynier, Frédéric; Göpel, Christa; Koeberl, Christian
2017-02-01
Non-mass dependent chromium isotopic signatures have been successfully used to determine the presence and identification of extra-terrestrial materials in terrestrial impact rocks. Paleoproterozoic spherule layers from Greenland (Grænsesø) and Russia (Zaonega), as well as some distal ejecta deposits (Lake Superior region) from the Sudbury impact (1849 ± 0.3 Ma) event, have been analyzed for their Cr isotope compositions. Our results suggest that 1) these distal ejecta deposits are all of impact origin, 2) the Grænsesø and Zaonega spherule layers contain a distinct carbonaceous chondrite component, and are possibly related to the same impact event, which could be Vredefort (2023 ± 4 Ma) or another not yet identified large impact event from that of similar age, and 3) the Sudbury ejecta record a complex meteoritic signature, which is different from the Grænsesø and Zaonega spherule layers, and could indicate the impact of a heterogeneous chondritic body.
The interaction of core-collapse supernova ejecta with a companion star
Liu, Zheng-Wei; Tauris, T. M.; Röpke, F. K.; Moriya, T. J.; Kruckow, M.; Stancliffe, R. J.; Izzard, R. G.
2015-12-01
Context. The progenitors of many core-collapse supernovae (CCSNe) are expected to be in binary systems. After the SN explosion in a binary, the companion star may suffer from mass stripping and be shock heated as a result of the impact of the SN ejecta. If the binary system is disrupted by the SN explosion, the companion star is ejected as a runaway star, and in some cases as a hypervelocity star. Aims: By performing a series of three-dimensional (3D) hydrodynamical simulations of the collision of SN ejecta with the companion star, we investigate how CCSN explosions affect their binary companion. Methods: We use the BEC stellar evolution code to construct the detailed companion structure at the moment of SN explosion. The impact of the SN blast wave on the companion star is followed by means of 3D smoothed particle hydrodynamics (SPH) simulations using the Stellar GADGET code. Results: For main-sequence (MS) companion stars, we find that the amount of removed stellar mass, the resulting impact velocity, and the chemical contamination of the companion that results from the impact of the SN ejecta strongly increases with decreasing binary separation and increasing explosion energy. Their relationship can be approximately fitted by power laws, which is consistent with the results obtained from impact simulations of Type Ia SNe. However, we find that the impact velocity is sensitive to the momentum profile of the outer SN ejecta and, in fact, may decrease with increasing ejecta mass, depending on the modeling of the ejecta. Because most companion stars to Type Ib/c CCSNe are in their MS phase at the moment of the explosion, combined with the strongly decaying impact effects with increasing binary separation, we argue that the majority of these SNe lead to inefficient mass stripping and shock heating of the companion star following the impact of the ejecta. Conclusions: Our simulations show that the impact effects of Type Ib/c SN ejecta on the structure of MS companion
Spatial Distribution of Mg-Rich Ejecta in LMC Supernova Remnant N49B
Park, Sangwook; Bhalerao, Jayant
2016-01-01
The supernova remnant (SNR) N49B in the Large Magellanic Cloud is a peculiar example of a core-collapse SNR to show the shocked metal-rich ejecta enriched only in Mg without evidence for a similar overabundance in O and Ne. Based on archival Chandra data we present results from our extensive spatially-resolved spectral analysis of N49B. We find that the Mg-rich ejecta gas extends from the central regions of the SNR out to the southeastern outermost boundary of the SNR. This elongated feature ...
Knots and surfaces a guide to discovering mathematics
Farmer, David W
1995-01-01
In most mathematics textbooks, the most exciting part of mathematics-the process of invention and discovery-is completely hidden from the reader. The aim of Knots and Surfaces is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequi
Explorations in topology map coloring, surfaces and knots
Gay, David
2013-01-01
Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigation
Punctured torus groups and 2-bridge knot groups
Akiyoshi, Hirotaka; Wada, Masaaki; Yamashita, Yasushi
2007-01-01
This monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory. Although Jorgensen's original work was not published in complete form, it has been a source of inspiration. In particular, it has motivated and guided Thurston's revolutionary study of low-dimensional geometric topology. In this monograph, we give an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.
Knotted Picture of a Quantum Network of Two Nodes
QIAN Shang-Wu; GU Zhi-Yu
2004-01-01
This article discusses the variation of the knotted picture of the quantum pure state |X〉 = α| ↑↓〉 + β|↓↑〉with the varintion of the complex coefficients a and β. It is shown that there are three kinds of link that correspond tc three different ranks of the matrix of covariance correlation tensor, i.e., the zero rank corresponds to trivial link, the rank one corresponds to the two-component link with two crossings, and the rank three corresponds to the two-component link with four crossings.
Design and performance of the APPLE-Knot undulator.
Ji, Fuhao; Chang, Rui; Zhou, Qiaogen; Zhang, Wei; Ye, Mao; Sasaki, Shigemi; Qiao, Shan
2015-07-01
Along with the development of accelerator technology, synchrotron emittance has continuously decreased. This results in increased brightness, but also causes a heavy heat load on beamline optics. Recently, optical surfaces with 0.1 nm micro-roughness and 0.05 µrad slope error (r.m.s.) have become commercially available and surface distortions due to heat load have become a key factor in determining beamline performance, and heat load has become a serious problem at modern synchrotron radiation facilities. Here, APPLE-Knot undulators which can generate photons with arbitrary polarization, with low on-axis heat load, are reported.
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
Adams, Colin; Bennett, Hanna; Davis, Christopher James;
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots ...
First report of the root-knot nematode Meloidogyne ethiopica on tomato in Slovenia
Sirca, S.; Urek, G.; Karssen, G.
2004-01-01
The root-knot nematode Meloidogyne ethiopica Whitehead originally described from Tanzania is also distributed in South Africa, Zimbabwe, and Ethiopia (3). Although this species is a relatively unknown root-knot nematode, M. ethiopica parasitizes several economical important crops, such as tomato, co
Repeat knot formation in a patient with an indwelling ureteral stent
Brian Eisner
2006-06-01
Full Text Available A patient treated for nephrolithiasis formed knots in 2 occasions, in 2 separate indwelling ureteral stents. This rare complication may make stent removal difficult. To our knowledge, this is the first case report of repeat knot formation in a single patient.
Totally geodesic Seifert surfaces in hyperbolic knot and link complements II
Adams, Colin; Bennett, Hanna; Davis, Christopher James
2008-01-01
We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots...
Onrust, J.; de Fouw, J.; Oudman, T.; van der Geest, M.; Piersma, T.; van Gils, J.A.
2013-01-01
Capsule Context-specific equations are needed to reconstruct diet composition and intake rate of Red Knots by the use of shell fragments retrieved from droppings.Aims To explore whether the method to reconstruct Red Knot diet described by Dekinga & Piersma [Dekinga, A. & Piersma, T. 1993. Reconstruc
Onrust, Jeroen; De Fouw, Jimmy; Oudman, Thomas; Van der Geest, Matthijs; Piersma, Theunis; Van Gils, Jan A.
2013-01-01
Capsule Context-specific equations are needed to reconstruct diet composition and intake rate of Red Knots by the use of shell fragments retrieved from droppings. Aims To explore whether the method to reconstruct Red Knot diet described by Dekinga & Piersma [Dekinga, A. & Piersma, T. 1993. Reconstru
Why do few Afro-Siberian Knots Calidris canutus canutus now visit Britain?
Boyd, H; Piersma, T
2001-01-01
The nominate (Afro-Siberian) subspecies of the Knot Calidris canutus canutus breeds on the Taimyr Peninsula in Siberia and occurs commonly in the westernmost Wadden Sea during migration to West and South Africa. The recoveries and controls of 2045 Knots ringed in Britain and Ireland provide no evide
Expression of almond KNOTTED1 homologue (PdKn1) anticipates adventitious shoot initiation
Background and Aims: The transcription factor encoded by the gene Knotted1 is a nuclear homeodomain protein, regulating meristematic cells at the shoot apical meristem. It has been proven that Knotted1 (KN1) has a role in the switch from an indeterminate to determinate cell fate and as such this gen...
Verboven, N.; Piersma, T.
1995-01-01
To test whether Knot Calidris canutus wintering in the tropics suffer higher rates of water loss through evaporation than do Knot wintering at temperate latitudes, we tried to develop a physically realistic model to predict evaporative heat loss from air temperature, wind and humidity. In separate e
Knot Physics -- an Ultimate Unified Theory of Matter and its Motion
Kou, Su-Peng
2016-01-01
A Theory of Everything (TOE) is physics theory that unifies all the fundamental interactions of nature: gravitation, strong interaction, weak interaction, and electromagnetism.\\ Now, TOE becomes the Holy Grail of modern physics. In this paper, knot physics becomes a new candidate of TOE that not only unified all the fundamental interactions but also explores the underline physics of quantum mechanics. In knot physics, our universe is a standard knot-crystal, a particular periodic entanglement-pattern between two 3-branes (three dimensional branes/manifolds), of which the low energy effective theory not only reproduces the Standard model -- an SU(3)*SU(2)*U(1) gauge theory but also leads to the physics of general relativity. The collective motions of the standard knot-crystal are described by fermionic elementary particles and gauge fields. Fermionic elementary particles are topological excitations that correspond to different types of knots.
Knots on a Torus: A Model of the Elementary Particles
Jack S. Avrin
2012-02-01
Full Text Available Two knots; just two rudimentary knots, the unknot and the trefoil. That’s all we need to build a model of the elementary particles of physics, one with fermions and bosons, hadrons and leptons, interactions weak and strong and the attributes of spin, isospin, mass, charge, CPT invariance and more. There are no quarks to provide fractional charge, no gluons to sequester them within nucleons and no “colors” to avoid violating Pauli’s principle. Nor do we require the importation of an enigmatic Higgs boson to confer mass upon the particles of our world. All the requisite attributes emerge simply (and relativistically invariant as a result of particle conformation and occupation in and of spacetime itself, a spacetime endowed with the imprimature of general relativity. Also emerging are some novel tools for systemizing the particle taxonomy as governed by the gauge group SU(2 and the details of particle degeneracy as well as connections to Hopf algebra, Dirac theory, string theory, topological quantum field theory and dark matter. One exception: it is found necessary to invoke the munificent geometry of the icosahedron in order to provide, as per the group “flavor” SU(3, a scaffold upon which to organize the well-known three generations—no more, no less—of the particle family tree.
A Knot Model Sugugested by the Standard Electroweak Theory
Finkelstein, R J
2004-01-01
We attempt to go beyond the standard electroweak theory by replacing the underlying Lie algebra with its q-deformation: SU_q(2) x SU(1). This step introduces new degrees of freedom that we interpret as indicative of non-locality and as a possible basis for a solitonic model of the elementary particles. The solitons are conjectured to be knotted flux tubes labelled by the irreducible representations of SU_q(2), an algebra which is not only closely related to the standard theory but also plays a role in the description of knots. Each of the four families of elementary fermions is conujectured to be represented by one of the four possible trefoils. The three individual fermions belonging to any family then occupy the three lowest states in the excitation spectrum of the trefoil for that family. The dimensionless deformation parameter, q, is assumed to be a function of the Higgs field and to be an effective measure of the influence of the new degrees of freedom introduced by the deformation of SU(2). One finds a ...
Small-body deflection techniques using spacecraft: techniques in simulating the fate of ejecta
Schwartz, Stephen R; Michel, Patrick; Jutzi, Martin
2016-01-01
We define a set of procedures to numerically study the fate of ejecta produced by the impact of an artificial projectile with the aim of deflecting an asteroid. Here we develop a simplified, idealized model of impact conditions that can be adapted to fit the details of specific deflection-test scenarios, such as what is being proposed for the AIDA project. Ongoing studies based upon the methodology described here can be used to inform observational strategies and safety conditions for an observing spacecraft. To account for ejecta evolution, the numerical strategies we are employing are varied and include a large N-Body component, a smoothed-particle hydrodynamics (SPH) component, and an application of impactor scaling laws. Simulations that use SPH-derived initial conditions show high-speed ejecta escaping at low angles of inclination, and very slowly moving ejecta lofting off the surface at higher inclination angles, some of which re-impacts the small-body surface. We are currently investigating the realism...
X-ray illumination of the ejecta of supernova 1987A.
Larsson, J; Fransson, C; Ostlin, G; Gröningsson, P; Jerkstrand, A; Kozma, C; Sollerman, J; Challis, P; Kirshner, R P; Chevalier, R A; Heng, K; McCray, R; Suntzeff, N B; Bouchet, P; Crotts, A; Danziger, J; Dwek, E; France, K; Garnavich, P M; Lawrence, S S; Leibundgut, B; Lundqvist, P; Panagia, N; Pun, C S J; Smith, N; Sonneborn, G; Wang, L; Wheeler, J C
2011-06-08
When a massive star explodes as a supernova, substantial amounts of radioactive elements--primarily (56)Ni, (57)Ni and (44)Ti--are produced. After the initial flash of light from shock heating, the fading light emitted by the supernova is due to the decay of these elements. However, after decades, the energy powering a supernova remnant comes from the shock interaction between the ejecta and the surrounding medium. The transition to this phase has hitherto not been observed: supernovae occur too infrequently in the Milky Way to provide a young example, and extragalactic supernovae are generally too faint and too small. Here we report observations that show this transition in the supernova SN 1987A in the Large Magellanic Cloud. From 1994 to 2001, the ejecta faded owing to radioactive decay of (44)Ti as predicted. Then the flux started to increase, more than doubling by the end of 2009. We show that this increase is the result of heat deposited by X-rays produced as the ejecta interacts with the surrounding material. In time, the X-rays will penetrate farther into the ejecta, enabling us to analyse the structure and chemistry of the vanished star.
Modeling the Ballistic Behavior of Solid Ejecta from the Deep Impact Cratering Event
Richardson, J. E.; Melosh, H. J.
2006-03-01
We describe results from a forward model of the first-order, solid ejecta particle behavior from the impact produced by the Deep Impact mission. The expansion rate of the plume places constraints on the gravity field, mass, and density of Tempel 1.
Detailed Analysis of the Intra-Ejecta Dark Plains of Caloris Basin, Mercury
Buczkowski, Debra L.; Seelos, K. S.
2010-01-01
The Caloris basin on Mercury is floored by light-toned plains and surrounded by an annulus of dark-toned material interpreted to be ejecta blocks and smooth, dark, ridged plains. Strangely, preliminary crater counts indicate that these intra-ejecta dark plains are younger than the light-toned plains within the Caloris basin. This would imply a second, younger plains emplacement event, possibly involving lower albedo material volcanics, which resurfaced the original ejecta deposit. On the other hand, the dark plains may be pre-Caloris light plains covered by a thin layer of dark ejecta. Another alternative to the hypothesis of young, dark volcanism is the possibility that previous crater counts have not thoroughly distinguished between superposed craters (fresh) and partly-buried craters (old) and therefore have not accurately determined the ages of the Caloris units. This abstract outlines the tasks associated with a new mapping project of the Caloris basin, intended to improve our knowledge of the geology and geologic history of the basin, and thus facilitate an understanding of the thermal evolution of this region of Mercury.
Simulations and experiments of ejecta generation in twice-shocked metals
Karkhanis, Varad; Ramaprabhu, Praveen; Buttler, William; Hammerberg, James; Cherne, Frank; Andrews, Malcolm
2016-11-01
Using continuum hydrodynamics embedded in the FLASH code, we model ejecta generation in recent target experiments, where a metallic surface was loaded by two successive shock waves. The experimental data were obtained from a two-shockwave, high-explosive tool at Los Alamos National Laboratory, capable of generating ejecta from a shocked tin surface in to a vacuum. In both simulations and experiment, linear growth is observed following the first shock event, while the second shock strikes a finite-amplitude interface leading to nonlinear growth. The timing of the second incident shock was varied systematically in our simulations to realize a finite-amplitude re-initialization of the RM instability driving the ejecta. We find the shape of the interface at the event of second shock is critical in determining the amount of ejecta, and thus must be used as an initial condition to evaluate subsequent ejected mass using a source model. In particular, the agreement between simulations, experiments and the mass model is improved when shape effects associated with the interface at second shock are incorporated. This work was supported in part by the (U.S.) Department of Energy (DOE) under Contract No. DE-AC52-06NA2-5396.
The morphology of the ejecta in Supernova 1987A: a study over time and wavelength
Larsson, Josefin; Kjaer, Karina; Jerkstrand, Anders; Kirshner, Robert P; Leibundgut, Bruno; Lundqvist, Peter; Mattila, Seppo; McCray, Richard; Sollerman, Jesper; Spyromilio, Jason; Wheeler, J Craig
2012-01-01
We present a study of the morphology of the ejecta in Supernova 1987A based on images and spectra from the HST as well as integral field spectroscopy from VLT/SINFONI. The HST observations were obtained between 1994 - 2011 and primarily probe the outer hydrogen-rich zones of the ejecta. The SINFONI observations were obtained in 2005 and 2011 and instead probe the [Si I]/[Fe II] emission from the inner regions. We find a strong temporal evolution of the morphology in the HST images, from a roughly elliptical shape before ~5,000 days, to a more irregular, edge-brightened morphology thereafter. We demonstrate that this transition is a natural consequence of the change in the dominant energy source powering the ejecta, from radioactive decay before ~5,000 days to X-ray input from the circumstellar interaction thereafter. The [Si I]/[Fe II] images display a more uniform morphology, which may be due to a remaining significant contribution from radioactivity in the inner ejecta and the higher abundance of these elem...
Dissecting a SN impostor's circumstellar medium: MUSEing about the SHAPE of eta Car's outer ejecta
Mehner, A; Groh, J H; Vogt, F P A; Baade, D; Boffin, H M J; Davidson, K; de Wit, W J; Humphreys, R M; Martayan, C; Oudmaijer, R D; Rivinius, T; Selman, F
2016-01-01
Aims. The structural inhomogeneities and kinematics of massive star nebulae are tracers of their mass-loss history. We conduct a three-dimensional morpho-kinematic analysis of the ejecta of eta Car outside its famous Homunculus nebula. Methods. We carried out the first large-scale integral field unit observations of eta Car in the optical, covering a field of view of 1'x1' centered on the star. Observations with the Multi Unit Spectroscopic Explorer (MUSE) at the Very Large Telescope (VLT) reveal the detailed three-dimensional structure of eta Car's outer ejecta. Morpho-kinematic modeling of these ejecta is conducted with the code SHAPE. Results. The largest coherent structure in eta Car's outer ejecta can be described as a bent cylinder with roughly the same symmetry axis as the Homunculus nebula. This large outer shell is interacting with the surrounding medium, creating soft X-ray emission. We establish the shape and extent of the ghost shell in front of the southern Homunculus lobe and confirm that the NN...
Subsurface volatile content of martian double-layer ejecta (DLE) craters
Viola, Donna; McEwen, Alfred S.; Dundas, Colin M.; Byrne, Shane
2017-03-01
Excess ice is widespread throughout the martian mid-latitudes, particularly in Arcadia Planitia, where double-layer ejecta (DLE) craters also tend to be abundant. In this region, we observe the presence of thermokarstically-expanded secondary craters that likely form from impacts that destabilize a subsurface layer of excess ice, which subsequently sublimates. The presence of these expanded craters shows that excess ice is still preserved within the adjacent terrain. Here, we focus on a 15-km DLE crater that contains abundant superposed expanded craters in order to study the distribution of subsurface volatiles both at the time when the secondary craters formed and, by extension, remaining today. To do this, we measure the size distribution of the superposed expanded craters and use topographic data to calculate crater volumes as a proxy for the volumes of ice lost to sublimation during the expansion process. The inner ejecta layer contains craters that appear to have undergone more expansion, suggesting that excess ice was most abundant in that region. However, both of the ejecta layers had more expanded craters than the surrounding terrain. We extrapolate that the total volume of ice remaining within the entire ejecta deposit is as much as 74 km3 or more. The variation in ice content between the ejecta layers could be the result of (1) volatile preservation from the formation of the DLE crater, (2) post-impact deposition in the form of ice lenses; or (3) preferential accumulation or preservation of subsequent snowfall. We have ruled out (2) as the primary mode for ice deposition in this location based on inconsistencies with our observations, though it may operate in concert with other processes. Although none of the existing DLE formation hypotheses are completely consistent with our observations, which may merit a new or modified mechanism, we can conclude that DLE craters contain a significant quantity of excess ice today.
Dynamics, nucleosynthesis, and kilonova signature of black hole—neutron star merger ejecta
Fernández, Rodrigo; Foucart, Francois; Kasen, Daniel; Lippuner, Jonas; Desai, Dhruv; Roberts, Luke F.
2017-08-01
We investigate the ejecta from black hole—neutron star mergers by modeling the formation and interaction of mass ejected in a tidal tail and a disk wind. The outflows are neutron-rich, giving rise to optical/infrared emission powered by the radioactive decay of r-process elements (a kilonova). Here we perform an end-to-end study of this phenomenon, where we start from the output of a fully-relativistic merger simulation, calculate the post-merger hydrodynamical evolution of the ejecta and disk winds including neutrino physics, determine the final nucleosynthetic yields using post-processing nuclear reaction network calculations, and compute the kilonova emission with a radiative transfer code. We study the effects of the tail-to-disk mass ratio by scaling the tail density. A larger initial tail mass results in fallback matter becoming mixed into the disk and ejected in the subsequent disk wind. Relative to the case of a disk without dynamical ejecta, the combined outflow has lower mean electron fraction, faster speed, larger total mass, and larger absolute mass free of high-opacity Lanthanides or Actinides. In most cases, the nucleosynthetic yield is dominated by the heavy r-process contribution from the unbound part of the dynamical ejecta. A Solar-like abundance distribution can however be obtained when the total mass of the dynamical ejecta is comparable to the mass of the disk outflows. The kilonova has a characteristic duration of 1 week and a luminosity of ∼ 1041 erg s-1 , with orientation effects leading to variations of a factor ∼2 in brightness. At early times (< 1 d) the emission includes an optical component from the (hot) Lanthanide-rich material, but the spectrum evolves quickly to the infrared thereafter.
Subsurface volatile content of martian double-layer ejecta (DLE) craters
Viola, Donna; McEwen, Alfred S.; Dundas, Colin M.; Byrne, Shane
2017-01-01
Excess ice is widespread throughout the martian mid-latitudes, particularly in Arcadia Planitia, where double-layer ejecta (DLE) craters also tend to be abundant. In this region, we observe the presence of thermokarstically-expanded secondary craters that likely form from impacts that destabilize a subsurface layer of excess ice, which subsequently sublimates. The presence of these expanded craters shows that excess ice is still preserved within the adjacent terrain. Here, we focus on a 15-km DLE crater that contains abundant superposed expanded craters in order to study the distribution of subsurface volatiles both at the time when the secondary craters formed and, by extension, remaining today. To do this, we measure the size distribution of the superposed expanded craters and use topographic data to calculate crater volumes as a proxy for the volumes of ice lost to sublimation during the expansion process. The inner ejecta layer contains craters that appear to have undergone more expansion, suggesting that excess ice was most abundant in that region. However, both of the ejecta layers had more expanded craters than the surrounding terrain. We extrapolate that the total volume of ice remaining within the entire ejecta deposit is as much as 74 km3 or more. The variation in ice content between the ejecta layers could be the result of (1) volatile preservation from the formation of the DLE crater, (2) post-impact deposition in the form of ice lenses; or (3) preferential accumulation or preservation of subsequent snowfall. We have ruled out (2) as the primary mode for ice deposition in this location based on inconsistencies with our observations, though it may operate in concert with other processes. Although none of the existing DLE formation hypotheses are completely consistent with our observations, which may merit a new or modified mechanism, we can conclude that DLE craters contain a significant quantity of excess ice today.
Supernova Ejecta in the Youngest Galactic Supernova Remnant G1.9+0.3
Borkowski, Kazimierz J.; Reynolds, Stephen P.; Hwang, Una; Green, David A.; Petre, Robert; Krishnamurthy, Kalyani; Willett, Rebecca
2013-01-01
G1.9+0.3 is the youngest known Galactic supernova remnant (SNR), with an estimated supernova (SN) explosion date of approximately 1900, and most likely located near the Galactic Center. Only the outermost ejecta layers with free-expansion velocities (is) approximately greater than 18,000 km s-1 have been shocked so far in this dynamically young, likely Type Ia SNR. A long (980 ks) Chandra observation in 2011 allowed spatially-resolved spectroscopy of heavy-element ejecta. We denoised Chandra data with the spatio-spectral method of Krishnamurthy et al., and used a wavelet based technique to spatially localize thermal emission produced by intermediate-mass elements (IMEs: Si and S) and iron. The spatial distribution of both IMEs and Fe is extremely asymmetric, with the strongest ejecta emission in the northern rim. Fe K alpha emission is particularly prominent there, and fits with thermal models indicate strongly oversolar Fe abundances. In a localized, outlying region in the northern rim, IMEs are less abundant than Fe, indicating that undiluted Fe-group elements (including 56Ni) with velocities greater than 18,000 km s-1 were ejected by this SN. But in the inner west rim, we find Si- and S-rich ejecta without any traces of Fe, so high-velocity products of O-burning were also ejected. G1.9+0.3 appears similar to energetic Type Ia SNe such as SN 2010jn where iron-group elements at such high free-expansion velocities have been recently detected. The pronounced asymmetry in the ejecta distribution and abundance inhomogeneities are best explained by a strongly asymmetric SN explosion, similar to those produced in some recent 3D delayed-detonation Type Ia models.
SUPERNOVA EJECTA IN THE YOUNGEST GALACTIC SUPERNOVA REMNANT G1.9+0.3
Borkowski, Kazimierz J.; Reynolds, Stephen P. [Department of Physics, North Carolina State University, Raleigh, NC 27695-8202 (United States); Hwang, Una [Department of Astronomy, University of Maryland, College Park, MD 20742 (United States); Green, David A. [Cavendish Laboratory, 19 J.J. Thomson Ave., Cambridge CB3 0HE (United Kingdom); Petre, Robert [NASA/GSFC, Code 660, Greenbelt, MD 20771 (United States); Krishnamurthy, Kalyani; Willett, Rebecca, E-mail: kborkow@unity.ncsu.edu [Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708 (United States)
2013-07-01
G1.9+0.3 is the youngest known Galactic supernova remnant (SNR), with an estimated supernova (SN) explosion date of {approx}1900, and most likely located near the Galactic center. Only the outermost ejecta layers with free-expansion velocities {approx}>18,000 km s{sup -1} have been shocked so far in this dynamically young, likely Type Ia SNR. A long (980 ks) Chandra observation in 2011 allowed spatially resolved spectroscopy of heavy-element ejecta. We denoised Chandra data with the spatio-spectral method of Krishnamurthy et al., and used a wavelet-based technique to spatially localize thermal emission produced by intermediate-mass elements (IMEs; Si and S) and iron. The spatial distribution of both IMEs and Fe is extremely asymmetric, with the strongest ejecta emission in the northern rim. Fe K{alpha} emission is particularly prominent there, and fits with thermal models indicate strongly oversolar Fe abundances. In a localized, outlying region in the northern rim, IMEs are less abundant than Fe, indicating that undiluted Fe-group elements (including {sup 56}Ni) with velocities >18,000 km s{sup -1} were ejected by this SN. However, in the inner west rim, we find Si- and S-rich ejecta without any traces of Fe, so high-velocity products of O-burning were also ejected. G1.9+0.3 appears similar to energetic Type Ia SNe such as SN 2010jn where iron-group elements at such high free-expansion velocities have been recently detected. The pronounced asymmetry in the ejecta distribution and abundance inhomogeneities are best explained by a strongly asymmetric SN explosion, similar to those produced in some recent three-dimensional delayed-detonation Type Ia models.
THE MORPHOLOGY OF THE EJECTA IN SUPERNOVA 1987A: A STUDY OVER TIME AND WAVELENGTH
Larsson, Josefin [KTH, Department of Physics, and the Oskar Klein Centre, AlbaNova, SE-106 91 Stockholm (Sweden); Fransson, Claes; Lundqvist, Peter; Sollerman, Jesper [Department of Astronomy and the Oskar Klein Centre, Stockholm University, AlbaNova, SE-106 91 Stockholm (Sweden); Kjaer, Karina; Leibundgut, Bruno; Spyromilio, Jason [ESO, Karl-Schwarzschild-Strasse 2, D-85748 Garching (Germany); Jerkstrand, Anders [Astrophysics Research Centre, School of Maths and Physics, Queens University Belfast, Belfast BT7 1NN (United Kingdom); Kirshner, Robert P. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, MS-78, Cambridge, MA 02138 (United States); Mattila, Seppo [Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Vaeisaelaentie 20, FI-21500 Piikkioe (Finland); McCray, Richard [JILA, University of Colorado, Boulder, CO 80309-0440 (United States); Wheeler, J. Craig [Department of Astronomy, University of Texas, Austin, TX 78712-0259 (United States)
2013-05-01
We present a study of the morphology of the ejecta in Supernova 1987A based on images and spectra from the Hubble Space Telescope (HST) as well as integral field spectroscopy from VLT/SINFONI. The HST observations were obtained between 1994 and 2011 and primarily probe the outer H-rich zones of the ejecta. The SINFONI observations were obtained in 2005 and 2011 and instead probe the [Si I]+[Fe II] emission from the inner regions. We find a strong temporal evolution of the morphology in the HST images, from a roughly elliptical shape before {approx}5000 days, to a more irregular, edge-brightened morphology with a ''hole'' in the middle thereafter. This transition is a natural consequence of the change in the dominant energy source powering the ejecta, from radioactive decay before {approx}5000 days to X-ray input from the circumstellar interaction thereafter. The [Si I]+[Fe II] images display a more uniform morphology, which may be due to a remaining significant contribution from radioactivity in the inner ejecta and the higher abundance of these elements in the core. Both the H{alpha} and the [Si I]+[Fe II] line profiles show that the ejecta are distributed fairly close to the plane of the inner circumstellar ring, which is assumed to define the rotational axis of the progenitor star. The H{alpha} emission extends to higher velocities than [Si I]+[Fe II], as expected from theoretical models. There is no clear symmetry axis for all the emission. Instead, we find that the emission is concentrated to clumps and that the emission is distributed somewhat closer to the ring in the north than in the south. This north-south asymmetry may be partially explained by dust absorption. We compare our results with explosion models and find some qualitative agreement, but note that the observations show a higher degree of large-scale asymmetry.
On the Braids for 810 Knot = 810 Düğümünün Örgüsü Hakkında
Ahmet KÜÇÜK
2001-06-01
Full Text Available This paper is concerned with 810 knots and its braids. The braids structure is very important role in Knots Theory. In view of this structure, we obtained braids for that knot and we will give the representations of Artin and we examine Garside Word problem. And then we will examine the positivity structure for these knots.
Some Sufficient Conditions for Tunnel Numbers of Connected Sum of Two Knots Not to Go Down
Guo Qiu YANG; Feng Chun LEI
2011-01-01
In this paper,we show the following result:Let Ki be a knot in a closed orientable 3-manifold Mi such that (Mi,Ki) is not homeomorphic to (S2 × S1,x0 × S1),i =1,2.Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(Ki) is less than the difference of one and twice of the tunnel number of Ki.Then the tunnel number of their connected sum will not go down.If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2,then the tunnel number of their connected sum is super additive.We further show that if the distance of a Heegaard splitting of each knot complement is strictly bigger than twice the tunnel number of the knot (twice the sum of the tunnel number of the knot and one,respectively),then the tunnel number of connected sum of two such knots is additive (super additive,respectively).
Effects of horseshoe crab harvest in delaware bay on red knots: Are harvest restrictions working?
Niles, L.J.; Bart, J.; Sitters, H.P.; Dey, A.D.; Clark, K.E.; Atkinson, P.W.; Baker, A.J.; Bennett, K.A.; Kalasz, K.S.; Clark, N.A.; Clark, J.; Gillings, S.; Gates, A.S.; Gonzalez, P.M.; Hernandez, D.E.; Minton, C.D.T.; Morrison, R.I.G.; Porter, R.R.; Ross, R.K.; Veitch, C.R.
2009-01-01
Each May, red knots (Calidris canutus rufa) congregate in Delaware Bay during their northward migration to feed on horseshoe crab eggs (Limulus polyphemus) and refuel for breeding in the Arctic. During the 1990s, the Delaware Bay harvest of horseshoe crabs for bait increased 10-fold, leading to a more than 90% decline in the availability of their eggs for knots. The proportion of knots achieving weights of more than 180 grams by 26-28 May, their main departure period, dropped from 0.6-0.8 to 0.14-0.4 over 1997-2007. During the same period, the red knot population stopping in Delaware Bay declined by more than 75%, in part because the annual survival rate of adult knots wintering in Tierra del Fuego declined. Despite restrictions, the 2007 horseshoe crab harvest was still greater than the 1990 harvest, and no recovery of knots was detectable. We propose an adaptive management strategy with recovery goals and annual monitoring that, if adopted, will both allow red knot and horseshoe crab populations to recover and permit a sustainable harvest of horseshoe crabs.
Helicity, Topology and Kelvin Waves in reconnecting quantum knots
di Leoni, P Clark; Brachet, M E
2016-01-01
Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes and ribbons. As such, it has found myriads of applications in astrophysics and solar physics, in fluid dynamics, in atmospheric sciences, and in biology. In quantum flows, where topology-changing reconnection events are a staple, helicity appears as a key quantity to study. However, the usual definition of helicity is not well posed in quantum vortices, and its computation based on counting links and crossings of vortex lines can be downright impossible to apply in complex and turbulent scenarios. We present a new definition of helicity which overcomes these problems. With it, we show that only certain reconnection events conserve helicity. In other cases helicity can change abruptly during reconnection. Furthermore, we show that these events can also excite Kelvin waves, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum turbulence.
Numerical simulation of the knotted nylon netting panel
Li Yuwei
2016-01-01
Full Text Available A piece of netting, consists of the 8 8 meshes, fixed on a square frame, was simulated and the tensions and their distribution, the positions of knots and netting shape were calculated by means of MATLAB in computer. The dynamic mathematic model was developed based on lumped mass method, the netting was treated as spring-mass system, the Runge-Kutta fifth-order and sixth-order method was used to solve the differential equations for every step, then the displacement and tension of each mass point were obtained. For verify this model, the tests have been carried out in a flume tank. The results of the numerical simulation fully agreed with the experiments.
Symmetric alteration of four knots of B-spline and NURBS surfaces
LI Ya-juan; WANG Guo-zhao
2006-01-01
Modifying the knots ofa B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface,the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.
Knot detection in X-ray images of wood planks using dictionary learning
Hansson, Nils Mattias; Enescu, Alexandru; Brandt, Sami Sebastian
2015-01-01
This paper considers a novel application of x-ray imaging of planks, for the purpose of detecting knots in high quality furniture wood. X-ray imaging allows the detection of knots invisible from the surface to conventional cameras. Our approach is based on texture analysis, or more specifically......, discriminative dictionary learning. Experiments show that the knot detection and segmentation can be accurately performed by our approach. This is a promising result and can be directly applied in industrial processing of furniture wood....
Multiple folding pathways of proteins with shallow knots and co-translational folding
Chwastyk, Mateusz
2015-01-01
We study the folding process in the shallowly knotted protein MJ0366 within two variants of a structure-based model. We observe that the resulting topological pathways are much richer than identified in previous studies. In addition to the single knot-loop events, we find novel, and dominant, two-loop mechanisms. We demonstrate that folding takes place in a range of temperatures and the conditions of most successful folding are at temperatures which are higher than those required for the fastest folding. We also demonstrate that nascent conditions are more favorable to knotting than off-ribosome folding.
Successful retrieval of a knotted pulmonary artery catheter trapped in the tricuspid valve apparatus
Muhammad Ishaq; Nicki Alexander; David H. T. Scott
2013-01-01
We report the case of a 64-year-old patient in whom a pulmonary artery catheter formed a knot fixed within the right ventricle in the region of the tricuspid valve apparatus. Knot formation is a recognized complication associated with pulmonary artery catheters (PAC) insertion. This problem is usually dealt with by simply withdrawing the PAC until the knot impacts onto the introducer and after enlarging the puncture site by a small skin incision removing the introducer-PAC as one unit. Howeve...
Nematicides and nonconventional soil amendments in the management of root-knot nematode on cotton.
Jorgenson, E C
1984-04-01
Granular and liquid commercial humates, with micronutrients, and a microbial fermentation product were compared in several combinations with nematicides for their effects on cotton lint yield and root-knot nematode suppression. Fumigant nematicides effectively reduced cotton root galling caused by root-knot nematodes, and cotton lint yields increased. Organophosphates and carbamates were not effective. Occasionally, cotton lint yields were increased or maintained with combination treatments o f humates, micronutrients, and a microbial fermentation product, but galling o f cotton roots by root-knot nematodes was usually not reduced by these treatments.
Ejecta of Eta Carinae: What We Learn about N-Rich Chemistry
Gull, Theodore
2006-01-01
At least one member of the binary system, Eta Carinae, is in the late stages of CNO-cycle. At least ten solar masses of ejecta make up the Homunculus, a neutral bi-polar shell ejected in the 1840s and the Little Homunculus, an internal, ionized bi-polar shell ejected in the 1890s. HST/STIS and VLTAJVES high dispersion spectroscopy revealed absorptions of multiple elements and diatomic molecules in these shells, some, such as V II and Sr II have not been seen previously in the ISM. The skirt region between the bi-lobes includes the very bright Weigelt blobs, within 0.1 to 0.3" of the central source, and the more distant, unusual Strontium Filament, a neutral emission nebula photoexcited by Balmer continuum, but shielded by Fe II from Lyman radiation. The 600+ emission lines are due to metals usually tied up in dust, but underabundances of C and O prevent precipitation as oxides onto the dust grains. Indications are that Ti/Ni is 100X solar, likely due not to nuclear processing, but the very different photo-excitation environments coupled with N-rich, C-, O-poor chemistry. In the Homunculus, level populations of the molecules indicate 60K gas; the metal absorption lines, 760K; that of the Little Homunculus 6400K during the broad spectroscopic maximum, relaxing to 5000K for the few month long minimum. Lyman radiation, including both continuum and Lyman lines, is trapped across periastron. leading to temporary relaxation of the ejecta. These ejecta are a treasure trove of information on material thrown out of massive stars in the CNO-cycle, well before the helium burning phase. Curiously, spectra of three very recent SWIFT GRBs indicate the presence of warm, photoexcited ejecta in the vicinity of the protoGRBs, but obviously of very different abundances. However, the ejecta of Eta Carinae promise to be a nearby example of massive ejecta, the study of which should lead to increased insight of earlier, very distant massive stars.
Mehner, A.; Steffen, W.; Groh, J. H.; Vogt, F. P. A.; Baade, D.; Boffin, H. M. J.; Davidson, K.; de Wit, W. J.; Humphreys, R. M.; Martayan, C.; Oudmaijer, R. D.; Rivinius, T.; Selman, F.
2016-11-01
Aims: The role of episodic mass loss is one of the outstanding questions in massive star evolution. The structural inhomogeneities and kinematics of their nebulae are tracers of their mass-loss history. We conduct a three-dimensional morpho-kinematic analysis of the ejecta of η Car outside its famous Homunculus nebula. Methods: We carried out the first large-scale integral field unit observations of η Car in the optical, covering a field of view of 1'× 1' centered on the star. Observations with the Multi Unit Spectroscopic Explorer (MUSE) at the Very Large Telescope (VLT) reveal the detailed three-dimensional structure of η Car's outer ejecta. Morpho-kinematic modeling of these ejecta is conducted with the code SHAPE. Results: The largest coherent structure in η Car's outer ejecta can be described as a bent cylinder with roughly the same symmetry axis as the Homunculus nebula. This large outer shell is interacting with the surrounding medium, creating soft X-ray emission. Doppler velocities of up to 3000 km s-1 are observed. We establish the shape and extent of the ghost shell in front of the southern Homunculus lobe and confirm that the NN condensation can best be modeled as a bowshock in the orbital/equatorial plane. Conclusions: The SHAPE modeling of the MUSE observations provides a significant gain in the study of the three-dimensional structure of η Car's outer ejecta. Our SHAPE modeling indicates that the kinematics of the outer ejecta measured with MUSE can be described by a spatially coherent structure, and that this structure also correlates with the extended soft X-ray emission associated with the outer debris field. The ghost shell immediately outside the southern Homunculus lobe hints at a sequence of eruptions within the time frame of the Great Eruption from 1837-1858 or possibly a later shock/reverse shock velocity separation. Our 3D morpho-kinematic modeling and the MUSE observations constitute an invaluable dataset to be confronted with future
Evolution of fluid-like granular ejecta generated by sphere impact
Marston, Jeremy
2012-05-01
We present results from an experimental study of the speed and shape of the ejecta formed when a solid sphere impacts onto a granular bed. We use high-speed imaging at frame rates up to 100 000 f.p.s. to provide direct measurement of individual grain velocities and ejecta angles as well as the overall evolution of the granular ejecta. For larger grain sizes, the emergence velocities of the grains during the early stage flow, i.e. before the main ejecta curtain forms, increase with the kinetic energy of the impacting sphere but are inversely proportional to the time from impact. We also observe that the fastest grains, which can obtain velocities up to five times that of the impacting sphere (V g/V 0 = 5), generally emerge at the earliest times and with the lowest ejection angles. As the grain size is decreased, a more fluid-like behaviour is observed whereby the ejected material first emerges as a thin sheet of grains between the sphere and the bed surface, which is also seen when a sphere impacts a liquid pool. In this case, the sheet velocity is approximately double that of the impacting sphere (V s/V 0 = 2) and independent of the bulk packing fraction. For the finest grains we provide evidence of the existence of a vortex ring inside the ejecta curtain where grains following the air flow are entrained through the curtain. In contrast to predictions from previous studies, we find that the temporal evolution of the ejecta neck radius is not initially quadratic but rather approaches a square-root dependence on time, for the finest grains with the highest impact kinetic energy. The evolution therefore approaches that seen for the crown evolution in liquid drop impacts. By using both spherical glass beads and coarse sands, we show that the size and shape distribution are critical in determining the post-impact dynamics whereby the sands exhibit a qualitatively different response to impact, with grains ejected at lower speeds and at later times than for the glass
Impact ejecta-induced melting of surface ice deposits on Mars
Weiss, David K.; Head, James W.
2016-12-01
Fluvial features present around impact craters on Mars can offer insight into the ancient martian climate and its relationship to the impact cratering process. The widespread spatial and temporal distribution of surface ice on Mars suggests that the interaction between impact cratering and surface ice could have been a relatively frequent occurrence. We explore the thermal and melting effects on regional surface ice sheets in this case, where an impact event occurs in regional surface ice deposits overlying a regolith/bedrock target. We provide an estimate for the post-impact temperature of martian ejecta as a function of crater diameter, and conduct thermal modeling to assess the degree to which contact melting of hot ejecta superposed on surface ice deposits can produce meltwater and carve fluvial features. We also evaluate whether fluvial features could form as a result of basal melting of the ice deposits in response to the thermal insulation provided by the overlying impact ejecta. Contact melting is predicted to occur immediately following ejecta emplacement over the course of hundreds of years to tens of kyr. Basal melting initiates when the 273 K isotherm rises through the crust and reaches the base of the ice sheet ∼0.1 to ∼1 Myr following the impact. We assess the range of crater diameters predicted to produce contact and basal melting of surface ice sheets, as well as the melt fluxes, volumes, timescales, predicted locations of melting (relative to the crater), and the associated hydraulic and hydrologic consequences. We find that the heat flux and surface temperature conditions required to produce contact melting are met throughout martian history, whereas the heat flux and surface temperature conditions to produce basal melting are met only under currently understood ancient martian thermal conditions. For an impact into a regional ice sheet, the contact and basal melting mechanisms are predicted to generate melt volumes between ∼10-1 and 105 km3
Jones, Eriita; Caprarelli, Graziella; Osinski, Gordon R.
2016-06-01
Layered ejecta craters on Mars have been interpreted to indicate the presence of volatiles in the substrate, making them important targets for the investigation of sites of astrobiological significance. If the ejecta are associated with the presence of water in the substratum, specific surface grain size trends are expected. In this study we explore the distribution of grain sizes in the layered ejecta of impact craters located in Chryse Planitia, using Thermal Emission Imaging System (THEMIS) thermal infrared data. Ejecta grain size trends, in conjunction with ejecta mobility and lobateness values, are applied to assess the degree of surface flow of the ejecta, and in turn to constrain the plausible volatile abundance, cohesion, and fine particle content of the target materials. Craters with a larger fraction of small grain sizes in their ejecta showed greater ejecta mobility and lobateness, consistent with a water-rich and/or a low-cohesion target. Craters displaying decreasing grain size with increasing radius had smaller diameters and lower ejecta mobility and lobateness, indicating only a minimal component of surface ejecta flow. Ejecta grain size trends varied with crater diameter, from which the presence of vertical compositional stratigraphy in Chryse Planitia is inferred and interpreted. Our observations are synthesized into a number of plausible geologic scenarios for Chryse Planitia.
Asymmetric High-Velocity Ejecta in the Youngest Galactic SNR G1.9+0.3
Borkowski, Kazimierz
2014-11-01
Chandra has revealed highly asymmetric supernova ejecta in G1.9+0.3. Iron dominates thermal emission in the radio-bright northern rim, while only intermediate-mass elements are found along the SE-NW axis. The measured X-ray expansion rates decrease radially by about 60% along this axis from 0.84% yr^{-1) to 0.52% yr^{-1}. This corresponds to undecelerated ages of 120 - 190 yr, confirming the young age of G1.9+0.3, and implying that the blast wave is much more decelerated than the reverse shock. Only the outermost ejecta with very high (>18,000 km s^{-1}) free-expansion velocities have been shocked so far. We discuss G1.9+0.3 in the framework of recent asymmetric 3D delayed-detonation Type Ia explosions from Seitenzahl et al. (2013). Their N3 model provides the best match.
Synthetic line and continuum linear-polarisation signatures of axisymmetric type II supernova ejecta
Dessart, Luc
2011-01-01
We present synthetic single-line and continuum linear-polarisation signatures due to electron scattering in axially-symmetric Type II supernovae (SNe) which we calculate using a Monte Carlo and a long-characteristic radiative-transfer code. Aspherical ejecta are produced by prescribing a latitudinal scaling or stretching of SN ejecta inputs obtained from 1-D non-LTE time-dependent calculations. We study polarisation signatures as a function of inclination, shape factor, wavelength, line identity, post-explosion time. At early times, cancellation and optical-depth effects make the polarisation intrinsically low, causing complicated sign reversals with inclination or continuum wavelength, and across line profiles. While the line polarisation is positive (negative) for an oblate (prolate) morphology at the peak and in the red wing, the continuum polarisation may be of any sign. These complex polarisation variations are produced not just by the asymmetric distribution of scatterers but also of the flux. Our early...
US Fish and Wildlife Service, Department of the Interior — This FY2014 progress report documents project activity for determining critical wintering sites and migration routes for juvenile red knots. Project goals, expected...
Knot numbers used as labels for identifying subject matter of a khipu
Alberto Saez-Rodriguez
2013-03-01
Full Text Available This investigation presents a new way to look at the numerical khipu, a knotted-string recording device from Pachacamac (Peru, and the types of information it contains. In addition to celestial coordinates, khipu knots apparently pertain to an early form of double-entry accounting. This study hypothesizes that the khipu sample has the recording capacity needed to register double-entry-like accounts. After the identification of its subject matter, the khipu sample was studied in an attempt to ascertain whether the knot values could represent instructions from the Inca state administration to a local accounting center. The results indicate that the numerical information in the pairing quadrants (determined by the distribution of S- and Z-knots should be read from top to bottom along the full length of the string and can then provide certain complementary details regarding the projected corn stocks of the Inca stat
PRESENCE OF RED KNOT (CALIDRIS CANUTUS IN ITE WETLANDS, TACNA, PERU
Jhonson K. Vizcarra
2012-06-01
Full Text Available The presence of Red Knot (Calidris canutus, Linnaeus 1758 in Ite Wetlands, Tacna, Peru is documented. Two individuals were observed in October 2011. This species had only one occurrence without details in this area.
The algebraic crossing number and the braid index of knots and links
Kawamuro, Keiko
2009-01-01
It has been conjectured that the algebraic crossing number of a link is uniquely determined in minimal braid representation. This conjecture is true for many classes of knots and links. The Morton-Franks-Williams inequality gives a lower bound for braid index. And sharpness of the inequality on a knot type implies the truth of the conjecture for the knot type. We prove that there are infinitely many examples of knots and links for which the inequality is not sharp but the conjecture is still true. We also show that if the conjecture is true for K and L, then it is also true for the (p,q)-cable of K and for the connect sum of K and L.
Some Dimensions of Spaces of Finite Type Invariants of Virtual Knots
Bar-Natan, Dror; Leung, Louis; Roukema, Fionntan
2009-01-01
We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of "weight systems", finding everything to be in agreement with the conjecture that "every weight system integrates".
Biocontrol (Formulation of Bacillus firmus (BioNem)) of Root-knot ...
Key words: Bacillus firmus, Biological control, Meloidogyne incognita, Tomato. Introduction ... levels of biocontrol formulation, BioNem on root-knot nematode infestation and plant ...... Journal of invertebrate Pathology 100 (2009)94-99.
Folding of small knotted proteins: Insights from a mean field coarse-grained model
Najafi, Saeed; Potestio, Raffaello, E-mail: potestio@mpip-mainz.mpg.de [Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz (Germany)
2015-12-28
A small but relevant number of proteins whose native structure is known features nontrivial topology, i.e., they are knotted. Understanding the process of folding from a swollen unknotted state to the biologically relevant native conformation is, for these proteins, particularly difficult, due to their rate-limiting topological entanglement. To shed some light into this conundrum, we introduced a structure-based coarse-grained model of the protein, where the information about the folded conformation is encoded in bonded angular interactions only, which do not favor the formation of native contacts. A stochastic search scheme in parameter space is employed to identify a set of interactions that maximizes the probability to attain the knotted state. The optimal knotting pathways of the two smallest knotted proteins, obtained through this approach, are consistent with the results derived by means of coarse-grained as well as full atomistic simulations.
On the species status of the root-knot nematode Meloidogyne mayaguensis Rammah & Hirschmann, 1988
Karssen, G.; Liao, J.; Kan, Z.; Heese, van E.; Nijs, L.J.M.F.
2012-01-01
Holo- and paratypes of the root-knot nematodes Meloidogyne mayaguensis Rammah & Hirschmann, 1988 and M. enterolobii Yang & Eisenback, 1983 were morphometrically and morphologically compared. All observed female, male and second-stage juvenile morphometrical and morphological characters are i
Ishaq, Muhammad; Alexander, Nicki; Scott, David H T
2013-04-01
We report the case of a 64-year-old patient in whom a pulmonary artery catheter formed a knot fixed within the right ventricle in the region of the tricuspid valve apparatus. Knot formation is a recognized complication associated with pulmonary artery catheters (PAC) insertion. This problem is usually dealt with by simply withdrawing the PAC until the knot impacts onto the introducer and after enlarging the puncture site by a small skin incision removing the introducer-PAC as one unit. However, we recently encountered a situation where the PAC was knotted around the tricuspid valve apparatus and could not be withdrawn. An interventional radiologist was able to unknot the catheter and release it from the tricuspid valve. We reviewed the literature related to this topic. We believe our experience could be of use to others.
Successful retrieval of a knotted pulmonary artery catheter trapped in the tricuspid valve apparatus
Muhammad Ishaq
2013-01-01
Full Text Available We report the case of a 64-year-old patient in whom a pulmonary artery catheter formed a knot fixed within the right ventricle in the region of the tricuspid valve apparatus. Knot formation is a recognized complication associated with pulmonary artery catheters (PAC insertion. This problem is usually dealt with by simply withdrawing the PAC until the knot impacts onto the introducer and after enlarging the puncture site by a small skin incision removing the introducer-PAC as one unit. However, we recently encountered a situation where the PAC was knotted around the tricuspid valve apparatus and could not be withdrawn. An interventional radiologist was able to unknot the catheter and release it from the tricuspid valve. We reviewed the literature related to this topic. We believe our experience could be of use to others.
Caudill, C. M.; Osinski, G. R.; Tornabene, L. L.
2016-08-01
In this study, we report the mapping and geologic interpretation of 150-km diameter Bakhuysen Crater, Mars, which supports previous work suggesting similar mechanisms of multi-unit ejecta emplacement on other comparable rocky bodies.
Experimental hypervelocity impact into quartz sand - Distribution and shock metamorphism of ejecta
Stoeffler, D.; Gault, D. E.; Wedekind, J.; Polkowski, G.
1975-01-01
Results are presented for vertical impacts of 0.3-g cylindrical plastic projectiles into noncohesive quartz sand in which vertical and horizontal reference strate were employed by using layers of colored sand. The impacts were performed at velocities of 5.9-6.9 km/sec with a vertical gun ballistic range. The craters, 30-33 cm in diameter, reveal a radial decay of the ejecta mass per unit area with a power of -2.8 to -3.5. Material displaced from the upper 15% of the crater depth d is represented within the whole ejecta blanked, material from deeper than 28% of d is deposited inside 2 crater radii, and no material from deeper than 33% of d was ejected beyond the crater rim. Shock-metamorphosed particles (glassy agglutinates, cataclastic breccias, and comminuted quartz) amount to some 4% of the total displaced mass and indicate progressive zones of decay of shock intensity from a peak pressure of 300 kbar. The shock-metamorphosed particles and the shock-induced change in the grain size distribution of ejected samples have close analogies to the basic characteristics of the lunar regolith. Possible applications to regolith formation and to ejecta formations of large-scale impact craters are discussed.
Accretion by a Neutron Star Moving at a High Kick Velocity in the Supernova Ejecta
Xu Zhang; Ye Lu; Yong-Heng Zhao
2007-01-01
We suggest a two-dimensional time dependent analytic model to describe the accretion of matter onto a neutron star moving at a high speed across the ejecta left in the aftermath of a supernova explosion. The formation of a strange star resulting from the accretion is also addressed. The newborn neutron star is assumed to move outward at a kick velocity of vns ～ 103 km s-1, and the accretion flow is treated as a dust flow. When the neutron star travels across the ejecta with high speed, it sweeps up material, and when the accreted mass has reached a critical value, the neutron star will undergo a phase transition,for instance, to become a strange star. Our results show that the accretion rate decreases in a complicated way in time, not just a power law dependence: it drops much faster than the power law derived by Colpi et al. We also found that the total accreted mass and the phase transition of the neutron star depend sensitively on the velocity of supernova ejecta.
X-Ray Illumination of the Ejecta of Supernova 1987A
Larsson, J.; Fransson, C.; Oestlin, G.; Groeningsson, P.; Jerkstrand, A.; Kozma, C.; Sollerman, J.; Challis, P.; Kirshner, R. P.; Chevalier, R. A.; Heng, K.; McCray, R.; Suntzeff, N. B.; Bouchet, P.; Crotts, A.; Danziger, J.; Dwek, E.; France, K.; Garnavich, P. M.; Lawrence, S. S.; Leibundgut, B.; Lundqvist, P.; Panagia, N.; Pun, C. S. J.; Sonneborn, G.
2011-01-01
When a massive star explodes as a supernova, substantial amounts of radioactive elements-primarily Ni-56, Ni-57 and Ti-44 are produced. After the initial from shock heating, the light emitted by the supernova is due to the decay of these elements. However, after decades, the energy powering a supernova remnant comes from the shock interaction between the ejecta and the surrounding medium. The transition to this phase has hitherto not been observed: supernovae occur too infrequently in the Milky Way to provide a young example, and extragalactic supernovae are generally too faint and too small. Here we report observations that show this transition in the supernova SN 1987A in the Large Magellan Cloud. From 1994 to 200l, the ejecta faded owing to radioactive decay of Ti-44 as predicted. Then the flux started to increase, more than doubling by the end of 2009. We show that this increase is the result of heat deposited by X-rays produced as the ejecta interacts with the surrounding material. In time, the X-rays will penetrate farther into the ejects, enabling us to analyse the structure and chemistry of the vanished star.
SULFUR MOLECULE CHEMISTRY IN SUPERNOVA EJECTA RECORDED BY SILICON CARBIDE STARDUST
Hoppe, Peter [Max Planck Institute for Chemistry, Hahn-Meitner-Weg 1, 55128 Mainz (Germany); Fujiya, Wataru [Department of Earth and Planetary Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Zinner, Ernst, E-mail: peter.hoppe@mpic.de, E-mail: fujiya@eps.s.u-tokyo.ac.jp, E-mail: ekz@wustl.edu [Laboratory for Space Sciences and Physics Department, Campus Box 1105, Washington University, St. Louis, MO 63130 (United States)
2012-02-15
We studied about 3400 presolar silicon carbide (SiC) grains from the Murchison CM2 meteorite for C- and Si-isotopic compositions. Among these grains we identified 7 unusual or type C SiC (U/C) grains, characterized by isotopically heavy Si, and 36 supernova type X SiC grains, characterized by isotopically light Si. Selected U/C and X grains were also measured for S-, Mg-Al-, and Ca-Ti-isotopic compositions. We show that the U/C grains incorporated radioactive {sup 44}Ti, which is evidence that they formed in the ejecta of Type II supernova (SNII) explosions. Abundances of radioactive {sup 26}Al and {sup 44}Ti are compatible with those observed in X grains. U/C and X grains carry light S with enrichments in {sup 32}S of up to a factor of 2.7. The combination of heavy Si and light S observed in U/C grains is not consistent with abundance predictions of simple supernova models. The isotope data suggest preferential trapping of S from the innermost supernova zones, the production site of radioactive {sup 44}Ti, by the growing silicon carbide particles. A way to achieve this is by sulfur molecule chemistry in the still unmixed ejecta. This confirms model predictions of molecule formation in SNII ejecta and shows that sulfur molecule chemistry operates in the harsh and hot environments of stellar explosions.
Gravitational waves and mass ejecta from binary neutron star mergers: Effect of the mass-ratio
Dietrich, Tim; Tichy, Wolfgang; Bernuzzi, Sebastiano; Bruegmann, Bernd
2016-01-01
We present new (3+1)D numerical relativity simulations of the binary neutron star (BNS) merger and postmerger phase. We focus on a previously inaccessible region of the binary parameter space spanning the binary's mass-ratio $q\\sim1.00-1.75$ for different total masses and equations of state, and up to $q\\sim2$ for a stiff BNS system. We study the mass-ratio effect on the gravitational waves (GWs) and on the possible electromagnetic emission associated to dynamical mass ejecta. We compute waveforms, spectra, and spectrograms of the GW strain including all the multipoles up to $l=4$. The mass-ratio has a specific imprint on the GW multipoles in the late-inspiral-merger signal, and it affects qualitatively the spectra of the merger remnant. The multipole effect is also studied by considering the dependency of the GW spectrograms on the source's sky location. Unequal mass BNSs produce more ejecta than equal mass systems with ejecta masses and kinetic energies depending almost linearly on $q$. We estimate luminosi...
Chicxulub ejecta plume: Influence of sedimentary target rock, volatiles and atmosphere
Salge, T.
Terrestrial impact structures provide evidence for cratering processes on planetary bodies with an atmosphere and volatiles in the target rocks. The target of the Chicxulub impact structure (˜180 km Ø) was composed of (1) a ˜3 km thick sedimentary and, thus, extremely volatile-rich target sequence, and (2) a crystalline silicate basement. The suevites of El Guayal ˜520 km SW from the crater centre and UNAM-7 near the crater rim recorded the distinct behaviour of sedimentary target rock, water and atmospheric interactions during ejecta emplacement. El Guayal: A ˜10 m thick suevite sequence contains shocked minerals, altered (to clay minerals) silicate melt and spherulitic carbonate melt particles. Fusion of silicate melt with carbonate induced calcite recrystallisation at >750°C. Release of CO2 is indicated by voids in silicate melt at the contact with calcite. Accretionary lapilli 350°C by slaking and from silicate melt particles. Conclusions: The following sequence of processes is proposed: (1) Vapour release changed ejecta distribution from ballistic to flow-like transport. (2) Ejecta plume collapse separated suevite from impactor material that had been lifted into the stratosphere. (3) Fusion of the different target components initiated a hot gas-driven lateral transport in a basal flow. (4) Accretionary lapilli formed in a coherent turbulent ash cloud. Acknowledgements: TS kindly thanks P. Claeys for providing samples, R. Tagle for PGE analyses and H. Stosnach for introduction to TXRF analyses.
Modeling post-explosion anisotropies of ejecta in SNR Cassiopeia A
Orlando, S.; Miceli, M.; Pumo, M.; Bocchino, F.
2016-06-01
Supernova remnats (SNRs) show a complex morphology characterized by an inhomogeneous spatial distribution of ejecta, believed to reflect pristine structures and features of the progenitor supernova (SN) explosion. Filling the gap between SN explosions and their remnants is very important for a comprehension of the origin of present-day structure of ejecta in SNRs and to probe and constraint current models of SN explosions. The SNR Cassiopeia A (Cas A) is an attractive laboratory for studying the SNe-SNRs connection, being one of the best studied SNRs for which its 3D structure is known. We present a three-dimensional hydrodynamic model describing the evolution of Cas A from the immediate aftermath of the SN explosion to its expansion through the interstellar medium, taking into account the distribution of element abundances of the ejecta, the back reaction of accelerated cosmic rays at the shock front, and the deviations from equilibrium of ionizazion for the most important elements. We use the model to derive the physical parameters characterizing the SN explosion and reproducing the today morphology of Cas A.
The Density and Mass of Unshocked Ejecta in Cassiopeia A through Low Frequency Radio Absorption
DeLaney, Tracey; Rudnick, Lawrence; Perley, R A
2014-01-01
Characterizing the ejecta in young supernova remnants is a requisite step towards a better understanding of stellar evolution. In Cassiopeia A the density and total mass remaining in the unshocked ejecta are important parameters for modeling its explosion and subsequent evolution. Low frequency (<100 MHz) radio observations of sufficient angular resolution offer a unique probe of unshocked ejecta revealed via free-free absorption against the synchrotron emitting shell. We have used the Very Large Array plus Pie Town Link extension to probe this cool, ionized absorber at 9 arcseconds and 18.5 arcseconds resolution at 74 MHz. Together with higher frequency data we estimate an electron density of 4.2 electrons per cubic centimeters and a total mass of 0.39 Solar masses with uncertainties of a factor of about 2. This is a significant improvement over the 100 electrons per cubic centimeter upper limit offered by infrared [S III] line ratios from the Spitzer Space Telescope. Our estimates are sensitive to a numb...
Supernova Ejecta in the Youngest Galactic Supernova Remnant G1.9+0.3
Borkowski, K J; Hwang, U; Green, D A; Petre, R; Krishnamurthy, K; Willett, R
2013-01-01
G1.9+0.3 is the youngest known Galactic supernova remnant (SNR), with an estimated supernova (SN) explosion date of about 1900, and most likely located near the Galactic Center. Only the outermost ejecta layers with free-expansion velocities larger than about 18,000 km/s have been shocked so far in this dynamically young, likely Type Ia SNR. A long (980 ks) Chandra observation in 2011 allowed spatially-resolved spectroscopy of heavy-element ejecta. We denoised Chandra data with the spatio-spectral method of Krishnamurthy et al., and used a wavelet-based technique to spatially localize thermal emission produced by intermediate-mass elements (IMEs: Si and S) and iron. The spatial distribution of both IMEs and Fe is extremely asymmetric, with the strongest ejecta emission in the northern rim. Fe Kalpha emission is particularly prominent there, and fits with thermal models indicate strongly oversolar Fe abundances. In a localized, outlying region in the northern rim, IMEs are less abundant than Fe, indicating tha...
The interaction of core-collapse supernova ejecta with a companion star
Liu, Zheng-Wei; Roepke, Friedrich K; Moriya, Takashi J; Kruckow, Matthias; Stancliffe, Richard J; Izzard, Robert G
2015-01-01
The progenitors of many CCSNe are expected to be in binary systems. After the SN explosion, the companion may suffer from mass stripping and be shock heated as a result of the impact of the SN ejecta. If the binary system is disrupted, the companion is ejected as a runaway or hypervelocity star. By performing a series of 3D hydrodynamical simulations of the collision of SN ejecta with the companion star, we investigate how CCSN explosions affect their companions. We use the BEC code to construct the detailed companion structure at the time of SN explosion. The impact of the SN blast wave on the companion is followed by means of 3D SPH simulations using the Stellar GADGET code. For main-sequence (MS) companions, we find that the amount of removed mass, impact velocity, and chemical contamination of the companion that results from the impact of the SN ejecta, strongly increases with decreasing binary separation and increasing explosion energy. Their relationship can be approximately fitted by power laws, which ...
The Contribution of Chemical Abundances in Nova Ejecta to the Interstellar Medium
Li, Fanger; Lu, Guoliang; Wang, Zhaojun
2016-01-01
According to the nova model from \\citet{Yaron2005} and \\citet{Jose1998} and using Monte Carlo simulation method, we investigate the contribution of chemical abundances in nova ejecta to the interstellar medium (ISM) of the Galaxy. We find that the ejected mass by classical novae (CNe) is about $2.7\\times10^{-3}$ $ \\rm M_\\odot\\ {\\rm yr^{-1}}$. In the nova ejecta, the isotopic ratios of C, N and O, that is, $^{13}$C/$^{12}$C, $^{15}$N/$^{14}$N and $^{17}$O/$^{16}$O, are higher about one order of magnitude than those in red giants. We estimate that about 10$\\%$, 5$\\%$ and 20$\\%$ of $^{13}$C, $^{15}$N and $^{17}$O in the ISM of the Galaxy come from nova ejecta, respectively. However, the chemical abundances of C, N and O calculated by our model can not cover all of observational values. This means that there is still a long way to go for understanding novae.
Knots: attractive places with high path tortuosity in mouse open field exploration.
Anna Dvorkin
2010-01-01
Full Text Available When introduced into a novel environment, mammals establish in it a preferred place marked by the highest number of visits and highest cumulative time spent in it. Examination of exploratory behavior in reference to this "home base" highlights important features of its organization. It might therefore be fruitful to search for other types of marked places in mouse exploratory behavior and examine their influence on overall behavior.Examination of path curvatures of mice exploring a large empty arena revealed the presence of circumscribed locales marked by the performance of tortuous paths full of twists and turns. We term these places knots, and the behavior performed in them-knot-scribbling. There is typically no more than one knot per session; it has distinct boundaries and it is maintained both within and across sessions. Knots are mostly situated in the place of introduction into the arena, here away from walls. Knots are not characterized by the features of a home base, except for a high speed during inbound and a low speed during outbound paths. The establishment of knots is enhanced by injecting the mouse with saline and placing it in an exposed portion of the arena, suggesting that stress and the arousal associated with it consolidate a long-term contingency between a particular locale and knot-scribbling.In an environment devoid of proximal cues mice mark a locale associated with arousal by twisting and turning in it. This creates a self-generated, often centrally located landmark. The tortuosity of the path traced during the behavior implies almost concurrent multiple views of the environment. Knot-scribbling could therefore function as a way to obtain an overview of the entire environment, allowing re-calibration of the mouse's locale map and compass directions. The rich vestibular input generated by scribbling could improve the interpretation of the visual scene.
An eddy-current-based sensor for preventing knots in metallic wire drawing processes
Esteban, Bernat; Riba, Jordi-Roger; Baquero, Grau; Ferrater, Cèsar
2011-06-01
During metallic wire drawing processes, the presence of knots and the failure to detect them can lead to long production interruptions, significant economic losses and a lower quality of final product. Consequently, there is a pressing need to develop methods for real-time detection and prevention of this fault. In this paper, a sensor to prevent the formation of knots during the metallic wire drawing process is presented and evaluated by means of experimental data. This fast, inexpensive, non-contact sensor is based on electromagnetic principles such as eddy current induction, magnetic reluctance variations and magnetic coupling. The proposed sensor without direct contact can detect knots in a target metallic wire by measuring the impedance variations of a calibrated sensing coil caused by either a knot or an unwound loop rising from a wire rod. The incorporation of this type of sensor into a wire-drawing machine can avoid the tightening of the knot, thereby reducing downtime and increasing the security and reliability of the process. Experiments were conducted using a scale model of the above proposed system. This allowed highlighting the sensor's potential by carrying out an automatic, real-time knot detection during steel wire drawing.
The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
Dijkgraaf, Robbert; Fuji, Hiroyuki; Manabe, Masahide
2011-08-01
We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard-Orantin topological recursion relation. We discuss the correspondence for the figure eight knot complement and the once punctured torus bundle over S with the monodromy LR up to the fifth order. For the torus knots, we find trivial the recursion relations on both sides.
The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
Dijkgraaf, Robbert, E-mail: r.h.dijkgraaf@uva.n [Institute for Theoretical Physics and KdV Institute for Mathematics, University of Amsterdam, Spui 21, 1012 WX Amsterdam (Netherlands); Fuji, Hiroyuki, E-mail: fuji@th.phys.nagoya-u.ac.j [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Manabe, Masahide, E-mail: d07002p@math.nagoya-u.ac.j [Graduate School of Mathematics, Nagoya University, Nagoya 464-8602 (Japan)
2011-08-01
We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard-Orantin topological recursion relation. We discuss the correspondence for the figure eight knot complement and the once punctured torus bundle over S{sup 1} with the monodromy L{sup 2}R up to the fifth order. For the torus knots, we find trivial the recursion relations on both sides.
The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
Dijkgraaf, Robbert; Manabe, Masahide
2010-01-01
We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard-Orantin topological recursion relation. We check the correspondence for the figure eight knot complement and the once punctured torus bundle over S^1 with the holonomy L^2R up to the fourth order. For the torus knots, we find trivial the recursion relations on both sides.
Condensates and instanton - torus knot duality. Hidden Physics at UV scale
Gorsky, A
2014-01-01
We establish the duality between the torus knot superpolynomials or the Poincare polynomials of the Khovanov homology and particular condensates in Omega-deformed 5D supersymmetric QED compactified on a circle with 5d Chern-Simons(CS) term. This is the generalization of the Witten's recipe of the evaluation of the knot polynomials via Wilson loops in 3d CS theory for case of the torus knots. It is explicitly shown that $n$-instanton contribution to the condensate of the massless flavor in the background of four-observable, which can be associated with some composite defect, exactly coincides with the superpolynomial of the T(n,nk+1) torus knot where k - is the level of CS term. In contrast to the previously known results, the particular torus knot corresponds not to the partition function of the gauge theory but to the particular instanton contribution and summation over the knots has to be performed in order to obtain the complete answer. The instantons are sitting almost at the top of each other and the phy...
The X-ray emission from the knots in 3C 120
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2010-01-01
3C 120 is a Seyfert galaxy with a well detected X-ray jet.We investigate the X-ray emission of its five jet knots and fit their spectral energy distributions(SEDs) from the radio to the X-ray bands with a single-zone lepton model.We find that the SEDs of knots k7,s2,and s3 can be explained by synchrotron radiation,and the X-rays are the simple extension of the radio-optical emission component,but that of the inner knot k4 requires the IC/CMB model,in which the X-rays are due to the inverse Compton scattering of the cosmic microwave background photons by relativistic electrons in the jet with a beaming factor δ-14.The outer knot k25 is resolved into a three-part sub-structure.It is shown that the fitting of the X-rays from this knot with the IC/CMB model needs an extraordinary beaming factor δ-15-25 for a jet at the kpc scale.If the X-rays of knot k25 are produced by synchrotron radiation similar to k7,s2,and s3,they may be contributed by a relativistic electron population whose radiations in other wavelengths are not detected.
Knotted Vortices: Entropic Lattice Boltzmann Method for Simulation of Vortex dynamics
Boesch, Fabian; Chikatamarla, Shyam; Karlin, Ilya
2013-11-01
Knotted and interlinked vortex structures in real fluids are conjectured to play a major role in hydrodynamic flow dissipation. Much interest lies in determining their temporal stability and the mechanism through which knots dissolve. Kleckner and Irvine recently have shown the existence of such knotted vortices experimentally by accelerating hydrofoils in water. In the present work we employ the entropic lattice Boltzmann method (ELBM) to perform DNS simulations of the creation and dynamics of knotted vortex rings inspired by the experimental setup in. ELBM renders LBM scheme unconditionally stable by restoring the second law of thermodynamics (the Boltzmann H-theorem), and thus enables simulations of large domains and high Reynolds numbers with DNS quality. The results presented in this talk provide an in-depth study of the dynamics of knotted vortices and vortex reconnection events and confirm the existence of trefoil knots in silicio for the first time. This work was supported by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID s347.
Survival of organic compounds in ejecta from hypervelocity impacts on ice
Bowden, S. A.; Parnell, J.; Burchell, M. J.
2009-01-01
Hypervelocity impacts (HVIs) where organic-bearing ice constitutes the target material are important in several aspects of planetary and space science: (1) sampling of planetary surfaces using a hypervelocity projectile to impact the surface and eject surface materials for measurement or collection by a spacecraft; (2) the transfer of organic material between planetary bodies; and (3) providing energy for chemical processes involving surface materials. While small organic molecules (~6 carbon atoms), if present in surface materials, will likely be present in HVI-ejecta, uncertainty remains for larger organic molecules. It is the larger molecular weight compounds which could constitute direct evidence of life, and thus their survival within an HVI-ejecta plume is of key importance when evaluating strategies for life detection on icy bodies. It is not currently known what large organic molecules, and in what concentrations, may be present on icy bodies in the Solar System, but it is highly likely some will be more chemically stable during a HVI than others. Accordingly, in this study we examined a range of chemicals (β,β carotene, stearic acid and anthracene) with molecular weights between 178 and 536 daltons, and three different types of chemical structure. The compounds were solvated in a dimethylsulfoxide/water mixture and frozen. The frozen targets were impacted with steel spheres 1 and 1.5 mm in diameter at velocities of about 4.9 km s-1. Ice ejected during the impact was collected and underwent chemical analysis. The most labile compound (β,β carotene) was only detected (in small amounts) in the ejecta (and only that emitted at the lowest angles of ejection), although the other compounds were present in larger quantities and at a range of ejection angles. A concentration gradient was observed within the ejecta as a function of angle of ejection. This was not the same for both stearic acid and anthracene: the greatest concentrations of stearic acid were
Optical vortex knots – one photon at a time
Tempone-Wiltshire, Sebastien J.; Johnstone, Shaun P.; Helmerson, Kristian
2016-01-01
Feynman described the double slit experiment as “a phenomenon which is impossible, absolutely impossible, to explain in any classical way and which has in it the heart of quantum mechanics”. The double-slit experiment, performed one photon at a time, dramatically demonstrates the particle-wave duality of quantum objects by generating a fringe pattern corresponding to the interference of light (a wave phenomenon) from two slits, even when there is only one photon (a particle) at a time passing through the apparatus. The particle-wave duality of light should also apply to complex three dimensional optical fields formed by multi-path interference, however, this has not been demonstrated. Here we observe particle-wave duality of a three dimensional field by generating a trefoil optical vortex knot – one photon at a time. This result demonstrates a fundamental physical principle, that particle-wave duality implies interference in both space (between spatially distinct modes) and time (through the complex evolution of the superposition of modes), and has implications for topologically entangled single photon states, orbital angular momentum multiplexing and topological quantum computing. PMID:27087642
Optical vortex knots - one photon at a time
Tempone-Wiltshire, Sebastien J.; Johnstone, Shaun P.; Helmerson, Kristian
2016-04-01
Feynman described the double slit experiment as “a phenomenon which is impossible, absolutely impossible, to explain in any classical way and which has in it the heart of quantum mechanics”. The double-slit experiment, performed one photon at a time, dramatically demonstrates the particle-wave duality of quantum objects by generating a fringe pattern corresponding to the interference of light (a wave phenomenon) from two slits, even when there is only one photon (a particle) at a time passing through the apparatus. The particle-wave duality of light should also apply to complex three dimensional optical fields formed by multi-path interference, however, this has not been demonstrated. Here we observe particle-wave duality of a three dimensional field by generating a trefoil optical vortex knot - one photon at a time. This result demonstrates a fundamental physical principle, that particle-wave duality implies interference in both space (between spatially distinct modes) and time (through the complex evolution of the superposition of modes), and has implications for topologically entangled single photon states, orbital angular momentum multiplexing and topological quantum computing.
Helicity, topology, and Kelvin waves in reconnecting quantum knots
Clark di Leoni, P.; Mininni, P. D.; Brachet, M. E.
2016-10-01
Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes, and ribbons. As such, it has found myriads of applications in astrophysics, fluid dynamics, atmospheric sciences, and biology. In quantum flows, where topology-changing reconnection events are a staple, helicity appears as a key quantity to study. However, the usual definition of helicity is not well posed in quantum vortices, and its computation based on counting links and crossings of centerline vorticity can be downright impossible to apply in complex and turbulent scenarios. We present a definition of helicity which overcomes these problems and which gives the expected result in the large-scale limit. With it, we show that certain reconnection events can excite Kelvin waves and other complex motions of the centerline vorticity, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum fluids. This process also results in the depletion of helicity in a fully turbulent quantum flow, in a way reminiscent of the decay of helicity in classical fluids.
Novel inhibitor cystine knot peptides from Momordica charantia.
Wen-Jun He
Full Text Available Two new peptides, MCh-1 and MCh-2, along with three known trypsin inhibitors (MCTI-I, MCTI-II and MCTI-III, were isolated from the seeds of the tropical vine Momordica charantia. The sequences of the peptides were determined using mass spectrometry and NMR spectroscopy. Using a strategy involving partial reduction and stepwise alkylation of the peptides, followed by enzymatic digestion and tandem mass spectrometry sequencing, the disulfide connectivity of MCh-1 was elucidated to be CysI-CysIV, CysII-CysV and CysIII-CysVI. The three-dimensional structures of MCh-1 and MCh-2 were determined using NMR spectroscopy and found to contain the inhibitor cystine knot (ICK motif. The sequences of the novel peptides differ significantly from peptides previously isolated from this plant. Therefore, this study expands the known peptide diversity in M. charantia and the range of sequences that can be accommodated by the ICK motif. Furthermore, we show that a stable two-disulfide intermediate is involved in the oxidative folding of MCh-1. This disulfide intermediate is structurally homologous to the proposed ancestral fold of ICK peptides, and provides a possible pathway for the evolution of this structural motif, which is highly prevalent in nature.
Park, Jong Taek; Cho, Dong Woo; Lee, Young Bok
2017-01-01
Epidural block is achieved either by single injection of local anesthetic through an epidural needle or as a continuous block by infusion pump through an epidural catheter. Complications associated with epidural catheters include breakage, entrapment, and knotting. Knotting of epidural catheters is very rare, but knotting in lumbar epidural catheters has been reported in a number of studies, and most of these cases involved removal difficulty. We report a case in which we inserted a cervical epidural catheter in a patient who was experiencing severe post-herpetic neuralgia and then removed the knotted catheter without complications. PMID:28261560
Lee, Jaepil
2015-01-01
In the bordered Floer theory, gluing thickened torus of positive meridional Dehn twist to the boundary of a knot complement result in the knot complement of increased framing. For a fixed knot K, we construct a direct system of positively framed knot complements and study the direct limit. We also study the morphism space between two type-DD modules, and derive type-DA morphisms from DD morphisms to derive the direct system maps. In addition, we introduce a direct limit invariant from the dir...
顾之雨; 钱尚武
2015-01-01
The GHZ states and W states are two fundamental types of three qubits quantum entangled states. For finding the knotted pictures of three nodes W states, on the one side, we empty any one node, thus obtaining three degenerated two-node W states, then we find the nonzero submatrix of the corresponding covariance correlation tensor in quantum network theory. On the other side, excepting the linkage 41 corresponding to Bell bases, we conjecture that the another one possible oriented link (which is composed of two-component knots entangled with each other and has four crossings) would be the required knotted pictures of the two nodes W states, thence obtain the nonzero submatrix of the Alexander relation matrix in the theory of knot crystals for these knotted pictures. The equality of the two nonzero submatrices of different kinds thus verify the exactness of our conjecture. The superposition of three knotted pictures of two-node W states from different choices of the emptied node gives the knotted pictures of three-node W states, thus shows the correspondence between three-node W states in quantum network theory and the oriented links in knot theory. Finally we point out that there is an intimate and simple relationship between the knotted pictures of GHZ states and W states.
Arakawa, M.; Wada, K.; Saiki, T.; Kadono, T.; Takagi, Y.; Shirai, K.; Okamoto, C.; Yano, H.; Hayakawa, M.; Nakazawa, S.; Hirata, N.; Kobayashi, M.; Michel, P.; Jutzi, M.; Imamura, H.; Ogawa, K.; Sakatani, N.; Iijima, Y.; Honda, R.; Ishibashi, K.; Hayakawa, H.; Sawada, H.
2016-10-01
The Small Carry-on Impactor (SCI) equipped on Hayabusa2 was developed to produce an artificial impact crater on the primitive Near-Earth Asteroid (NEA) 162173 Ryugu (Ryugu) in order to explore the asteroid subsurface material unaffected by space weathering and thermal alteration by solar radiation. An exposed fresh surface by the impactor and/or the ejecta deposit excavated from the crater will be observed by remote sensing instruments, and a subsurface fresh sample of the asteroid will be collected there. The SCI impact experiment will be observed by a Deployable CAMera 3-D (DCAM3-D) at a distance of ˜1 km from the impact point, and the time evolution of the ejecta curtain will be observed by this camera to confirm the impact point on the asteroid surface. As a result of the observation of the ejecta curtain by DCAM3-D and the crater morphology by onboard cameras, the subsurface structure and the physical properties of the constituting materials will be derived from crater scaling laws. Moreover, the SCI experiment on Ryugu gives us a precious opportunity to clarify effects of microgravity on the cratering process and to validate numerical simulations and models of the cratering process.
Arakawa, M.; Wada, K.; Saiki, T.; Kadono, T.; Takagi, Y.; Shirai, K.; Okamoto, C.; Yano, H.; Hayakawa, M.; Nakazawa, S.; Hirata, N.; Kobayashi, M.; Michel, P.; Jutzi, M.; Imamura, H.; Ogawa, K.; Sakatani, N.; Iijima, Y.; Honda, R.; Ishibashi, K.; Hayakawa, H.; Sawada, H.
2017-07-01
The Small Carry-on Impactor (SCI) equipped on Hayabusa2 was developed to produce an artificial impact crater on the primitive Near-Earth Asteroid (NEA) 162173 Ryugu (Ryugu) in order to explore the asteroid subsurface material unaffected by space weathering and thermal alteration by solar radiation. An exposed fresh surface by the impactor and/or the ejecta deposit excavated from the crater will be observed by remote sensing instruments, and a subsurface fresh sample of the asteroid will be collected there. The SCI impact experiment will be observed by a Deployable CAMera 3-D (DCAM3-D) at a distance of ˜1 km from the impact point, and the time evolution of the ejecta curtain will be observed by this camera to confirm the impact point on the asteroid surface. As a result of the observation of the ejecta curtain by DCAM3-D and the crater morphology by onboard cameras, the subsurface structure and the physical properties of the constituting materials will be derived from crater scaling laws. Moreover, the SCI experiment on Ryugu gives us a precious opportunity to clarify effects of microgravity on the cratering process and to validate numerical simulations and models of the cratering process.
Garvin, J. B.; Campbell, B. A.; Zisk, S. H.; Schaber, Gerald G.; Evans, C.
1989-01-01
Simple impact craters are known to occur on all of the terrestrial planets and the morphologic expression of their ejecta blankets is a reliable indicator of their relative ages on the Moon, Mars, Mercury, and most recently for Venus. It will be crucial for the interpretation of the geology of Venus to develop a reliable means of distinguishing smaller impact landforms from volcanic collapse and explosion craters, and further to use the observed SAR characteristics of crater ejecta blankets (CEB) as a means of relative age estimation. With these concepts in mind, a study was initiated of the quantitative SAR textural characteristics of the ejecta blanket preserved at Meteor Crater, Arizona, the well studied 1.2 km diameter simple crater that formed approx. 49,000 years ago from the impact of an octahedrite bolide. While Meteor Crater was formed as the result of an impact into wind and water lain sediments and has undergone recognizable water and wind related erosion, it nonetheless represents the only well studied simple impact crater on Earth with a reasonably preserved CEB. Whether the scattering behavior of the CEB can provide an independent perspective on its preservation state and style of erosion is explored. Finally, airborne laser altimeter profiles of the microtopography of the Meteor Crater CEB were used to further quantify the subradar pizel scale topographic slopes and RMS height variations for comparisons with the scattering mechanisms computed from SAR polarimetry. A preliminary assessment was summarized of the L-band radar scattering mechanisms within the Meteor Crater CEB as derived from a NASA/JPL DC-8 SAR Polarimetry dataset acquired in 1988, and the dominant scattering behavior was compared with microtopographic data (laser altimeter profiles and 1:10,000 scale topographic maps).
Geologic Mapping of Ejecta Deposits in Oppia Quadrangle, Asteroid (4) Vesta
Garry, W. Brent; Williams, David A.; Yingst, R. Aileen; Mest, Scott C.; Buczkowski, Debra L.; Tosi, Federico; Schafer, Michael; LeCorre, Lucille; Reddy, Vishnu; Jaumann, Ralf; Pieters, Carle M.; Russell, Christopher T.; Raymond, Carol A.
2014-01-01
Oppia Quadrangle Av-10 (288-360 deg E, +/- 22 deg) is a junction of key geologic features that preserve a rough history of Asteroid (4) Vesta and serves as a case study of using geologic mapping to define a relative geologic timescale. Clear filter images, stereo-derived topography, slope maps, and multispectral color-ratio images from the Framing Camera on NASA's Dawn spacecraft served as basemaps to create a geologic map and investigate the spatial and temporal relationships of the local stratigraphy. Geologic mapping reveals the oldest map unit within Av-10 is the cratered highlands terrain which possibly represents original crustal material on Vesta that was then excavated by one or more impacts to form the basin Feralia Planitia. Saturnalia Fossae and Divalia Fossae ridge and trough terrains intersect the wall of Feralia Planitia indicating that this impact basin is older than both the Veneneia and Rheasilvia impact structures, representing Pre-Veneneian crustal material. Two of the youngest geologic features in Av-10 are Lepida (approximately 45 km diameter) and Oppia (approximately 40 km diameter) impact craters that formed on the northern and southern wall of Feralia Planitia and each cross-cuts a trough terrain. The ejecta blanket of Oppia is mapped as 'dark mantle' material because it appears dark orange in the Framing Camera 'Clementine-type' colorratio image and has a diffuse, gradational contact distributed to the south across the rim of Rheasilvia. Mapping of surface material that appears light orange in color in the Framing Camera 'Clementine-type' color-ratio image as 'light mantle material' supports previous interpretations of an impact ejecta origin. Some light mantle deposits are easily traced to nearby source craters, but other deposits may represent distal ejecta deposits (emplaced greater than 5 crater radii away) in a microgravity environment.
Gravitational waves and mass ejecta from binary neutron star mergers: Effect of the mass ratio
Dietrich, Tim; Ujevic, Maximiliano; Tichy, Wolfgang; Bernuzzi, Sebastiano; Brügmann, Bernd
2017-01-01
We present new (3 +1 )D numerical relativity simulations of the binary neutron star (BNS) merger and postmerger phase. We focus on a previously inaccessible region of the binary parameter space spanning the binary's mass ratio q ˜1.00 - 1.75 for different total masses and equations of state, and up to q ˜2 for a stiff BNS system. We study the mass ratio effect on the gravitational waves (GWs) and on the possible electromagnetic (EM) emission associated with dynamical mass ejecta. We compute waveforms, spectra, and spectrograms of the GW strain including all the multipoles up to l =4 . The mass ratio has a specific imprint on the GW multipoles in the late-inspiral-merger signal, and it affects qualitatively the spectra of the merger remnant. The multipole effect is also studied by considering the dependency of the GW spectrograms on the source's sky location. Unequal mass BNSs produce more ejecta than equal mass systems with ejecta masses and kinetic energies depending almost linearly on q . We estimate luminosity peaks and light curves of macronova events associated with the mergers using a simple approach. For q ˜2 the luminosity peak is delayed for several days and can be up to 4 times larger than for the q =1 cases. The macronova emission associated with the q ˜2 BNS is more persistent in time and could be observed for weeks instead of a few days (q =1 ) in the near infrared. Finally, we estimate the flux of possible radio flares produced by the interaction of relativistic outflows with the surrounding medium. Also in this case a large q can significantly enhance the emission and delay the peak luminosity. Overall, our results indicate that the BNS merger with a large mass ratio has EM signatures distinct from the equal mass case and more similar to black hole-neutron star binaries.
Scenario Of The 4 kyr Extraterrestrial Impact : Crater Location, Ejecta-Dispersion and Consequences.
Courty, M.; Abbott, D. H.; Cortese, G.; Crisci, A.; Crosta, X.; de Wever, P.; Fedoroff, M.; Greenwood, P.; Grice, K.; Mermoux, M.; Scharer, U.; Smith, D. C.; Thiemens, M. H.
2006-12-01
The 4 kyr BP impact event has been identified from deep-sea, soil and archaeological records as the worldwide pulverisation of a volatile-rich debris jet(1). High resolution sequences show two stages of ejecta fallout linked to the impact-triggered doublet gaseous regime(2): scattered solid debris at the ground surface and spray of the vaporized hot fireball with thermal blast and local ignition. Ejecta debris consist of flow- textured impact glass, impact breccia and incompletely melted marine clasts: volcano-clastic sandy mudstone, calcareous mud, granite-gneiss, schists, volcanic breccia, kerogen and algal mud. Marine microfossils, organo-mineral markers, and the debris-fallout spatial pattern indicate two potential impact craters: an Antarctic source with an admixture of volcanic glass and ice rafted debris, from the vicinity of Heard Island and the Kerguelen plateau; a low latitude, shallow water one with hydrocarbons possibly from the Gulf of Mexico. Fine mixing of target materials from far distant source craters emphasizes a unique impact-ejecta. This matches the theoretical view of a debris jet channelled along the corridor cut through the atmosphere by the incoming projectile, raised upward, and dispersed widely(3). The isotopic anomaly of the sulphur phase in the kerogen volatile-component, indicating mass independent fractionation due to photolytic transformation, suggests launching at great heights, beyond the O2-O3 UV shield, responsible for climate disturbances. The incomplete melting of target rocks and global dispersion of impact breccia out of the craters would result from splash of small-sized projectile at rather great water depth and a low angle impact (10-15 degrees) into porous, highly compressible marine sediments. The spatially variable distribution of the organo-mineral and melt components, and the wide range of phase transformation reflect nonequilibrium shock-melting and micro-scale thermal processes in the heterogeneous vapor plume
Intra-vesical knot of bladder catheter in an extremely low birthweight neonate: A case report
Paula M.Y. Tang
2015-07-01
Full Text Available Premature and extremely low birth weight (ELBW neonates are at high risk of developing multiple co-morbidities and often require urinary catheterization for various medical indications. Intra-vesical knotting of bladder catheter is a known but uncommon complication of this procedure. We report a case of an ELBW baby boy with a knotted bladder catheter requiring surgical retrieval. After an elective operation for the closure of patent ductus arteriosus, a 4 French urinary catheter was inserted into an ELBW baby boy for urine output monitoring and left in-situ. Resistance was encountered in attempt to remove the urinary catheter. Abdominal X Ray confirmed intra-vesical knotting of the tube. Knot unravelling by interventional radiology was attempted but was unsuccessful. Open extra-peritoneal bladder exploration was performed for the retrieval of the tightly knotted catheter. A 6 French transurethral Foley catheter was inserted for bladder drainage. Upon removal of the Foley's catheter on day 5 post op, the baby was able to void spontaneously. With literature review, we postulated the potential risk factors resulting in this potentially avoidable iatrogenic unusual complication. Recommendations were suggested to avoid further incidences.
Hippo pathway/Yap regulates primary enamel knot and dental cusp patterning in tooth morphogenesis.
Kwon, Hyuk-Jae Edward; Li, Liwen; Jung, Han-Sung
2015-11-01
The shape of an individual tooth crown is primarily determined by the number and arrangement of its cusps, i.e., cusp patterning. Enamel knots that appear in the enamel organ during tooth morphogenesis have been suggested to play important roles in cusp patterning. Animal model studies have shown that the Hippo pathway effector Yap has a critical function in tooth morphogenesis. However, the role of the Hippo pathway/Yap in cusp patterning has not been well documented and its specific roles in tooth morphogenesis remain unclear. Here, we provide evidence that Yap is a key mediator in tooth cusp patterning. We demonstrate a correlation between Yap localization and cell proliferation in developing tooth germs. We also show that, between the cap stage and bell stage, Yap is crucial for the suppression of the primary enamel knot and for the patterning of secondary enamel knots, which are the future cusp regions. When Yap expression is stage-specifically knocked down during the cap stage, the activity of the primary enamel knot persists into the bell-stage tooth germ, leading to ectopic cusp formation. Our data reveal the importance of the Hippo pathway/Yap in enamel knots and in the proper patterning of tooth cusps.
Characterization of the Inner Knot of the Crab: The Site of the Gamma-ray Flares?
Rudy, A; DeLuca, A; Kolodziejczak, J; Tennant, A; Yuan, Y; Buehler, R; Arons, J; Blandford, R; Caraveo, P; Costa, E; Funk, S; Hays, E; Lobanov, A; Max, C; Mayer, M; Mignani, R; O'Dell, S L; Romani, R; Tavani, M; Weisskopf, M C
2015-01-01
One of the most intriguing results from the gamma-ray instruments in orbit has been the detection of powerful flares from the Crab Nebula. These flares challenge our understanding of pulsar wind nebulae and models for particle acceleration. We report on the portion of a multiwavelength campaign using Keck, HST, and Chandra concentrating on a small emitting region, the Crab's inner knot, located a fraction of an arcsecond from the pulsar. We find that the knot's radial size, tangential size, peak flux, and the ratio of the flux to that of the pulsar are correlated with the projected distance of the knot from the pulsar. A new approach, using singular value decomposition for analyzing time series of images, was introduced yielding results consistent with the more traditional methods while some uncertainties were substantially reduced. We exploit the characterization of the knot to discuss constraints on standard shock-model parameters that may be inferred from our observations assuming the inner knot lies near ...
Particle on a torus knot: Constrained dynamics and semi-classical quantization in a magnetic field
Das, Praloy; Pramanik, Souvik; Ghosh, Subir
2016-11-01
Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in Dirac's Hamiltonian framework, both in toroidal and Cartesian coordinate systems. This algebra has been used to study the dynamics, in particular small fluctuations in motion around a specific torus. The spatial symmetries of the system have also been studied. In the second part of the paper we have considered the quantum theory of a charge moving in a torus knot in the presence of a uniform magnetic field along the axis of the torus in a semiclassical quantization framework. We exploit the Einstein-Brillouin-Keller (EBK) scheme of quantization that is appropriate for multidimensional systems. Embedding of the knot on a specific torus is inherently two dimensional that gives rise to two quantization conditions. This shows that although the system, after imposing the knot condition reduces to a one dimensional system, even then it has manifested non-planar features which shows up again in the study of fractional angular momentum. Finally we compare the results obtained from EBK (multi-dimensional) and Bohr-Sommerfeld (single dimensional) schemes. The energy levels and fractional spin depend on the torus knot parameters that specifies its non-planar features. Interestingly, we show that there can be non-planar corrections to the planar anyon-like fractional spin.
Multispecies modeling for adaptive management of horseshoe crabs and red knots in the Delaware Bay
McGowan, Conor P.; Smith, David; Sweka, John A.; Martin, Julien; Nichols, James D.; Wong, Richard; Lyons, James E.; Niles, Lawrence J.; Kalasz, Kevin; Brust, Jeffrey; Klopfer, Michelle; Spear, Braddock
2011-01-01
Adaptive management requires that predictive models be explicit and transparent to improve decisions by comparing management actions, directing further research and monitoring, and facilitating learning. The rufa subspecies of red knots (Calidris canutus rufa), which has recently exhibited steep population declines, relies on horseshoe crab (Limulus polyphemus) eggs as their primary food source during stopover in Delaware Bay during spring migration. We present a model with two different parameterizations for use in the adaptive management of horseshoe crab harvests in the Delaware Bay that links red knot mass gain, annual survival, and fecundity to horseshoe crab dynamics. The models reflect prevailing hypotheses regarding ecological links between these two species. When reported crab harvest from 1998 to 2008 was applied, projections corresponded to the observed red knot population abundances depending on strengths of the demographic relationship between these species. We compared different simulated horseshoe crab harvest strategies to evaluate whether, given this model, horseshoe crab harvest management can affect red knot conservation and found that restricting harvest can benefit red knot populations. Our model is the first to explicitly and quantitatively link these two species and will be used within an adaptive management framework to manage the Delaware Bay system and learn more about the specific nature of the linkage between the two species.
Allotides: Proline-Rich Cystine Knot α-Amylase Inhibitors from Allamanda cathartica.
Nguyen, Phuong Q T; Luu, Thuy T; Bai, Yang; Nguyen, Giang K T; Pervushin, Konstantin; Tam, James P
2015-04-24
Cystine knot α-amylase inhibitors belong to a knottin family of peptidyl inhibitors of 30-32 residues and contain two to four prolines. Thus far, only four members of the group of cystine knot α-amylase inhibitors have been characterized. Herein, the discovery and characterization of five cystine knot α-amylase inhibitors, allotides C1-C5 (Ac1-Ac5) (1-5), from the medicinal plant Allamanda cathartica are reported using both proteomic and genomic methods. Proteomic analysis showed that 1-5 are 30 amino acids in length with three or four proline residues. NMR determination of 4 revealed that it has two cis- and one trans-proline residues and adopts two equally populated conformations in solution. Determination of disulfide connectivity of 2 by differential S-reduction and S-alkylation provided clues of its unfolding process. Genomic analysis showed that allotide precursors contain a three-domain arrangement commonly found in plant cystine knot peptides with conserved residues flanking the processing sites of the mature allotide domain. This work expands the number of known cystine knot α-amylase inhibitors and furthers the understanding of both the structural and biological diversity of this type of knottin family.
Sequence-specific size, structure, and stability of tight protein knots
Dzubiella, Joachim
2008-01-01
Approximately 1% of the known protein structures display knotted configurations in their native fold but their function is not understood. It has been speculated that the entanglement may inhibit mechanical protein unfolding or transport, e.g., as in cellular threading or translocation processes through narrow biological pores. Here we investigate tigh peptide knot (TPK) characteristics in detail by pulling selected 3_1 and 4_1-knotted peptides using all-atom molecular dynamics computer simulations. We find that the 3_1 and 4_1-TPK lengths are typically Delta l~4.7 nm and 6.9 nm, respectively, for a wide range of tensions (F < 1.5 nN), pointing to a pore diameter of ~2 nm below which a translocated knotted protein might get stuck. The 4_1-knot length is in agreement with recent AFM pulling experiments. Detailed TPK characteristics however, may be sequence-specific: we find a different size and structural behavior in polyglycines, and, strikingly, a strong hydrogen bonding and water molecule trapping capabi...
Condensates and instanton – torus knot duality. Hidden Physics at UV scale
A. Gorsky
2015-11-01
Full Text Available We establish the duality between the torus knot superpolynomials or the Poincaré polynomials of the Khovanov homology and particular condensates in Ω-deformed 5D supersymmetric QED compactified on a circle with 5d Chern–Simons (CS term. It is explicitly shown that n-instanton contribution to the condensate of the massless flavor in the background of four-observable exactly coincides with the superpolynomial of the T(n,nk+1 torus knot where k is the level of CS term. In contrast to the previously known results, the particular torus knot corresponds not to the partition function of the gauge theory but to the particular instanton contribution and summation over the knots has to be performed in order to obtain the complete answer. The instantons are sitting almost at the top of each other and the physics of the “fat point” where the UV degrees of freedom are slaved with point-like instantons turns out to be quite rich. Also we see knot polynomials in the quantum mechanics on the instanton moduli space. We consider the different limits of this correspondence focusing at their physical interpretation and compare the algebraic structures at the both sides of the correspondence. Using the AGT correspondence, we establish a connection between superpolynomials for unknots and q-deformed DOZZ factors.
Temim, Tea; Dwek, Eli
2013-01-01
Recent far-infrared (IR) observations of supernova remnants (SNRs) have revealed significantly large amounts of newly condensed dust in their ejecta, comparable to the total mass of available refractory elements. The dust masses derived from these observations assume that all the grains of a given species radiate at the same temperature, regardless of the dust heating mechanism or grain radius. In this paper, we derive the dust mass in the ejecta of the Crab Nebula, using a physical model for the heating and radiation from the dust. We adopt a power-law distribution of grain sizes and two different dust compositions (silicates and amorphous carbon), and calculate the heating rate of each dust grain by the radiation from the pulsar wind nebula. We find that the grains attain a continuous range of temperatures, depending on their size and composition. The total mass derived from the best-fit models to the observed IR spectrum is 0.019-0.13 Solar Mass, depending on the assumed grain composition. We find that the power-law size distribution of dust grains is characterized by a power-law index of 3.5-4.0 and a maximum grain size larger than 0.1 micron. The grain sizes and composition are consistent with what is expected for dust grains formed in a Type IIP supernova (SN). Our derived dust mass is at least a factor of two less than the mass reported in previous studies of the Crab Nebula that assumed more simplified two-temperature models. These models also require a larger mass of refractory elements to be locked up in dust than was likely available in the ejecta. The results of this study show that a physical model resulting in a realistic distribution of dust temperatures can constrain the dust properties and affect the derived dust masses. Our study may also have important implications for deriving grain properties and mass estimates in other SNRs and for the ultimate question of whether SNe are major sources of dust in the Galactic interstellar medium and in
Temim, Tea; Dwek, Eli, E-mail: tea.temim@nasa.gov [Observational Cosmology Lab, Code 665, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States)
2013-09-01
Recent far-infrared (IR) observations of supernova remnants (SNRs) have revealed significantly large amounts of newly condensed dust in their ejecta, comparable to the total mass of available refractory elements. The dust masses derived from these observations assume that all the grains of a given species radiate at the same temperature, regardless of the dust heating mechanism or grain radius. In this paper, we derive the dust mass in the ejecta of the Crab Nebula, using a physical model for the heating and radiation from the dust. We adopt a power-law distribution of grain sizes and two different dust compositions (silicates and amorphous carbon), and calculate the heating rate of each dust grain by the radiation from the pulsar wind nebula. We find that the grains attain a continuous range of temperatures, depending on their size and composition. The total mass derived from the best-fit models to the observed IR spectrum is 0.019-0.13 M{sub Sun }, depending on the assumed grain composition. We find that the power-law size distribution of dust grains is characterized by a power-law index of 3.5-4.0 and a maximum grain size larger than 0.1 {mu}m. The grain sizes and composition are consistent with what is expected for dust grains formed in a Type IIP supernova (SN). Our derived dust mass is at least a factor of two less than the mass reported in previous studies of the Crab Nebula that assumed more simplified two-temperature models. These models also require a larger mass of refractory elements to be locked up in dust than was likely available in the ejecta. The results of this study show that a physical model resulting in a realistic distribution of dust temperatures can constrain the dust properties and affect the derived dust masses. Our study may also have important implications for deriving grain properties and mass estimates in other SNRs and for the ultimate question of whether SNe are major sources of dust in the Galactic interstellar medium and in
Hemoglobinopathies: slicing the Gordian knot of Plasmodium falciparum malaria pathogenesis.
Taylor, Steve M; Cerami, Carla; Fairhurst, Rick M
2013-01-01
Plasmodium falciparum malaria kills over 500,000 children every year and has been a scourge of humans for millennia. Owing to the co-evolution of humans and P. falciparum parasites, the human genome is imprinted with polymorphisms that not only confer innate resistance to falciparum malaria, but also cause hemoglobinopathies. These genetic traits--including hemoglobin S (HbS), hemoglobin C (HbC), and α-thalassemia--are the most common monogenic human disorders and can confer remarkable degrees of protection from severe, life-threatening falciparum malaria in African children: the risk is reduced 70% by homozygous HbC and 90% by heterozygous HbS (sickle-cell trait). Importantly, this protection is principally present for severe disease and largely absent for P. falciparum infection, suggesting that these hemoglobinopathies specifically neutralize the parasite's in vivo mechanisms of pathogenesis. These hemoglobin variants thus represent a "natural experiment" to identify the cellular and molecular mechanisms by which P. falciparum produces clinical morbidity, which remain partially obscured due to the complexity of interactions between this parasite and its human host. Multiple lines of evidence support a restriction of parasite growth by various hemoglobinopathies, and recent data suggest this phenomenon may result from host microRNA interference with parasite metabolism. Multiple hemoglobinopathies mitigate the pathogenic potential of parasites by interfering with the export of P. falciparum erythrocyte membrane protein 1 (PfEMP1) to the surface of the host red blood cell. Few studies have investigated their effects upon the activation of the innate and adaptive immune systems, although recent murine studies suggest a role for heme oxygenase-1 in protection. Ultimately, the identification of mechanisms of protection and pathogenesis can inform future therapeutics and preventive measures. Hemoglobinopathies slice the "Gordian knot" of host and parasite
Hemoglobinopathies: slicing the Gordian knot of Plasmodium falciparum malaria pathogenesis.
Steve M Taylor
Full Text Available Plasmodium falciparum malaria kills over 500,000 children every year and has been a scourge of humans for millennia. Owing to the co-evolution of humans and P. falciparum parasites, the human genome is imprinted with polymorphisms that not only confer innate resistance to falciparum malaria, but also cause hemoglobinopathies. These genetic traits--including hemoglobin S (HbS, hemoglobin C (HbC, and α-thalassemia--are the most common monogenic human disorders and can confer remarkable degrees of protection from severe, life-threatening falciparum malaria in African children: the risk is reduced 70% by homozygous HbC and 90% by heterozygous HbS (sickle-cell trait. Importantly, this protection is principally present for severe disease and largely absent for P. falciparum infection, suggesting that these hemoglobinopathies specifically neutralize the parasite's in vivo mechanisms of pathogenesis. These hemoglobin variants thus represent a "natural experiment" to identify the cellular and molecular mechanisms by which P. falciparum produces clinical morbidity, which remain partially obscured due to the complexity of interactions between this parasite and its human host. Multiple lines of evidence support a restriction of parasite growth by various hemoglobinopathies, and recent data suggest this phenomenon may result from host microRNA interference with parasite metabolism. Multiple hemoglobinopathies mitigate the pathogenic potential of parasites by interfering with the export of P. falciparum erythrocyte membrane protein 1 (PfEMP1 to the surface of the host red blood cell. Few studies have investigated their effects upon the activation of the innate and adaptive immune systems, although recent murine studies suggest a role for heme oxygenase-1 in protection. Ultimately, the identification of mechanisms of protection and pathogenesis can inform future therapeutics and preventive measures. Hemoglobinopathies slice the "Gordian knot" of host and
Avian influenza virus antibodies in Pacific Coast Red Knots (Calidris canutus rufa)
Johnson, James A.; DeCicco, Lucas H.; Ruthrauff, Daniel R.; Krauss, Scott; Hall, Jeffrey S.
2014-01-01
Prevalence of avian influenza virus (AIV) antibodies in the western Atlantic subspecies of Red Knot (Calidris canutus rufa) is among the highest for any shorebird. To assess whether the frequency of detection of AIV antibodies is high for the species in general or restricted only to C. c. rufa, we sampled the northeastern Pacific Coast subspecies of Red Knot (Calidris canutus roselaari) breeding in northwestern Alaska. Antibodies were detected in 90% of adults and none of the chicks sampled. Viral shedding was not detected in adults or chicks. These results suggest a predisposition of Red Knots to AIV infection. High antibody titers to subtypes H3 and H4 were detected, whereas low to intermediate antibody levels were found for subtypes H10 and H11. These four subtypes have previously been detected in shorebirds at Delaware Bay (at the border of New Jersey and Delaware) and in waterfowl along the Pacific Coast of North America.
Stability of small-amplitude torus knot solutions of the localized induction approximation
Calini, Annalisa; Ivey, Thomas, E-mail: calinia@cofc.edu [Department of Mathematics, College of Charleston, Charleston, SC 29424 (United States)
2011-08-19
We study the linear stability of small-amplitude torus knot solutions of the localized induction approximation equation for the motion of a thin vortex filament in an ideal fluid. Such solutions can be constructed analytically through the connection with the focusing nonlinear Schroedinger equation using the method of isoperiodic deformations. We show that these (p, q) torus knots are generically linearly unstable for p < q, while we provide examples of neutrally stable (p, q) torus knots with p > q, in contrast with an earlier linear stability study by Ricca (1993 Chaos 3 83-95; 1995 Chaos 5 346; 1995 Small-scale Structures in Three-dimensional Hydro and Magneto-dynamics Turbulence (Lecture Notes in Physics vol 462) (Berlin: Springer)). We also provide an interpretation of the original perturbative calculation in Ricca (1995), and an explanation of the numerical experiments performed by Ricca et al (1999 J. Fluid Mech. 391 29-44), in light of our results.
Knot Invariants and New Weight Systems from General 3D TFTs
Qiu, Jian
2010-01-01
We introduce and study the Wilson loops in a general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the Ward identities of these theories imply that the expectation value of the Wilson loop is a pairing of two dual constructions of (co)cycles of certain extended graph complex (extended from Kontsevich's graph complex to accommodate the Wilson loop). We also prove that there is an isomorphism between the same complex and certain extended Chevalley-Eilenberg complex of Hamiltonian vector fields. This isomorphism allows us to generalize the Lie algebra weight system for knots to weight systems associated with any homological vector field and its representations. As an example we construct knot invariants using holomorphic vector bundle over hyperKahler manifolds.
Knot invariants and new weight systems from general 3D TFTs
Qiu, Jian; Zabzine, Maxim
2012-02-01
We introduce and study the Wilson loops in general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in the Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the Ward identities of these theories imply that the expectation value of the Wilson loop is a pairing of two dual constructions of (co)cycles of certain extended graph complex (extended from Kontsevich's graph complex to accommodate the Wilson loop). We also prove that there is an isomorphism between the same complex and certain extended Chevalley-Eilenberg complex of Hamiltonian vector fields. This isomorphism allows us to generalize the Lie algebra weight system for knots to weight systems associated with any homological vector field and its representations. As an example we construct knot invariants using holomorphic vector bundle over hyperKähler manifolds.
Backbone cyclization of a recombinant cystine-knot peptide by engineered Sortase A.
Stanger, Karen; Maurer, Till; Kaluarachchi, Harini; Coons, Mary; Franke, Yvonne; Hannoush, Rami N
2014-11-28
Cyclotides belong to the family of cyclic cystine-knot peptides and have shown promise as scaffolds for protein engineering and pharmacological modulation of cellular protein activity. Cyclotides are characterized by a cystine-knotted topology and a head-to-tail cyclic polypeptide backbone. While they are primarily produced in plants, cyclotides have also been obtained by chemical synthesis. However, there is still a need for methods to generate cyclotides in high yields to near homogeneity. Here, we report a biomimetic approach which utilizes an engineered version of the enzyme Sortase A to catalyze amide backbone cyclization of the recombinant cyclotide MCoTI-II, thereby allowing the efficient production of active homogenous species in high yields. Our results provide proof of concept for using engineered Sortase A to produce cyclic MCoTI-II and should be generally applicable to generating other cyclic cystine-knot peptides.
Dynamic High-speed Knotting of a Rope by a Manipulator
Yuji Yamakawa
2013-10-01
Full Text Available In this paper we suggest an entirely new strategy for the dexterous manipulation of a linear flexible object, such as rope or a cable, with a high-speed manipulator. We deal with a flexible rope as one example of the linear flexible object. The strategy involves manipulating the object at high-speed. By moving the robot at high-speed, we can assume that the dynamic behaviour of the flexible rope can be obtained by performing algebraic calculations of the high- speed robot motion. Based on this assumption, we derive a dynamic deformation model of the flexible rope and confirm the validity of the proposed model. Then we perform a simulation of dynamic, high-speed knotting based on the proposed model. We also discuss the possibility of forming the knot based on a simple analysis model. Finally, we show experimental results demonstrating dynamic, high-speed knotting with a high-speed manipulator.
A cactus-derived toxin-like cystine knot Peptide with selective antimicrobial activity.
Aboye, Teshome L; Strömstedt, Adam A; Gunasekera, Sunithi; Bruhn, Jan G; El-Seedi, Hesham; Rosengren, K Johan; Göransson, Ulf
2015-05-04
Naturally occurring cystine knot peptides show a wide range of biological activity, and as they have inherent stability they represent potential scaffolds for peptide-based drug design and biomolecular engineering. Here we report the discovery, sequencing, chemical synthesis, three-dimensional solution structure determination and bioactivity of the first cystine knot peptide from Cactaceae (cactus) family: Ep-AMP1 from Echinopsis pachanoi. The structure of Ep-AMP1 (35 amino acids) conforms to that of the inhibitor cystine knot (or knottin) family but represents a novel diverse sequence; its activity was more than 500 times higher against bacterial than against eukaryotic cells. Rapid bactericidal action and liposome leakage implicate membrane permeabilisation as the mechanism of action. Sequence homology places Ec-AMP1 in the plant C6-type of antimicrobial peptides, but the three dimensional structure is highly similar to that of a spider neurotoxin.
"Nara" knot for suturing of cleft lip in children to make removal easy
Obaidullah
2006-01-01
Full Text Available Cleft patients usually go through a lifetime of repeated hospital admissions and multiple procedures. Suture removal at a tender age and on a sensitive area like the lip becomes a challenge for the nursing staff. It is also emotionally demanding on the part of the parents. Hence, in most centres these patients are at least sedated if not anaesthetised. We have been using a simple knot and running prolene material so that undoing of the knot becomes easy and suture removal more or less atraumatic. We would like to share our experience with readers through this article. An analysis of 53 cleft lip repairs has shown that this knot is safe and easily removable.
Suzaku study on the Ejecta of the Supernova Remnant G272.2$-$3.2
Kamitsukasa, Fumiyoshi; Nakajima, Hiroshi; Hayashida, Kiyoshi; Mori, Koji; Katsuda, Satoru; Uchida, Hiroyuki; Tsunemi, Hiroshi
2015-01-01
We report re-analyses of the Suzaku observations of the Galactic supernova remnant (SNR), G272.2$-$3.2, for which the previous studies were limited below 3 keV. With careful data reduction and background subtraction, we discover the K-shell lines of Ar, Ca, and Fe above 3 keV. The X-ray spectrum of G272.2$-$3.2 consists of two components, a low-temperature collisional ionization equilibrium (CIE) plasma ($kT_{\\rm e} \\sim 0.2$ keV) and a high-temperature non-equilibrium ionization (NEI) plasma ($kT_{\\rm e} = 0.6$-$3$ keV). The CIE plasma has solar abundances over the entire area, hence it would originate from the interstellar medium. On the other hand, the abundances of the NEI plasma increase toward the inner region, suggesting the ejecta origin. The line center energy of the Fe K-shell emission ($\\sim 6.4$ keV) suggests that the ejecta are recently heated by the reverse shock, a common feature in Type Ia SNRs.
The effect of ambient pressure on ejecta sheets from free-surface ablation
Marston, J. O.
2016-04-16
We present observations from an experimental study of the ablation of a free liquid surface promoted by a focused laser pulse, causing a rapid discharge of liquid in the form of a very thin conical-shaped sheet. In order to capture the dynamics, we employ a state-of-the-art ultra-high-speed video camera capable of capturing events at (Formula presented.) fps with shutter speeds down to 20 ns, whereby we were able to capture not only the ejecta sheet, but also the shock wave, emerging at speeds of up to 1.75 km/s, which is thus found to be hypersonic (Mach 5). Experiments were performed at a range of ambient pressures in order to study the effect of air drag on the evolution of the sheet, which was always observed to dome over, even at pressures as low as 3.8 kPa. At reduced pressures, the extended sheet evolution led to the formation of interference fringe patterns from which, by comparison with the opening speed of rupture, we were able to determine the ejecta thickness. © 2016, Springer-Verlag Berlin Heidelberg.
Abundance anomalies in metal-poor stars from Population III supernova ejecta hydrodynamics
Sluder, Alan; Safranek-Shrader, Chalence; Milosavljevic, Milos; Bromm, Volker
2015-01-01
We present a simulation of the long-term evolution of a Population III supernova remnant in a cosmological minihalo. Employing passive Lagrangian tracer particles, we investigate how chemical stratification and anisotropy in the explosion can affect the abundances of the first low-mass, metal-enriched stars. We find that reverse shock heating can leave the inner mass shells at entropies too high to cool, leading to carbon-enhancement in the re-collapsing gas. This hydrodynamic selection effect could explain the observed incidence of carbon-enhanced metal-poor (CEMP) stars at low metallicity. We further explore how anisotropic ejecta distributions, recently seen in direct numerical simulations of core-collapse explosions, may translate to abundances in metal-poor stars. We find that some of the observed scatter in the Population II abundance ratios can be explained by an incomplete mixing of supernova ejecta, even in the case of only one contributing enrichment event. We demonstrate that the customary hypothes...
Effects of the Core-collapse Supernova Ejecta Impact on a Rapidly Rotating Massive Companion Star
Zhu, Chunhua; Lü, Guoliang; Wang, Zhaojun
2017-02-01
We investigate the effects of the core-collapse supernova (CCSN) ejecta on a rapidly rotating and massive companion star. We show that the stripped mass is twice as high as that of a massive but nonrotating companion star. In close binaries with orbital periods of about 1 day, the stripped masses reach up to ∼ 1 {M}ȯ . By simulating the evolutions of the rotational velocities of the massive companion stars based on different stripped masses, we find that the rotational velocity decreases greatly for a stripped mass higher than about 1 {M}ȯ . Of all the known high-mass X-ray binaries (HMXBs), Cygnus X-3 and 1WGA J0648.024418 have the shortest orbital periods, 0.2 and 1.55 days, respectively. The optical counterpart of the former is a Wolf-Rayet star, whereas it is a hot subdwarf for the latter. Applying our model to the two HMXBs, we suggest that the hydrogen-rich envelopes of their optical counterparts may have been stripped by CCSN ejecta.
Relativistic ejecta from X-ray flash XRF 060218 and the rate of cosmic explosions.
Soderberg, A M; Kulkarni, S R; Nakar, E; Berger, E; Cameron, P B; Fox, D B; Frail, D; Gal-Yam, A; Sari, R; Cenko, S B; Kasliwal, M; Chevalier, R A; Piran, T; Price, P A; Schmidt, B P; Pooley, G; Moon, D-S; Penprase, B E; Ofek, E; Rau, A; Gehrels, N; Nousek, J A; Burrows, D N; Persson, S E; McCarthy, P J
2006-08-31
Over the past decade, long-duration gamma-ray bursts (GRBs)--including the subclass of X-ray flashes (XRFs)--have been revealed to be a rare variety of type Ibc supernova. Although all these events result from the death of massive stars, the electromagnetic luminosities of GRBs and XRFs exceed those of ordinary type Ibc supernovae by many orders of magnitude. The essential physical process that causes a dying star to produce a GRB or XRF, and not just a supernova, is still unknown. Here we report radio and X-ray observations of XRF 060218 (associated with supernova SN 2006aj), the second-nearest GRB identified until now. We show that this event is a hundred times less energetic but ten times more common than cosmological GRBs. Moreover, it is distinguished from ordinary type Ibc supernovae by the presence of 10(48) erg coupled to mildly relativistic ejecta, along with a central engine (an accretion-fed, rapidly rotating compact source) that produces X-rays for weeks after the explosion. This suggests that the production of relativistic ejecta is the key physical distinction between GRBs or XRFs and ordinary supernovae, while the nature of the central engine (black hole or magnetar) may distinguish typical bursts from low-luminosity, spherical events like XRF 060218.
Shared origin for seven of Mars Trojans - impact ejecta from Mars?
Polishook, David; Jacobson, Seth A.; Aharonson, Oded
2016-10-01
Seven out of nine Mars Trojans belong to an orbital grouping that started to spread about 109 years ago (Cuk et al. 2015). We spectrally observed two of them (311999 and 385250) using the IRTF telescope and found that both present an identical olivine-rich reflectance spectrum, that is similar to the reflectance spectrum of (5261) Eureka, the largest of these seven Trojans (Rivkin et al. 2007). These measurements confirm the shared origin of the seven. Moreover, olivine-rich reflectance spectra is rare within asteroids, but is visible in numerous locations on Mars and is found within SNC meteorites that are argued to originate from Mars (Chassigny, ALHA77005; McSween 1985). This spectral resemblance encourages us to suggest that the seven Trojans are impact ejecta from Mars' plutonic rock. We will present dynamical calculations showing how the impact ejecta could have been caught in L5 and that there are enough size-relevant craters on Mars surface to produce these seven Trojans.
Notice of Release of ‘Truhart-NR’, a Root-knot Nematode Resistant, Pimento-type Pepper
The USDA has developed a high-yielding, pimento-type pepper (Capsicum annuum L.) cultivar that is highly resistant to root-knot nematodes. The new cultivar, Truhart-NR, is homozygous for the dominant N gene that conditions a high level of resistance to the southern root-knot nematode [Meloidogyne i...
WHY KNOT CALIDRIS-CANUTUS TAKE MEDIUM-SIZED MACOMA-BALTHICA WHEN 6 PREY SPECIES ARE AVAILABLE
ZWARTS, L; BLOMERT, AM
We quantified the prey selection and intake rate of a wading bird, knot Calidris canutus, when 6 different, intertidal prey species, the mud snail Peringia ulvae and the bivalves Macoma balthica, Cerastoderma edule, Mya arenaria, Scrobicularia plana and Mytilus edulis, were abundant. Knot usually
Gonzalez, PM; Piersma, T; Verkuil, Y; González, Patricia M.
1996-01-01
We studied the food and feeding ecology of Red Knots Calidris canutus rufa on an area of rocky flat, or restinga, near San Antonio Oeste in the northwest of Golfo San Matias, Provincia de Rio Negro, Argentina in March 1992. These Red Knots are on their way north, from ''wintering'' areas in Tierra d
WHY KNOT CALIDRIS-CANUTUS TAKE MEDIUM-SIZED MACOMA-BALTHICA WHEN 6 PREY SPECIES ARE AVAILABLE
ZWARTS, L; BLOMERT, AM
1992-01-01
We quantified the prey selection and intake rate of a wading bird, knot Calidris canutus, when 6 different, intertidal prey species, the mud snail Peringia ulvae and the bivalves Macoma balthica, Cerastoderma edule, Mya arenaria, Scrobicularia plana and Mytilus edulis, were abundant. Knot usually se
IS THE EVAPORATIVE WATER-LOSS OF KNOT CALIDRIS-CANUTUS HIGHER IN TROPICAL THAN IN TEMPERATE CLIMATES
VERBOVEN, N; PIERSMA, T
1995-01-01
To test whether Knot Calidris canutus wintering in the tropics suffer higher rates of water loss through evaporation than do Knot wintering at temperate latitudes, we tried to develop a physically realistic model to predict evaporative heat loss from air temperature, wind and humidity. In separate e
Leyrer, J.
2011-01-01
This thesis describes the possible selection pressures acting on survival and, indirectly, on reproduction of Afro-Siberian red knots Calidris canutus canutus while wintering and migrating. Afro-Siberian red knots are long-distance migrants. They travel between the West African wintering areas and t
Barnes, Jennifer; Wu, Meng-Ru; Mart'inez-Pinedo, Gabriel
2016-01-01
One of the most promising electromagnetic signatures of compact object mergers are kilonovae: approximately isotropic radioactively-powered transients that peak days to weeks post-merger. Key uncertainties in modeling kilonovae include the emission profiles of the radioactive decay products---non-thermal beta- and alpha-particles, fission fragments, and gamma-rays---and the efficiency with which they deposit their energy in the ejecta. The total radioactive energy and the efficiency of its thermalization sets the luminosity budget and is therefore necessary for predicting kilonova light curves. We outline the uncertainties in r-process decay, describe the physical processes by which the energy of the decay products is absorbed in the ejecta, and present time-dependent thermalization efficiencies for each particle type. We determine the net heating efficiency and explore its dependence on r-process yields---in particular, the production of translead nuclei that undergo alpha-decay---and on the ejecta's mass, v...
Grant, J. A.; Schultz, P. H.
1991-01-01
Previous ground penetrating radar (GRP) studies around 50,000 year old Meteor Crater revealed the potential for rapid, inexpensive, and non-destructive sub-surface investigations for deep reflectors (generally greater than 10 m). New GRP results are summarized focusing the shallow sub-surfaces (1-2 m) around Meteor Crater and the main crater at Odessa. The following subject areas are covered: (1) the thickness, distribution, and nature of the contact between surrounding alluvial deposits and distal ejecta; and (2) stratigraphic relationships between both the ejecta and alluvium derived from both pre and post crater drainages. These results support previous conclusions indicating limited vertical lowering (less than 1 m) of the distal ejecta at Meteor Crater and allow initial assessment of the gradational state if the Odessa craters.
Shore, Steven N
2013-01-01
There is increasing evidence that the geometry, and not only the filling factors, of nova ejecta is important in the interpretation of their spectral and photometric developments. Ensembles of spectra and light curves have provided general typographies. This Letter suggests how these can be unified.The observed spread in the maximum magnitude - rate of decline (MMRD) relation is argued to result from the range of opening angles and inclination of the ejecta, and not only to their masses and velocities. The spectroscopic classes can be similarly explained and linked to the behavior of the light curves. The secondary maximum observed in some dust forming novae is a natural consequence of the asphericity. Neither secondary ejections nor winds are needed to explain the phenomenology. The spectrophotometric development of classical novae can be understood within a single phenomenological model with bipolar, although not jet-like, mass ejecta. High resolution spectropolarimetry will be an essential analytical tool.
McGowan, Conor P.; Hines, James E.; Nichols, James D.; Lyons, James E.; Smith, David; Kalasz, Kevin S.; Niles, Lawrence J.; Dey, Amanda D.; Clark, Nigel A.; Atkinson, Philip W.; Minton, Clive D.T.; Kendall, William
2011-01-01
Understanding how events during one period of the annual cycle carry over to affect survival and other fitness components in other periods is essential to understanding migratory bird demography and conservation needs. Previous research has suggested that western Atlantic red knot (Calidris canutus rufa) populations are greatly affected by horseshoe crab (Limulus polyphemus) egg availability at Delaware Bay stopover sites during their spring northward migration. We present a mass-based multistate, capturerecapture/resighting model linking (1) red knot stopover mass gain to horseshoe crab spawning abundance and (2) subsequent apparent annual survival to mass state at the time of departure from the Delaware Bay stopover area. The model and analysis use capture-recapture/resighting data with over 16,000 individual captures and 13,000 resightings collected in Delaware Bay over a 12 year period from 1997–2008, and the results are used to evaluate the central management hypothesis that red knot populations can be influenced by horseshoe crab harvest regulations as part of a larger adaptive management effort. Model selection statistics showed support for a positive relationship between horseshoe crab spawning abundance during the stopover and the probability of red knots gaining mass (parameter coefficient from the top model b = 1.71, SE = 0.46). Our analyses also supported the link between red knot mass and apparent annual survival, although average estimates for the two mass classes differed only slightly. The addition of arctic snow depth as a covariate influencing apparent survival improved the fit of the data to the models (parameter coefficient from the top model b = 0.50, SE = 0.08). Our results indicate that managing horseshoe crab resources in the Delaware Bay has the potential to improve red knot population status.
Boehner, P.; Plewa, T.; Langer, N.
2017-02-01
We study supernova ejecta-companion interactions in a sample of realistic semidetached binary systems representative of Type Ia supernova progenitor binaries in a single-degenerate scenario. We model the interaction process with the help of a high-resolution hydrodynamic code assuming cylindrical symmetry. We find that the ejecta hole has a half-opening angle of 40-50° with the density by a factor of 2-4 lower, in good agreement with the previous studies. Quantitative differences from the past results in the amounts and kinematics of the stripped companion material and levels of contamination of the companion with the ejecta material can be explained by different model assumptions and effects due to numerical diffusion. We analyse and, for the first time, provide simulation-based estimates of the amounts and of the thermal characteristics of the shock-heated material responsible for producing a prompt, soft X-ray emission. Besides the shocked ejecta material, considered in the original model by Kasen, we also account for the stripped, shock-heated envelope material of stellar companions, which we predict partially contributes to the prompt emission. The amount of the energy deposited in the envelope is comparable to the energy stored in the ejecta. The total energy budget available for the prompt emission is by a factor of about 2-4 smaller than originally predicted by Kasen. Although the shocked envelope has a higher characteristic temperature than the shocked ejecta, the temperature estimates of the shocked material are in good agreement with the Kasen's model. The hottest shocked plasma is produced in the subgiant companion case.
Yu, Yang; Michel, Patrick; Schwartz, Stephen R.; Naidu, Shantanu P.; Benner, Lance A. M.
2017-01-01
An understanding of the post-impact dynamics of ejecta clouds are crucial to the planning of a kinetic impact mission to an asteroid, and also has great implications for the history of planetary formation. The purpose of this article is to track the evolution of ejecta produced by AIDA mission, which targets for kinetic impact the secondary of near-Earth binary asteroid (65803) Didymos on 2022, and to feedback essential informations to AIDA's ongoing phase-A study. We present a detailed dynamic model for the simulation of an ejecta cloud from a binary asteroid that synthesizes all relevant forces based on a previous analysis of the mechanical environment. We apply our method to gain insight into the expected response of Didymos to the AIDA impact, including the subsequent evolution of debris and dust. The crater scaling relations from laboratory experiments are employed to approximate the distributions of ejecta mass and launching speed. The size distribution of fragments is modeled with a power law fitted from observations of real asteroid surface. A full-scale demonstration is simulated using parameters specified by the mission. We report the results of the simulation, which include the computed spread of the ejecta cloud and the recorded history of ejecta accretion and escape. The violent period of the ejecta evolution is found to be short, and is followed by a stage where the remaining ejecta is gradually cleared. Solar radiation pressure proves to be efficient in cleaning dust-size ejecta, and the simulation results after two weeks shows that large debris on polar orbits (perpendicular to the binary orbital plane) has a survival advantage over smaller ejecta and ejecta that keeps to low latitudes.
Appendico-ileal knotting resulting in closed-loop obstruction in a child
Yang, Albert D. [Department of Radiology, Changhua Christian Hospital, 135 Nan Siau Street, Changhua, Taiwan 50050 (Taiwan); Lee, Chien-Hsing [Department of Paediatric Surgery, Changhua Christian Hospital, Taiwan (Taiwan)
2002-12-01
A 1-year 7-month-old boy presented with sudden onset of severe vomiting and abdominal pain. Barium enema revealed the caecum was elevated by a mass and the ileocaecal junction was visualised with a very short segment of terminal ileum showing a 'bird's-beak' appearance. At surgery, an unusually long necrotic appendix knotting the terminal ileum resulted in strangulation of a segment of the terminal ileum. There was no evidence of torsion of the terminal ileum or appendix. To our knowledge, this is the first case of the appendix knotting the terminal ileum resulting in a strangulated closed-loop obstruction. (orig.)
Asymptotics of the quantum invariants for surgeries on the figure 8 knot
Andersen, Jørgen Ellegaard; Hansen, Søren Kold
2006-01-01
We investigate the Reshetikhin–Turaev invariants associated to SU(2) for the 3-manifolds M obtained by doing any rational surgery along the figure 8 knot. In particular, we express these invariants in terms of certain complex double contour integrals. These integral formulae allow us to propose a....... Moreover, we calculate the leading asymptotics of the colored Jones polynomial of the figure 8 knot following R.Kashaev. This leads to a slightly finer asymptotic description of the invariant than predicted by the volume conjecture due to R.Kashaev, H.Murakami and J.Murakami....
Lodha, Abhay; Ly, Linh; McNamara, Patrick J. [Hospital for Sick Children, Division of Neonatology, Toronto (Canada); Brindle, Mary [Hospital for Sick Children, Department of Surgery, Toronto (Canada); Daneman, Alan [Hospital for Sick Children, Department of Radiology, Toronto (Canada)
2005-07-01
We report a case where a knot developed in a urinary catheter and became lodged within the urethra of a very-low-birth-weight (VLBW) preterm infant. The catheter was removed with the assistance of a urologist. We recommend using caution when placing urinary catheters in VLBW infants and question the appropriateness of feeding tubes as catheters. Recognition on radiographs of malpositioned bladder catheters is vital to the care of these patients. All staff involved in the insertion, maintenance or removal of these catheters should be suitably trained to minimize the risk of knots and related complications. (orig.)
Potential of tissue culture for breeding root-knot nematode resistance into vegetables.
Fassuliotis, G; Bhatt, D P
1982-01-01
Plant protoplast technology is being investigated as a means of transferring root-knot nematode resistance factors from Solanum sisymbriifolium into the susceptible S. melongena. Solanum sisymbriifolium plants regenerated from callus lost resistance to Meloidogyne javanica but retained resistance to M. incognita. Tomato plants cloned from leaf discs of the root-knot nematode resistant 'Patriot' were completely susceptible to M. incognita, while sections of stems and leaves rooted in sand in the absence of growth hormones retained resistance. Changes in resistance persisted for three generations. It is postulated that the exogenous hormonal constituents of the culture medium are modifying the expression of genetic resistance.
Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors
Bartoň, Michael
2017-03-21
We provide explicit quadrature rules for spaces of C1C1 quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. Each rule is optimal, that is, requires the minimal number of nodes, for a given function space. For each of nn subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/32/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as nn grows, to the “two-third” quadrature rule of Hughes et al. (2010) for infinite domains.
Modelling H2 Infrared Emission of the Helix Nebula Cometary Knots
Aleman, Isabel; Matsuura, Mikako; Gruenwald, Ruth; Kimura, Rafael
2010-01-01
In the present work, we use a photoionisation code to study the H2 emission of the Helix nebula (NGC 7293) cometary knots, particularly that produced in the interface H+/H0 of the knot, where a significant fraction of the H2 1-0 S(1) emission seems to be produced. Our results show that the production of molecular hydrogen in such region may explain several characteristics of the observed emission, particularly the high excitation temperature of the H2 infrared lines.
"Knot Stent": An Unusual Cause of Acute Renal Failure in Solitary Kidney
Kamal Moufid
2012-01-01
Full Text Available The insertion of indwelling ureteric stents is a routine procedure in urology practice. Complications secondary to the insertion of these stents have also increased, such as stent encrustation, stent fragmentation, stone formation, and recurrent urinary tract infections. Knot formation within the renal pelvis or in the coiled portion of the ureteral stent is an extremely rare condition, with less than 15 cases reported in literature. The authors report a rare case of knotted stent, complicated by an obstructive acute renal failure and urosepsis, in a patient with a solitary functioning kidney.
Quantum invariants a study of knots, 3-manifolds, and their sets
Ohtsuki, Tomotada
2002-01-01
This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of
2010-01-01
... light-sport aircraft that has a VH greater than 87 knots CAS? 61.327 Section 61.327 Aeronautics and... operate a light-sport aircraft that has a VH greater than 87 knots CAS? If you hold a sport pilot certificate and you seek to operate a light-sport aircraft that has a VH greater than 87 knots CAS you...
Fahnestock, Eugene G.; Yu, Yang; Hamilton, Douglas P.; Schwartz, Stephen; Stickle, Angela; Miller, Paul L.; Cheng, Andy F.; Michel, Patrick; AIDA Impact Simulation Working Group
2016-10-01
The proposed Asteroid Impact Deflection and Assessment (AIDA) mission includes NASA's Double Asteroid Redirection Test (DART), whose impact with the secondary of near-Earth binary asteroid 65803 Didymos is expected to liberate large amounts of ejecta. We present efforts within the AIDA Impact Simulation Working Group to comprehensively simulate the behavior of this impact ejecta as it moves through and exits the system. Group members at JPL, OCA, and UMD have been working largely independently, developing their own strategies and methodologies. Ejecta initial conditions may be imported from output of hydrocode impact simulations or generated from crater scaling laws derived from point-source explosion models. We started with the latter approach, using reasonable assumptions for the secondary's density, porosity, surface cohesive strength, and vanishingly small net gravitational/rotational surface acceleration. We adopted DART's planned size, mass, closing velocity, and impact geometry for the cratering event. Using independent N-Body codes, we performed Monte Carlo integration of ejecta particles sampled over reasonable particle size ranges, and over launch locations within the crater footprint. In some cases we scaled the number of integrated particles in various size bins to the estimated number of particles consistent with a realistic size-frequency distribution. Dynamical models used for the particle integration varied, but all included full gravity potential of both primary and secondary, the solar tide, and solar radiation pressure (accounting for shadowing). We present results for the proportions of ejecta reaching ultimate fates of escape, return impact on the secondary, and transfer impact onto the primary. We also present the time history of reaching those outcomes, i.e., ejecta clearing timescales, and the size-frequency distribution of remaining ejecta at given post-impact durations. We find large numbers of particles remain in the system for several
Eichelberger, H. U.; Prattes, G.; Schwingenschuh, K.; Wolbang, D.; Boudjada, M. Y.; Rozhnoi, A.; Solovieva, M.; Biagi, P. F.; Maggipinto, T.; Stachel, M.; Jernej, I.; Aydogar, Ö.; Besser, B. P.
2012-04-01
In the frame of the European VLF/LF radio receiver network (International Network for Frontier Research on Earthquake Precursors - INFREP) we investigate radio paths between several transmitters and receivers, among them the Graz VLF facility. For this knot the data coverage spans more than two years of continuous samples from 11 transmitters with a network wide 20 seconds temporal resolution. The main scientific objective is the characterisation of VLF fluctuations in amplitude and phase related with artificial and natural sources, e.g. disturbances due to seismic phenomena. Examples of VLF disturbances due to seismic activity are given by Rozhnoi et al. (2009) and complementary investigations are carried out by Prattes et al. (2011). For VLF usually the (i) nighttime amplitude variations and (ii) terminator time methods are used. They have been regularly applied in data analysis of seismic events mainly in Asian area. Paths crossing the earthquake preparation zone and control links are used for earthquake events. Various VLF waveguide properties are important, e.g. the length of the individual paths, the lower lithospheric-surface boundary and the upper {day, night}-time ionospheric {D, E}-layer physics. Beside the nominal diurnal and seasonal behaviour we are measuring natural variations, e.g. solar flare effects and manmade noise, i.e. local disturbances related with the urban environment of the receiver location. Measurements indicate that above a threshold of magnitude M 5 the methods are successful applicable. We show for a time span of more than two years how VLF fluctuations and their seasonal variations relate with atmospheric parameters, e.g. temperatures, zonal wind, and heat- and momentum-fluxes and discuss the impact on seismic event detection via VLF methods. Complementary ground- and satellite-based investigations, e.g. in nearby ULF or LF frequency ranges, are useful.
Vajda, Vivi; Ocampo, Adriana; Ferrow, Embaie
2015-01-01
Life on Earth was sharply disrupted 66 Ma ago as an asteroid hit the sea-floor in what is today Yucatan Peninsula, Mexico. Approximately 600 km3 of sedimentary rock were vapourized, ejected into the atmosphere and subsequently deposited globally as an ejecta apron and fallout layer. Proximal ejecta...
The role of ejecta in the small crater populations on the mid-sized saturnian satellites
Bierhaus, Edward B.; Dones, Luke; Alvarellos, José Luis; Zahnle, Kevin
2012-03-01
We find evidence, by both observation and analysis, that primary crater ejecta play an important role in the small crater (less than a few km) populations on the saturnian satellites, and more broadly, on cratered surfaces throughout the Solar System. We measure crater populations in Cassini images of Enceladus, Rhea, and Mimas, focusing on image data with scales less than 500 m/pixel. We use recent updates to crater scaling laws and their constants (Housen, K.R., Holsapple, K.A. [2011]. Icarus 211, 856-875) to estimate the amount of mass ejected in three different velocity ranges: (i) greater than escape velocity, (ii) less than escape velocity and faster than the minimum velocity required to make a secondary crater (vmin), and (iii) velocities less than vmin. Although the vast majority of mass on each satellite is ejected at speeds less than vmin, our calculations demonstrate that the differences in mass available in the other two categories should lead to observable differences in the small crater populations; the predictions are borne out by the measurements we have made to date. In particular, Rhea, Tethys, and Dione have sufficient surface gravities to retain ejecta moving fast enough to make secondary crater populations. The smaller satellites, such as Enceladus but especially Mimas, are expected to have little or no traditional secondary populations because their escape velocities are near the threshold velocity necessary to make a secondary crater. Our work clarifies why the Galilean satellites have extensive secondary crater populations relative to the saturnian satellites. The presence, extent, and sizes of sesquinary craters (craters formed by ejecta that escape into temporary orbits around Saturn before re-impacting the surface, see Dobrovolskis, A.R., Lissauer, J.J. [2004]. Icarus 169, 462-473; Alvarellos, J.L., Zahnle, K.J., Dobrovolskis, A.R., Hamill, P. [2005]. Icarus 178, 104-123; Zahnle, K., Alvarellos, J.L., Dobrovolskis, A.R., Hamill, P. [2008
Rootstock assessment for root-knot nematode management in grafted honeydew melon
Root-knot nematodes (RKN) are one of the most damaging soilborne pathogens of honeydew melon (Cucumis melo var. inodorus). Currently their management is dependent on soil fumigation. Vegetable grafting with resistant rootstocks may be an effective approach for RKN management in the sustainable produ...
‘Truhart-NR’, A Root-knot Nematode Resistant, Pimento-type Pepper
Efforts to develop a high-yielding, pimento-type pepper (Capsicum annuum L.) cultivar that is highly resistant to root-knot nematodes were completed with the official release of Truhart-NR on October 20, 2009. The new cultivar is homozygous for the dominant N gene that conditions a high level of re...
The southern root-knot nematode, Meloidogyne incognita, and Phytophthora capsici, the causal agent of Phytophthora blight, are both important pathogens of pepper (Capsicum annuum L.) in the U.S. and worldwide. Although there is significant information in the literature about the responses of pepper...
Truhart-NR, A Root-knot Nematode Resistant, Pimento-type Pepper Cultivar
Efforts to develop a high-yielding, pimento-type pepper (Capsicum annuum L.) cultivar that is highly resistant to root-knot nematodes were completed with the official release of Truhart-NR on October 20, 2009. The new cultivar is homozygous for the dominant N gene that conditions a high level of re...
Karssen, G.; Van Aelst, A.; Van der Putten, W.H.
1998-01-01
A root-knot nematode, Meloidogyne duytsi n. sp., is described and illustrated from Elymus farctus (Viv.) Melderis from Dutch coastal foredunes. This new species is characterized by the following characters: female with styler slightly curved dorsally, 13.3 mu m long, with large transversely ovoid kn
Southern root-knot nematode (RKN), Meloidogyne incognita, is an important re-emerging pest of watermelon. Several factors have contributed to re-emergence of RKN including: 1) ban of methyl bromide for soil fumigation; 2) reduced land area for crop rotation; and 3) continuous cropping of cucurbits u...
On the implications of recent observations of the inner knot in the Crab nebula
Yuan, Yajie; Blandford, Roger D.
2015-12-01
Recent observations of the Crab nebula (Rudy et al.) have maintained its reputation for high-energy astrophysical enlightenment and its use as a test-bed for theories of the behaviour of magnetized, relativistic plasma. In particular, new observations of the inner knot located 0.65 arcsec SE from the pulsar confirm that it is compact, elongated transversely to the symmetry axis and curved concave towards the pulsar. 60 per cent polarization has been measured along the symmetry axis (Moran et al.). The knot does not appear to be involved in the gamma-ray flares. The new observations both reinforce the interpretation of the knot as dissipation of the pulsar wind at a strong shock and challenge the details of existing models of this process. In particular, it is argued that the compactness, high polarization, and curvature are difficult to reconcile with simple relativistic shock models. Alternative possibilities include deflection of the outflow ahead of the shock and spatial variation in which the knot is interpreted as a caustic. Some future observations are proposed and new theoretical investigations are suggested.
On the Implications of Recent Observations of the Inner Knot in the Crab Nebula
Yuan, Yajie
2015-01-01
Recent observations of the Crab Nebula (Rudy et al 2015) have maintained its reputation for high energy astrophysical enlightenment and its use as a testbed for theories of the behaviour of magnetized, relativistic plasma. In particular, new observations of the inner knot located 0.65'' SE from the pulsar confirm that it is compact, elongated transversely to the symmetry axis and curved concave towards the pulsar. 60 percent polarization has been measured along the symmetry axis (Moran et al 2013). The knot does not appear to be involved in the gamma ray flares. The new observations both reinforce the interpretation of the knot as dissipation of the pulsar wind at a strong shock and challenge the details of existing models of this process. In particular, it is argued that the compactness, high polarization and curvature are difficult to reconcile with simple relativistic shock models. Alternative possibilities include deflection of the outflow ahead of the shock and spatial variation in which the knot is inte...
Knot Optimization for Biharmonic B-splines on Manifold Triangle Meshes.
Hou, Fei; He, Ying; Qin, Hong; Hao, Aimin
2017-09-01
Biharmonic B-splines, proposed by Feng and Warren, are an elegant generalization of univariate B-splines to planar and curved domains with fully irregular knot configuration. Despite the theoretic breakthrough, certain technical difficulties are imperative, including the necessity of Voronoi tessellation, the lack of analytical formulation of bases on general manifolds, expensive basis re-computation during knot refinement/removal, being applicable for simple domains only (e.g., such as euclidean planes, spherical and cylindrical domains, and tori). To ameliorate, this paper articulates a new biharmonic B-spline computing paradigm with a simple formulation. We prove that biharmonic B-splines have an equivalent representation, which is solely based on a linear combination of Green's functions of the bi-Laplacian operator. Consequently, without explicitly computing their bases, biharmonic B-splines can bypass the Voronoi partitioning and the discretization of bi-Laplacian, enable the computational utilities on any compact 2-manifold. The new representation also facilitates optimization-driven knot selection for constructing biharmonic B-splines on manifold triangle meshes. We develop algorithms for spline evaluation, data interpolation and hierarchical data decomposition. Our results demonstrate that biharmonic B-splines, as a new type of spline functions with theoretic and application appeal, afford progressive update of fully irregular knots, free of singularity, without the need of explicit parameterization, making it ideal for a host of graphics tasks on manifolds.
Population divergence times and historical demography in red knots and dunlins
Buehler, DM; Baker, AJ
2005-01-01
We employed Bayesian coalescent modeling of samples of mitochondrial control region sequences in two species of shorebird, Red Knots (Calidris canutus) and Durdins (Calidris alpina) to estimate evolutionary effective population size, population divergence times, and time to most recent common ancest
A knotted1-like homeobox protein regulates abscission in tomato by modulating the auxin pathway
KD1, a gene encoding a KNOTTED1-LIKE HOMEOBOX transcription factor is known to be involved, in tomato, in ontogeny of the compound leaf. KD1 is also highly expressed in both leaf and flower abscission zones. Reducing abundance of transcripts of this gene in tomato, using both virus induced gene sile...
Redirection of auxin flow in Arabidopsis thaliana roots after infection by root-knot nematodes
Kyndt, Tina; Goverse, Aska; Haegeman, Annelies; Warmerdam, Sonja; Wanjau, Cecilia; Jahani, Mona; Engler, Gilbert; Almeida Engler, De Janice; Gheysen, Godelieve
2016-01-01
Plant-parasitic root-knot nematodes induce the formation of giant cells within the plant root, and it has been recognized that auxin accumulates in these feeding sites. Here, we studied the role of the auxin transport system governed by AUX1/LAX3 influx proteins and different PIN efflux proteins dur
Unusual patterns in 15N blood values after a diet switch in red knot shorebirds
Dietz, M.W.; Piersma, T.; Dekinga, A.; Korthals, H.; Klaassen, M.
2013-01-01
When a diet switch results in a change in dietary isotopic values, isotope ratios of the consumer's tissues will change until a new equilibrium is reached. This change is generally best described by an exponential decay curve. Indeed, after a diet switch in captive red knot shorebirds (Calidris
Knots in $SU\\left(M|N\\right) $ Chern-Simons Field Theory
Liu, Xin
2010-01-01
Knots in the Chern-Simons field theory with Lie super gauge group $SU\\left(M|N\\right) $ are studied, and the $% S_{L}\\left(\\alpha,\\beta,z\\right) $ polynomial invariant with skein relations are obtained under the fundamental representation of $\\mathfrak{su}\\left(M|N\\right) $.
Trapping of root-knot nematodes by the adhesive hyphae-forming fungus Arthrobotrys oligospora.
den Belder, E.
1994-01-01
The present study addresses the ecology of a particular isolate of Arthrobotrys oligospora (CBS 289.82) in relation to its efficacy in controlling the root-knot nematode, Meloidogyne hapla.This isolate was selected because it differs from most nematode-trapping fungi in that it captures nematodes wi
Endogenous circannual rhythmicity in a non-passerine migrant, the Knot Calidris canutus
Cadée, Niels; Piersma, Theunis; Daan, Serge
1996-01-01
We present experimental evidence for endogenous control of circannual rhythms in a long-distance migratory wader, the Knot Calidris canutus. Six individuals of the subspecies canutus were caught during northward migration whilst staging in France, and were held together under constant temperature an
Basal metabolic rate declines during long-distance migratory flight in great knots
Battley, PF; Dekinga, A; Dietz, MW; Piersma, T; Tang, SX; Hulsman, K; Battley, Phil F.; Tang, Sixian
2001-01-01
Great Knots (Calidris tenuirostris) make one of the longest migratory flights in the avian world, flying almost 5500 km from Australia to China during northward migration. We measured basal metabolic rate (BMR) and body composition in birds before and after this flight and found that BMR decreased 4
Eliasen, Rasmus; Andresen, Thomas L.; Conde-Frieboes, Kilian W.
2012-01-01
Gurmarin is a 35 amino acid peptide with three disulfide bridges in an inhibitor cystine knot. It is found in the plant Gymnema sylvestre, and has been identified as a sweet taste inhibitor in rodents. In this article we provide an efficient route for the synthesis of gurmarin by a controlled...
First report of the root-knot nematode Meloidogyne minor on turfgrass in Belgium
Viaene, N.; Wiseborn, D.B.; Karssen, G.
2007-01-01
The root-knot nematode, Meloidogyne minor, was described during 2004 after it was found on potato roots in a field in the Netherlands and in golf courses in England, Wales, and Ireland (2). Since it is associated with yellow patch disease in turf grass and causes deformation of potato tubers (2), it