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Sample records for moessbauer recoilless fraction

  1. Recoilless fractions calculated with the nearest-neighbour interaction model by Kagan and Maslow

    NASA Astrophysics Data System (ADS)

    Kemerink, G. J.; Pleiter, F.

    1986-08-01

    The recoilless fraction is calculated for a number of Mössbauer atoms that are natural constituents of HfC, TaC, NdSb, FeO, NiO, EuO, EuS, EuSe, EuTe, SnTe, PbTe and CsF. The calculations are based on a model developed by Kagan and Maslow for binary compounds with rocksalt structure. With the exception of SnTe and, to a lesser extent, PbTe, the results are in reasonable agreement with the available experimental data and values derived from other models.

  2. Anomalous Moessbauer Fraction in Superparamagnetic Systems.

    NASA Astrophysics Data System (ADS)

    Mohie-Eldin, Mohie-Eldin Yehia

    The biological molecule ferritin and its proven synthetic counterpart polysaccharide iron complex (P.I.C.) have been shown to contain small (<100 ^circ in diameter) antiferromagnetic cores at their centers. Mossbauer studies of these molecules have revealed an anomalous drop in the Mossbauer fraction (f-factor) as the temperature rises above 30^ circK for mammalian ferritin and 60 ^circK for P.I.C. Above the blocking temperature, superparamagnetic relaxation results in the disappearance of hyperfine splitting. This thesis investigates and attempts to resolve this Lamb-Mossbauer f-Factor anomaly in these superparamagnetically relaxing systems. Chapter I deals with a basic review of theories of Mossbauer spectroscopy and superparamagnetism. The analogies in the composition of the two molecules is examined in Chapter II. The long range order technique of magnetization measurements is used in Chapter III to compare magnetic properties of both molecules and to verify the suggestion that the P.I.C. molecule is a good "biomimic" to ferritin based on the identification of ferrihydrite as the major mineral in both, by short range probing techniques such as X-ray diffraction. The anomaly is confirmed in P.I.C.'s Mossbauer spectra in Chapter IV. Different absorbers are used to experimentally investigate the absorber thickness effect on the Mossbauer spectra. The anomaly persists for thin absorbers. Also in Chapter V, data that is treated with FFT procedures to eliminate the thickness effect still exhibit this anomaly. We then investigated the effect of superparamagnetic relaxation on the f-factor. In Chapter VI, spin-lattice relaxation was excluded based upon a calculation of the rate of energy transfer from the spin system to the lattice. We introduce a theory in Chapter VII based on the following process as a plausible explanation of the anomaly: Superparamagnetic relaxation brings about a dynamical displacement of the Mossbauer nucleus through magnetostriction. These

  3. Interior Ballistics of Recoilless Guns

    DTIC Science & Technology

    1943-09-08

    PROCEDURE 14. Calculation of pressure -travel and velocity-travel curves ........................................... 17 PART IV. CHAPACTERISTICS OF...of a recoilless gun .............. 2 2. Comparison betw,:een pressure -travel curve calculated by the methods of this report and that obtained by...numerical integration ............................. 23 3. Theoretical pressure -travel and velocity-travel curves for the German 7.5-cm Leichtes Geschltz

  4. Crystallization behavior and recoilless fraction determination of amorphous and nanocrystalline Fe56 Co24 Nb4 B13 Si2 Cu1 system

    NASA Astrophysics Data System (ADS)

    Sorescu, Monica; Limongelli, Julia; Stroh, Christopher; Byerly, Kevin

    2015-03-01

    Amorphous ferromagnetic alloy with the composition Fe56Co24Nb4B13Si2Cu1 was obtained by rapid quenching from the melt. Samples cut from the ribbons were annealed at 450, 550, 650 and 750 C in a vacuum furnace. 57Fe Mossbauer spectroscopy was used to identify the phases formed based on the refined values of the hyperfine parameters. The as-quenched specimen was analyzed with a hyperfine magnetic field distribution and corresponded to an in-plane orientation of the magnetic moment directions. The sample annealed at 450 C was found to be in a nanocrystalline state due to observation of the (FeCo)-Si alloy with the DO3 structure. The balance of the composition was represented by a metalloid-enriched amorphous grain boundary phase. In contradistinction to this, the samples annealed at 550-750 C were totally crystallized, but the new phases formed were alpha-(FeCo), (FeCo)2(BSi) and (FeCo)3(BSi). The f factor value dropped from 0.6 to 0.37 for the sample annealed at 450 C, consistent with the onset of nanocrystallization in the system. For the completely crystallized specimens, the f factor maintained values close to 0.5. This indicates that the presence of quenched-in stresses may play a role in the ability of samples to undergo recoilless emission and absorption of gamma rays. NSF-DMR-0854794.

  5. Investigation into the fabrication of a composite top attack recoilless rifle

    NASA Technical Reports Server (NTRS)

    Miner, Kevin R.

    1990-01-01

    The fabrication of a lightweight, expendable recoilless rifle using composite materials was investigated. Filament winding and braiding were successfully employed in the construction of several of these shoulder-fired weapons.

  6. Mark of the Moessbauer

    NASA Technical Reports Server (NTRS)

    2004-01-01

    This image, taken by an instrument called the microscopic imager on the Mars Exploration Rover Spirit, reveals an imprint left by another instrument, the Moessbauer spectrometer. The imprint is at a location within the rover wheel track named 'Middle of Road.' Both instruments are located on the rover's instrument deployment device, or 'arm.'

    Not only was the Moessbauer spectrometer able to gain important mineralogical information about this site, it also aided in the placement of the microscopic imager. On hard rocks, the microscopic imager uses its tiny metal sensor to determine proper placement for best possible focus. However, on the soft martian soil this guide would sink, prohibiting proper placement of the microscopic imager. After the Moessbauer spectrometer's much larger, donut-shaped plate touches the surface, Spirit can correctly calculate where to position the microscopic imager.

    Scientists find this image particularly interesting because of the compacted nature of the soil that was underneath the Moessbauer spectrometer plate. Also of interest are the embedded, round grains and the fractured appearance of the material disturbed within the hole. The material appears to be slightly cohesive. The field of view in this image, taken on Sol 43 (February 16, 2004), measures approximately 3 centimeters (1.2 inches) across.

  7. γ -ray-pulse formation in a vibrating recoilless resonant absorber

    NASA Astrophysics Data System (ADS)

    Antonov, V. A.; Radeonychev, Y. V.; Kocharovskaya, Olga

    2015-08-01

    We study propagation of γ radiation from a Mössbauer radioactive source through a vibrating recoilless resonant absorber and find the optimal conditions to produce a periodic train of γ -ray pulses with maximum peak intensity, several times higher than the intensity from the source, and minimum duration, much shorter than the lifetime of the emitting nuclear state of the source. The shape, duration, and repetition rate of the pulses are tunable in a wide range. We propose modifications of the recently reported experiment [F. Vagizov et al., Nature (London) 508, 80 (2014), 10.1038/nature13018] to produce pulses with higher peak intensity and shorter duration using absorbers enriched by the resonant nuclei and discuss possible applications of the generated pulses for the time-domain Mössbauer spectroscopy.

  8. Coherent control of the waveforms of recoilless γ-ray photons.

    PubMed

    Vagizov, Farit; Antonov, Vladimir; Radeonychev, Y V; Shakhmuratov, R N; Kocharovskaya, Olga

    2014-04-03

    The concepts and ideas of coherent, nonlinear and quantum optics have been extended to photon energies in the range of 10-100 kiloelectronvolts, corresponding to soft γ-ray radiation (the term used when the radiation is produced in nuclear transitions) or, equivalently, hard X-ray radiation (the term used when the radiation is produced by electron motion). The recent experimental achievements in this energy range include the demonstration of parametric down-conversion in the Langevin regime, electromagnetically induced transparency in a cavity, the collective Lamb shift, vacuum-assisted generation of atomic coherences and single-photon revival in nuclear absorbing multilayer structures. Also, realization of single-photon coherent storage and stimulated Raman adiabatic passage were recently proposed in this regime. More related work is discussed in a recent review. However, the number of tools for the coherent manipulation of interactions between γ-ray photons and nuclear ensembles remains limited. Here we suggest and implement an efficient method to control the waveforms of γ-ray photons coherently. In particular, we demonstrate the conversion of individual recoilless γ-ray photons into a coherent, ultrashort pulse train and into a double pulse. Our method is based on the resonant interaction of γ-ray photons with an ensemble of nuclei with a resonant transition frequency that is periodically modulated in time. The frequency modulation, which is achieved by a uniform vibration of the resonant absorber, owing to the Doppler effect, renders resonant absorption and dispersion both time dependent, allowing us to shape the waveforms of the incident γ-ray photons. We expect that this technique will lead to advances in the emerging fields of coherent and quantum γ-ray photon optics, providing a basis for the realization of γ-ray-photon/nuclear-ensemble interfaces and quantum interference effects at nuclear γ-ray transitions.

  9. Moessbauer analysis of heat affected zones of an SA 508 steel weld

    SciTech Connect

    Kwon, S.J.; Oh, S.J.; Kim, S.; Lee, S.; Kim, J.H.

    1998-12-18

    Microstructure of a heat affected zone (HAZ) in a weld is influenced by many factors such as chemical composition, welding condition, and peak temperature. It is more complex under multi-pass welding because of the repeated heat input. For the analysis of the HAZ microstructure, optical microscope, electron microscope, and X-ray diffraction techniques have been widely used. However, their application is limited since they can hardly make quantitative analysis of HAZ where numerous phases such as martensite, bainite, ferrite, pearlite, austenite, and carbides are co-existing. Moessbauer spectroscopy, in such a case, is particularly useful due to the capability of quantitative analysis on the fraction of each phase. In this study, phases present in the HAZ of an SA 508 steel were identified, and their fractions were quantitatively determined by Moessbauer spectroscopy in conjunction with microscopic observations.

  10. Fe-57 Moessbauer study of tektites

    NASA Technical Reports Server (NTRS)

    Evans, B. J.; Leung, L. K.

    1976-01-01

    Moessbauer measurements were made on selected moldavite, australite, philippinite, and Georgia tektites. The spectra consist of two apparent lines, but at least two quadrupole doublets can be fitted to these spectra. The Moessbauer parameters for these doublets indicate that they arise from Fe2+ ions with local environments, which are relatively rich and relatively poor in calcium, respectively, similar to those in clinopyroxenes. No evidence for Fe3+/Fe2+ ratios above 0.01 (estimated detection limit) have been found in any tektite. Tektites are considerably more reduced than previously believed, and the extent of the reduction shows little or no variation among different types of tektites. These results limit the source materials of tektites to minerals in which the iron is uniformly highly reduced and in which the iron is contained clinopyroxene-like phases.

  11. Moessbauer search for ferric oxide phases in lunar materials and simulated lunar materials

    NASA Technical Reports Server (NTRS)

    Forester, D. W.

    1973-01-01

    Moessbauer studies were carried out on lunar fines and on simulated lunar glasses containing magnetic-like precipitates with the primary objective of determining how much, if any, ferric oxide is present in the lunar soils. Although unambiguous evidence of lunar Fe(3+) phases was not obtained, an upper limit was estimated from different portions of the Moessbauer spectra to be between 0.1 and 0.4 wt.% (as Fe3O4). A smaller than 62 microns fraction of 15021,118 showed 0.5 wt.% ferromagnetic iron at 300 K in as-returned condition. After heating to 650 C in an evacuated, sealed quartz tube for 1400 hours, the same sample exhibited 1 wt.% ferromagnetic iron at room temperature. An accompanying decrease in excess absorption area near zero velocity was noted. Thus, the result of the vacuum heat treatment was to convert fine grained iron to larger particles, apparently without the oxidation effects commonly reported.

  12. Surface analysis of mixed-conducting ferrite membranes by the conversion-electron Moessbauer spectroscopy

    SciTech Connect

    Waerenborgh, J.C.; Tsipis, E.V.; Yaremchenko, A.A.; Kharton, V.V.

    2011-09-15

    Conversion-electron Moessbauer spectroscopy analysis of iron surface states in the dense ceramic membranes made of {sup 57}Fe-enriched SrFe{sub 0.7}Al{sub 0.3}O{sub 3-{delta}} perovskite, shows no traces of reductive decomposition or carbide formation in the interfacial layers after operation under air/CH{sub 4} gradient at 1173 K, within the limits of experimental uncertainty. The predominant trivalent state of iron cations at the membrane permeate-side surface exposed to flowing dry methane provides evidence of the kinetic stabilization mechanism, which is only possible due to slow oxygen-exchange kinetics and enables long-term operation of the ferrite-based ceramic reactors for natural gas conversion. At the membrane feed-side surface exposed to air, the fractions of Fe{sup 4+} and Fe{sup 3+} are close to those in the powder equilibrated at atmospheric oxygen pressure, suggesting that the exchange limitations to oxygen transport are essentially localized at the partially reduced surface. - Graphical Abstract: Conversion-electron Moessbauer spectroscopy analysis of dense ceramic membranes made of {sup 57}Fe-enriched SrFe{sub 0.7}Al{sub 0.3}O{sub 3-{delta}} perovskite, shows no reductive decomposition in thin interfacial layers after testing under air/CH{sub 4} gradient, enabling stable operation of the ferrite-based ceramic reactors for partial oxidation of methane. Highlights: > Conversion-electron Moessbauer spectroscopy is used for mixed-conducting membranes. > No decomposition is detected in the membrane surface layers under air/CH{sub 4} gradient. > Due to kinetic stabilization, Fe{sup 3+} states prevail at the surface exposed to methane. > Transmission Moessbauer spectra show perovskite decomposition on equlibration in CH{sub 4}. > Ferrite-based ceramic reactors can stably operate under air/CH{sub 4} gradient.

  13. Moessbauer effect: Study of disordered magnetic systems

    SciTech Connect

    Chang, Xiao Sha.

    1989-01-01

    This dissertation describes Moessbauer spectroscopy studies of two chemically disordered binary, crystalline alloys having the composition A{sub 1-x}B{sub x}. Both systems are random 3d Heisenberg ferromagnets. In each case both A and B atoms carry a magnetic moment. The first study concerns a Moessbauer absorber experiment on Fe{sub 1-x} V{sub x}, in which the disorder in the critical region is of the annealed random exchange type. To eliminate the effect of concentration inhomogeneity, the measurement of the critical exponent {beta} was done on the alloy with x = 0.125, where dT{sub C}/dx = 0, yielding {beta} = 0.362(8) over the reduced temperature range 1.4 {times} 10{sup {minus}3} < t < 4.88 {times} 10{sup {minus}1}. This result confirms the theoretical prediction that the annealed disorder is irrelevant to critical behavior in this case. As expected the critical exponent {beta} is consistent with the expectation for the 3d Heisenberg model as well as the measured exponent of pure Fe. The second study involves a Moessbauer source experiment on {sup 57} CoPd{sub 0.80}Co{sub 0.20}, in which disorder is of the quenched random exchange type perturbed by a very weak random anisotropy interaction. The critical exponent {beta} deduced over the range 1 {times} 10{sup {minus}2} < t < 2 {times} 10{sup {minus}1} is 0.385(20), and is consistent with the theoretical prediction for quenched disordered 3d Heisenberg systems: the disorder is irrelevant to the critical behavior. However, because of the restricted range of reduced temperature, the result is insufficiently asymptotic to serve as a conclusive test of the theory. Outside the critical region the distribution of Fe{sup 57} hyperfine field in Pd{sub 0.80}Co{sub 0.20} is observed to have an anomalous temperature dependence characterized by a linear increase in the width of the field distribution for T/T{sub C} {ge} 0.6.

  14. Conversion of recoilless γ radiation into a periodic sequence of short intense pulses in a set of several sequentially placed resonant absorbers

    NASA Astrophysics Data System (ADS)

    Radeonychev, Y. V.; Antonov, V. A.; Vagizov, F. G.; Shakhmuratov, R. N.; Kocharovskaya, Olga

    2015-10-01

    An efficient technique for producing a periodic sequence of short nearly bandwidth-limited pulses of recoilless γ radiation via its transmission through an optically thick vibrating resonant absorber was demonstrated recently [Nature (London) 508, 80 (2014), 10.1038/nature13018]. In this paper we extend the theoretical analysis to a case of multiple absorbers. We analyze a simple physical model describing control of spectral content of a frequency modulated γ radiation by adjusting the amplitudes and initial phases of spectral components, using the resonant absorption and dispersion in a set of several sequentially placed resonant absorbers. On the basis of analytical solutions, we determine the ultimate possibilities of the proposed technique.

  15. Inelastic scattering in condensed matter with high intensity Moessbauer radiation

    SciTech Connect

    Yelon, W.B.; Schupp, G.

    1993-02-01

    The QUEGS facility at MURR has produced a number of new results and demonstrated the range of potential applications of high resolution, high intensity Moessbauer scattering. This work has been carried out by both MU and Purdue researchers and includes published results on Na, W, pentadecane, polydimethylsiloxane and other systems, manuscripts submitted on alkali halides (Phys. Rev. B) and accurate Moessbauer lineshape measurements (Phys. Rev. C), and manuscripts in preparation on glycerol, NiAl and Moessbauer spectra obtained by modulating a scattering crystal. Recently, new collaborations have been initiated which will substantially enhance our efforts. These are with W. Steiner (Vienna), G. Coddens (Saclay), and R. D. Taylor (Los Alamos). Steiner is experienced with Fe-57 Moessbauer scattering, while Coddens specializes in quasielastic neutron scattering; both of these areas naturally complement our work. R. D. Taylor has pioneered Moessbauer spectroscopy from the time of its discovery and has already made important contributions to our study of lattice dynamics and superconductivity for lead alloyed with small quantities of tin. At the same time, a significant instrument upgrade is underway, funded in part by the DOE-URIP program.

  16. Moessbauer Analysis of Low-Temperature Bainite

    SciTech Connect

    Bruna, P.; Crespo, D.; Garcia-Mateo, C.; Bhadeshia, H.K.D.H.

    2005-04-26

    Low-temperature bainite, obtained by the transformation of austenite at temperatures as low as 200 deg. C for times as large as several days, has been reported to have extraordinary mechanical properties including the highest reported hardness of any bainitic steel. The unusual properties are a consequence of the fine scale of the microstructure, which contains bainite plates with thickness in the range 20-40 nm. The microstructure also contains carbon-enriched retained austenite which contributes to the properties via a number of mechanisms. In this work, the microstructure of a high carbon bainitic steel with Si to avoid cementite precipitation and Co to accelerate the transformation has been studied using Moessbauer spectroscopy for a series of samples transformed isothermally at 200 deg. C for time periods of 26, 34 and 96 hours. The total austenite content is almost identical ({approx}13 wt%) for these samples although the carbon concentrations of the phases differ as a function of transformation time. The austenite increases its carbon content from 5.4 atomic % after 26 h transformation to 6.3 at.% after 96 h, while the final bainitic phase retains about 2.2 at.% of C. These results are consistent with data obtained using atom probe tomography for samples transformed isothermally for 12 days.

  17. Moessbauer spectroscopy study on the corrosion resistance of plasma nitrided ASTM F138 stainless steel in chloride solution

    SciTech Connect

    Souza, S.D. de; Olzon-Dionysio, M.; Basso, R.L.O.; Souza, S. de

    2010-10-15

    Plasma nitriding of ASTM F138 stainless steel samples has been carried out using dc glow discharge under 80% H{sub 2}-20% N{sub 2} gas mixture, at 673 K, and 2, 4, and 7 h time intervals, in order to investigate the influence of treatment time on the microstructure and the corrosion resistance properties. The samples were characterized by scanning electron microscopy, glancing angle X-ray diffraction and conversion electron Moessbauer spectroscopy, besides electrochemical tests in NaCl aerated solution. A modified layer of about 6 {mu}m was observed for all the nitrided samples, independent of nitriding time. The X-ray diffraction analysis shows broad {gamma}{sub N} phase peaks, signifying a great degree of nitrogen supersaturation. Besides {gamma}{sub N,} the Moessbauer spectroscopy results indicated the occurrence of {gamma}' and {epsilon} phases, as well as some other less important phases. Corrosion measurements demonstrate that the plasma nitriding time affects the corrosion resistance and the best performance is reached at 4 h treatment. It seems that the {epsilon}/{gamma}' fraction ratio plays an important role on the resistance corrosion. Additionally, the Moessbauer spectroscopy was decisive in this study, since it was able to identify and quantify the iron phases that influence the corrosion resistance of plasma nitrided ASTM F138 samples.

  18. Moessbauer Spectroscopy of Martian and Sverrefjell Carbonates

    NASA Technical Reports Server (NTRS)

    Agresti, David G.; Morris, Richard V.

    2011-01-01

    Mars, in its putative "warmer, wetter: early history, could have had a CO2 atmosphere much denser than its current value of <10 mbar. The question of where all this early CO2 has gone has long been debated. Now, several instruments on Mars Exploration Rover (MER) Spirit, including its Moessbauer spectrometer MIMOS II, have identified Mg-Fe carbonate in rock outcrops at Comanche Spur in the Columbia Hills of Gusev Crater. With this finding, carbonate cements in volcanic breccia collected on Sverrefjell Volcano on Spitzbergen Island in the Svalbard Archipelago (Norway) during the AMASE project are mineralogical and possible process analogues of the newly discovered martian carbonate. We report further analyses of Mossbauer spectra from Comanche Spur and discuss their relationship to Mossbauer data acquired on Sverrefjell carbonates. The spectra were velocity calibrated with MERView and fit using MERFit. Instead of the "average temperature" Comanche spectrum (data from all temperature windows summed), we refit the Comanche data for QS within each temperature window, modeling as doublets for Fe2+(carbonate), Fe2+(olivine), and Fe3+(npOx). The temperature dependences of QS for the Comanche carbonate and for a low-Ca carbonate from Chocolate Pots in Yellowstone National Park (YNP) are shown; they are the same within error. For Comanche carbonate summed over 210-270 K, (CS, QS) = (1.23, 1.95) mm/s. The value of QS for Sverrefjell carbonate at 295 K, (CS, QS) = (1.25, 1.87) mm/s, is also plotted, and the plot shows that the QS for the Sverrefjell carbonate agrees within error with the Comanche data extrapolated to 295 K. This agreement is additional evidence that the Sverrefjell carbonates are Mossbauer analogues for the Comanche carbonates, and that both carbonates might have precipitated from solutions that became carbonate rich by passing through buried carbonate deposits.

  19. (Gamma scattering in condensed matter with high intensity Moessbauer radiation)

    SciTech Connect

    Not Available

    1992-01-01

    This report discusses: quasielastic scattering studies on glycerol; gamma-ray scattering from alkali halides; lattice dynamics in metals; Moessbauer neutron scattering, x-ray diffraction, and macroscopic studies of high {Tc} superconductors containing tungsten; NiAl scattering studies; and atomic interference factors and nuclear Casimir effect.

  20. Interpretation of the Moessbauer Spectra of the Magnetic Nanoparticles in Mouse Spleen

    SciTech Connect

    Chuev, Mikhail A.; Cherepanov, Valery M.; Polikarpov, Mikhail A.; Panchenko, Vladislav Y.; Deyev, Sergey M.; Mischenko, Iliya N.; Nikitin, Maxim P.

    2010-12-02

    We have developed a stochastic model for description of relaxation effects in the system of homogeneously magnetized single-domain particles and applied the model to the analysis of Moessbauer spectra of magnetic nanoparticles (Chemicell ARA) and mouse spleen after i.v. injection into animals. We estimate that the fraction of exogenous iron in nanoparticles in the mouse spleen 3 months after injection was 0.27{+-}0.03. The spectra of the residual nanoparticles in the spleen had almost the same isomer shift but smaller mean hyperfine magnetic field values indicating decrease in the magnetic anisotropy energy (size) of the particles compared to the initial ones in the course of biodegradation. Concentration of ferritin-like iron was about three-fold higher than that in the spleen of untreated animals showing ferritin-like forms in the mouse spleen.

  1. Moessbauer Spectroscopy on the Martian Surface: Constraints on Interpretation of MER Data

    NASA Technical Reports Server (NTRS)

    Dyar, M. D.; Schaefer, M. W.

    2003-01-01

    Moessbauer spectrometers will be used on martian landers and rovers to identify and quantify relative amounts of Fe-bearing minerals, as well as to determine their Fe(3+)/Fe(2+) ratios, allowing more realistic modeling of martian mineralogy and evolution. However, derivation of mineral modes, Fe(3+)/Fe(2+) ratios, and phase identification via Moessbauer spectroscopy (MS) does have limitations. We discuss here the exciting potential of MS for remote planetary exploration, as well as constraints on interpretation of remote Moessbauer data.

  2. Moessbauer Mineralogy on the Moon: The Lunar Regolith

    NASA Technical Reports Server (NTRS)

    Morris, Richard V.; Korotev, Randy L..; Shelfer, Tad D.; Klingelhoefer, Goestar

    1997-01-01

    A first-order requirement for spacecraft missions that land on solid planetary objects is instrumentation for mineralogical analyses. For purposes of providing diagnostic information about naturally-occurring materials, the element iron is particularly important because it is abundant and multivalent. Knowledge of the oxidation state of iron and its distribution among iron-bearing mineralogies tightly constrains the types of materials present and provides information about formation and modification (weathering) processes. Because Moessbauer spectroscopy is sensitive to both the valence of iron and its local chemical environment, the technique is unique in providing information about both the relative abundance of iron-bearing phases and oxidation state of the iron. The Moessbauer mineralogy of lunar regolith samples (primarily soils from the Apollo 16 and 17 missions to the Moon) were measured in the laboratory to demonstrate the strength of the technique for in situ mineralogical exploration of the Moon. The regolith samples were modeled as mixtures of five iron-bearing phases: olivine, pyroxene, glass, ilmenite, and metal. Based on differences in relative proportions of iron associated with these phases, volcanic ash regolith can be distinguished from impact-derived regolith, impact-derived soils of different geologic affinity (e.g., highlands, maria) can be distinguished on the basis of their constituent minerals, and soil maturity can be estimated. The total resonant absorption area of the Moessbauer spectrum can be used to estimate total FeO concentrations.

  3. Moessbauer measurements of microstructural change in aged duplex stainless steel

    SciTech Connect

    Kirihigashi, A.; Sakamoto, N.; Yamaoka, T.; Nasu, S.

    1995-08-01

    A duplex stainless steel (ASME SA351 CF8M) has usually been manufactured by a continuous casting technique. It consists of a paramagnetic austenite phase and a ferromagnetic ferrite phase. It has been known that the ferrite phase decomposition occurs in this steel after aging between 300 and 450 C. As a result of phase decomposition, a Fe-rich phase and a Cr-rich phase are produced in the ferrite phase. It is difficult to detect the phase decomposition even by not only optical microscopy but also transmission electron microscopy, since the decomposed structure is very fine. However, Moessbauer measurements that can detect the magnetic hyperfine field of magnetic substance may detect the microstructural change. An averaged magnetic hyperfine field increases in the ferrite phase, due to the production of the Fe-rich phase which has high magnetic hyperfine field. Therefore, the authors investigated the phase decomposition of the duplex stainless steel caused by aging, utilization Moessbauer spectroscopy which has capability of detecting this structural change in the atomic level quantitatively. The authors also investigated the potential of backscattering Moessbauer method for NDE technique.

  4. Moessbauer Characterization of Magnetite/Polyaniline Magnetic Nanocomposite

    SciTech Connect

    Rodriguez, Anselmo F. R.; Faria, Fernando S. E. D. V.; Lopez, Jorge L.; Mesquita, Antonio G. G.; Coaquira, Jose A. H.; Oliveira, Aderbal C.; Morais, Paulo C.; Azevedo, Ricardo B.; Araujo, Ana C. V. de; Alves, Severino Jr.; Azevedo, Walter M. de

    2010-12-02

    Aniline surface coated Fe{sub 3}O{sub 4} nanoparticles have been successfully synthesized by UV irradiation varying the time and the acid media (HCl, HNO{sub 3}, or H{sub 2}SO{sub 4}). The synthesized material represents a promising platform for application in nerve regeneration. XRD patterns are consistent with the crystalline structure of magnetite. Nevertheless, for UV irradiation times longer than 2 h, extra XRD lines reveal the presence of goethite. The mean crystallite size of uncoated particles is estimated to be 25.4 nm, meanwhile that size is reduced to 19.9 nm for the UV irradiated sample in HCl medium for 4 h. Moessbauer spectra of uncoated nanoparticles reveal the occurrence of thermal relaxation at room temperature, while the 77 K-Moessbauer spectrum suggests the occurrence of electron localization effects similar to that expected in bulk magnetite. The Mossbauer spectra of UV irradiated sample in HCl medium during 4 h, confirms the presence of the goethite phase. For this sample, the thermal relaxation is more evident, since the room temperature spectrum shows larger spectral area for the nonmagnetic component due to the smaller crystallite size. Meanwhile, the 77 K-Moessbauer spectrum suggests the absence of the electron localization effect above 77 K.

  5. Study of Vitamins and Dietary Supplements Containing Ferrous Fumarate and Ferrous Sulfate Using Moessbauer Spectroscopy

    SciTech Connect

    Oshtrakh, M. I.; Novikov, E. G.; Semionkin, V. A.; Dubiel, S. M.

    2010-07-13

    A study of several samples of vitamins and dietary supplements containing ferrous fumarate and ferrous sulfate was carried out using Moessbauer spectroscopy with a high velocity resolution. A presence of ferrous and ferric impurities was revealed. Small variations of Moessbauer hyperfine parameters were found for both ferrous fumarates and ferrous sulfates in the investigated medicines.

  6. Extraterrestrial Moessbauer Spectroscopy: More than Three Years of Mars Exploration and Developments for Future Missions

    NASA Technical Reports Server (NTRS)

    Schroeder, Christian; Klingelhoefer, Goestar; Morris, Richard V.; Rodionov, Daniel S.; Fleischer, Iris; Blumers, Mathias

    2007-01-01

    The NASA Mars Exploration Rovers (MER), Spirit and Opportunity, landed on the Red Planet in January 2004. Both rovers are equipped with a miniaturized Moessbauer spectrometer MIMOS II. Designed for a three months mission, both rovers and both Moessbauer instruments are still working after more than three years of exploring the Martian surface. At the beginning of the mission, with a landed intensity of the Moessbauer source of 150 mCi, a 30 minute touch and go measurement produced scientifically valuable data while a good quality Moessbauer spectrum was obtained after approximately eight hours. Now, after about five halflives of the sources have passed, Moessbauer integrations are routinely planned to last approx.48 hours. Because of this and other age-related hardware degradations of the two rover systems, measurements now occur less frequently, but are still of outstanding quality and scientific importance. Summarizing important Moessbauer results, Spirit has traversed the plains from her landing site in Gusev crater and is now, for the greater part of the mission, investigating the stratigraphically older Columbia Hills. Olivine in rocks and soils in the plains suggests that physical rather than chemical processes are currently active.

  7. Moessbauer spectroscopy and scanning electron microscopy of the Murchison meteorite

    NASA Technical Reports Server (NTRS)

    Brown, Christopher L.; Oliver, Frederick W.; Hammond, Ernest C., Jr.

    1989-01-01

    Meteorites provide a wealth of information about the solar system's formation, since they have similar building blocks as the Earth's crust but have been virtually unaltered since their formation. Some stony meteorites contain minerals and silicate inclusions, called chondrules, in the matrix. Utilizing Moessbauer spectroscopy, we identified minerals in the Murchison meteorite, a carbonaceous chondritic meteorite, by the gamma ray resonance lines observed. Absorption patterns of the spectra were found due to the minerals olivine and phyllosilicate. We used a scanning electron microscope to describe the structure of the chondrules in the Murchison meteorite. The chondrules were found to be deformed due to weathering of the meteorite. Diameters varied in size from 0.2 to 0.5 mm. Further enhancement of the microscopic imagery using a digital image processor was used to describe the physical characteristics of the inclusions.

  8. The big and little of fifty years of Moessbauer spectroscopy at Argonne.

    SciTech Connect

    Westfall, C.

    2005-09-20

    Using radioactive materials obtained by chance, a turntable employing gears from Heidelberg's mechanical toy shops, and other minimal equipment available in post World War II Germany, in 1959 Rudolf Moessbauer confirmed his suspicion that his graduate research had yielded ground-breaking results. He published his conclusion: an atomic nucleus in a crystal undergoes negligible recoil when it emits a low energy gamma ray and provides the entire energy to the gamma ray. In the beginning Moessbauer's news might have been dismissed. As Argonne nuclear physicist Gilbert Perlow noted: ''Everybody knew that nuclei were supposed to recoil when emitting gamma rays--people made those measurements every day''. If any such effect existed, why had no one noticed it before? The notion that some nuclei would not recoil was ''completely crazy'', in the words of the eminent University of Illinois condensed matter physicist Frederich Seitz. Intrigued, however, nuclear physicists as well as condensed matter (or solid state) physicists in various locations--but particularly at the Atomic Energy Research Establishment at Harwell in Britain and at Argonne and Los Alamos in the U.S.--found themselves pondering the Moessbauer spectra with its nuclear and solid state properties starting in late 1959. After an exciting year during which Moessbauer's ideas were confirmed and extended, the physics community concluded that Moessbauer was right. Moessbauer won the Nobel Prize for his work in 1961. In the 1960s and 1970s Argonne physicists produced an increasingly clear picture of the properties of matter using the spectroscopy ushered in by Moessbauer. The scale of this traditional Moessbauer spectroscopy, which required a radioactive source and other simple equipment, began quite modestly by Argonne standards. For example Argonne hosted traditional Moessbauer spectroscopy research using mostly existing equipment in the early days and equipment that cost $100,000 by the 1970s alongside work at

  9. The Miniaturized Moessbauer Spectrometer MIMOS II for the Asteroid Redirect Mission(ARM): Quantative Iron Mineralogy And Oxidation States

    NASA Technical Reports Server (NTRS)

    Schroeder, C.; Klingelhoefer, G; Morris, R. V.; Yen, A. S.; Renz, F.; Graff, T. G.

    2016-01-01

    The miniaturized Moessbauer spectrometer MIMOS II is an off-the-shelf instrument with proven flight heritage. It has been successfully deployed during NASA’s Mars Exploration Rover (MER) mission and was on-board the UK-led Beagle 2 Mars lander and the Russian Phobos-Grunt sample return mission. A Moessbauer spectrometer has been suggested for ASTEX, a DLR Near-Earth Asteroid (NEA) mission study, and the potential payload to be hosted by the Asteroid Redirect Mission (ARM). Here we make the case for in situ asteroid characterization with Moessbauer spectroscopy on the ARM employing one of three available fully-qualified flight-spare Moessbauer instruments.

  10. New direct method for evaluating recoilless f-factors of two iron-sites in Fe-bearing compounds using Mössbauer spectrometry.

    PubMed

    Barrero, C A; García, K E

    2013-07-21

    We propose a new direct method for calculating simultaneously two recoilless f-factors of any iron-bearing compound relative to that of a reference material by collecting only a single-temperature Mössbauer spectrum. This methodology is comparatively much simpler than the usual one which requires taking Mössbauer spectra of the compound at several temperatures and subsequently fitting the temperature dependence of the subspectral area or the isomer shift data with a lattice vibrational model. We demonstrate the applicability of this new methodology in the case of three common iron-bearing compounds: magnetite, akaganeite and goethite, but of course this type of study can be extended to other materials. The two f-factors for each compound were related to iron ions located in sites of different origin: for magnetite, these were related to irons with two different oxidation states; for akaganeite to irons in two different crystallographic sites; and for goethite to irons in similar crystal sites but located in grains of different sizes. In the case of magnetite, we found that the f-factors for the Fe(3+) and Fe(2.5+) sites relative to that of metallic iron powder were of fFe (3+)∕fFe = 0.97 ± 0.05 and fFe (2.5+)∕fFe = 0.92 ± 0.05, respectively. Interestingly, the quotient of these two f-factors, i.e., fFe (2.5+)∕fFe (3+), is equal to 0.95 ± 0.05, which compares fairly well with a value reported in literature obtained using the complex methodology based on the temperature dependence of the absolute subspectral area and the Debye approximation. For akaganeite, the f-factors of the doublet 1, D1, and doublet 2, D2, sites relative to that of metallic iron powder were of fD 1∕fFe = 0.95 ± 0.08 and fD 2∕fFe = 0.98 ± 0.15, respectively. And for goethite we found that the f-factors of the sextet 1, G1, and sextet 2, G2, sites relative to that of metallic iron powder were of fG 1∕fFe = 0.80 ± 0.02 and fG 2∕fFe = 0.80 ± 0.02, respectively. The

  11. Moessbauer study of iron redox in West Valley glass

    SciTech Connect

    Yaschenko, E.; Salahuddin, H.; Muller, I.S.; Pegg, I.L.; Macedo, P.B.

    1994-12-31

    High-level nuclear wastes at West Valley are high in iron which results in a target glass composition for the vitrification process that contains about 12 wt% Fe{sub 2}O{sub 3}. We have developed a series of high-iron glass formulations (up to 21 wt% Fe{sub 2}O{sub 3}) in order to accommodate all reasonable waste stream variability. An additional process control variable is the glass redox ratio, Fe{sup 2+}/(Fe{sup 2+}+Fe{sup 3+}), since this affects the resultant glass properties including durability, crystallization, glass transition temperature, and melt viscosity. In this study, a range of redox states was obtained by bubbling CO/CO{sub 2} mixtures through the melts. The redox state was determined by Moessbauer spectroscopy and correlations between redox state and CO/CO{sub 2} ratio, flow rate, and time were obtained. Analysis of the spectroscopic data provides additional information on changes in the occupation of tetrahedral and octahedral sites with redox state.

  12. Studies in Moessbauer spectroscopy, neutron activation analysis, x-ray fluorescence

    SciTech Connect

    Nomai, M.

    1985-01-01

    The Moessbauer Effects was employed to study cyclopentadienyliron arene compounds. The isomer shift, delta, in these compounds ranges from 0.206 to 0.257 mm/s relative to /sup 5//sub 7/Co/Cu source and ..delta..E/sub Q/ values are from 1.632 to 1.918 mm/s at liquid nitrogen temperature. Room temperature spectra showed low absorption due to small recoil-free fractions the deltas and ..delta..E/sub Q/s can be correlated with the electron withdrawing effects of the alkyl groups bonded to benzene. In polynuclear aromatic system extending over two benzene rings, electron charge density is difficult to explain. Isomer shifts of PF/sub 6//sup -/ and Fe(NCS)/sub 6//sup 3 -/ are more or less independent of the counteranion, while ..delta..E/sub Q/ is slightly influenced by it. (Fe(arene)Cp)/sub 3//sup +/FE(NCS)/sub 6//sup 3 -/ compounds show only two peaks, with parameters almost identical to the PF/sub 6//sup -/ compounds. An isomer shift peak due to Fe(NCS)/sub 6//sup 3 -/, Fe d/sup 5/ state, is not observed and it is believed to coincide with the second right hand peak of the cation. Experimental procedures and results of hydrogen determination in samples of coal and other comparative samples, e.g., NA/sub 2/EDTA.2H/sub 2/O, in a paraffin moderated thermal neutron flux from 1 ..mu..Ci of /sup 252/Cf source are described. Simple instrumentation is used. Accuracy of about 10% or better is possible with stronger neutron source. Other moderators that were tried, but were unsuccessful, were water and graphite. Factors that can affect the neutron flux and prompt ..gamma..-ray distribution in the samples are H, O, and C concentrations. Results of the determination of uranium and other elements in sandstone uranium samples from Zambia are presented.

  13. Cronstedtite and iron sulfide mineralogy of CM-type carbonaceous chondrites from cryogenic Moessbauer spectra

    NASA Technical Reports Server (NTRS)

    Fisher, Duncan S.; Burns, Roger G.

    1993-01-01

    Determinations of oxidation states and the crystal chemistry of iron-bearing minerals in CM meteorites by Moessbauer spectroscopy are complicated by thermally-induced electron hopping in cronstedtite and by ill-defined contributions from the hydrous iron sulphide phase believed to be tochilinite. Moessbauer spectral measurements at 30 K of several cronstedtite and tochilinite specimens have enabled modal proportions of these minerals, as well as Fe(3+)/Fe(2+) ratios, to be determined quantitatively for a suite of CM-type carbonaceous chondrites that included Murchison, Murray, Cold Bokkeveld, ALH 83100, and LEW 90500.

  14. Micromagnetic and Moessbauer spectroscopic investigation of strain-induced martensite in austenitic stainless steel

    SciTech Connect

    Meszaros, I.; Kaldor, M.; Hidasi, B.; Vertes, A.; Czako-Nagy, I.

    1996-08-01

    Strain-induced martensite in 18/8 austenitic stainless steel was studied. Magnetic measurements and Moessbauer spectroscopic investigations were performed to characterize the amount of {alpha}{prime}-martensite due to room-temperature plastic tensile loading. The effects of cold work and annealing heat treatment were explored using magnetic Barkhausen noise, saturation polarization, coercive force, hardness, and conversion electron Moessbauer spectroscopy. The suggested Barkhausen noise measurement technique proved to be a useful quantitative and nondestructive method for determining the ferromagnetic phase ratio of the studied alloy.

  15. Moessbauer spectroscopy of Mg(0.9)Fe(0.1)SiO3 perovskite

    NASA Technical Reports Server (NTRS)

    Jeanloz, Raymond; O'Neill, Bridget; Pasternak, Moshe P.; Taylor, R. D.; Bohlen, Steven R.

    1992-01-01

    Ambient pressure Moessbauer spectra of Mg(0.9)Fe-57(0.1)SiO3 perovskite synthesized at pressure-temperature conditions of about 50 GPa and 1700 K show that the iron is entirely high-spin Fe(2+) and appears to be primarily located in the octahedral site within the crystal structure. We observe broad Moessbauer lines, suggesting a distribution of electric-field gradients caused by disorder associated with the Fe ions. Also, the perovskite exhibits magnetic ordering at temperatures lower than 5 K, implying that there is a magnetic contribution to the absolute ('third-law') entropy of this phase.

  16. An Overview of Moessbauer Mineralogy at Gusev Crater, Mars

    NASA Technical Reports Server (NTRS)

    Klingelhoefer, G.; Schroeder, C.; Rodionov, D.; Yen, A.

    2006-01-01

    The Mars Exploration Rover (MER) Spirit landed on the plains of Gusev Crater on 4 January 2004 [1]. The scientific objective of the Moessbauer (MB) spectrometer on Spirit is to provide quantitative information about the distribution of Fe among its oxidation and coordination states, identification of Fe-bearing phases, and relative distribution of Fe among those phases. The speciation and distribution of Fe in Martian rock and soil constrains the primary rock types, redox conditions under which primary minerals crystallized, the extent of alteration and weathering, the type of alteration and weathering products, and the processes and environmental conditions for alteration and weathering.We discuss the Fe-bearing phases detected by Spirit s MB instrument during its first 540 sols of exploration [2,3]. Spirit roved eastward across the plains from its landing site to the Columbia Hills during the first approx.150 sols. Rocks are unweathered to weakly weathered olivine basalt, with olivine, pyroxene (Ol > Px), magnetite (Mt), and minor hematite (Hm) and nanophase ferric oxide (npOx) as their primary Fe-bearing minerals. Soils are generally similar basaltic materials, except that the proportion of npOx is much higher (up to approx.40%). NpOx is an oct-Fe3+ alteration product whose concentration is highest in fine-grained soils and lowest in rock interiors exposed by grinding with the Rock Abrasion Tool (RAT). Spirit explored the lower slopes of the Columbia Hills (West Spur) during sols approx.150-320. West Spur rocks are highly altered, even for interior surfaces exposed by grinding (Fe3+/FeT approx.0.56-0.84). High concentrations of npOx, Hm, and Mt are present. One rock (Clovis) contains significant quantities of goethite (alpha-FeOOH; approx.40% of total Fe). The detection of goethite is very significant because it is a mineralogical marker for aqueous alteration.

  17. Speciation of triphenyltin compounds using Moessbauer spectroscopy. Final report

    SciTech Connect

    Eng, G.

    1993-11-01

    Organotin compounds have been used widely as the active agent in antifouling marine paints. Organotin compounds, i.e., tributyltin compounds (TBTs) and triphenyltin compounds (TPTs) have been found to be effective in preventing the unwanted attachment and development of aquatic organisms such as barnacles, sea grass and hydroids on ships, hulls and underwater surfaces. However, these organotin compounds have been found to be toxic to non-targeted marine species as well. While speciation of tributyltins in environmental water systems has received much attention in the literature, little information concerning the speciation of triphenyltins is found. Therefore, it would be important to study the fate of TPTs in the aquatic environment, particularly in sediments, both oxic and anoxic, in order to obtain speciation data. Since marine estuaries consist of areas with varying salinity and pH, it is important to investigate the speciation of these compounds under varying salinity conditions. In addition, evaluation of the speciation of these compounds as a function of pH would give an insight into how these compounds might interact with sediments in waters where industrial chemical run-offs can affect the pH of the estuarine environment. Finally, since organotins are present in both salt and fresh water environments, the speciation of the organotins in seawater and distilled water should also be studied. Moessbauer spectroscopy would provide a preferred method to study the speciation of triphenyltins as they leach from marine paints into the aquatic environment. Compounds used in this study are those triphenyltin compounds that are commonly incorporated into marine paints such as triphenyltin fluoride (TPTF), triphenyltin acetate (TPTOAc), triphenyltin chloride (TPTCl) and triphenyltin hydroxide (TPTOH).

  18. Investigation of the Moessbauer Spectrum Quality as a Dependence on the Frequency of the Velocity Signal

    SciTech Connect

    Pechousek, J.

    2010-07-13

    This paper is focused on a quality characterizing the Moessbauer spectra measured for various frequencies of the velocity signal. Standard electromechanical double-loudspeaker drive and digital PID velocity controller were used for calibration spectra measurement in the frequency interval from 4 up to 100 Hz. Several parameters were evaluated for recommendation of the suitable velocity signal frequency.

  19. Use of Moessbauer spectroscopy to study reaction products of polyphenols and iron compounds

    SciTech Connect

    Gust, J. ); Suwalski, J. )

    1994-05-01

    Moessbauer spectroscopy was used to study parameters of the reaction products of iron compounds (Fe[sup III]) and polyphenols with hydroxyl (OH) groups in ortho positions. Polyphenols used in the reaction were catechol, pyrogallol, gallic acid, and oak tannin. The Fe-containing compounds were hydrated ferric sulfate (Fe[sub 2][SO[sub 4

  20. Moessbauer study in thin films of FeSi2 and FeSe systems

    NASA Technical Reports Server (NTRS)

    Escue, W. J.; Aggarwal, K.; Mendiratta, R. G.

    1978-01-01

    Thin films of FeSi2 and FeSe were studied using Moessbauer spectroscopy information regarding dangling bond configuration and nature of crystal structure in thin films was derived. A significant influence of crystalline aluminum substrate on film structure was observed.

  1. Moessbauer medium with a hidden nuclear population inversion and negative absorption of gamma quanta

    SciTech Connect

    Rivlin, Lev A

    2011-06-30

    We consider physical foundations of an eventual experiment aimed at observing stimulated gamma-photon emission of long-lived Moessbauer isomers through selective frequency modulation of gamma-resonances establishing hidden population inversion without exceeding the number of excited nuclei over unexcited ones and without additional pumping. The examples of suitable nuclei and numerical estimates of the parameters are presented. (active media)

  2. Antiferromagnetism in Co-57-doped La2CuO(4-y) studied by Moessbauer spectroscopy

    NASA Technical Reports Server (NTRS)

    Jha, S.; Mitros, C.; Lahamer, Amer; Yehia, Sherif; Julian, Glenn M.

    1989-01-01

    Moessbauer effect studies of Co-57-doped La2CuO(4-y) were performed at temperatures between 4.2 K and room temperature. These confirm the antiferromagnetic ordering of these compounds below room temperature. Temperature dependence of the quadrupole splitting shows that the hyperfine field is at an angle with the c-axis.

  3. Mineralogical diversity (spectral reflectance and Moessbauer data) in compositionally similar impact melt rocks from Manicouagan Crater, Canada

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; Bell, J. F., III; Golden, D. C.; Lauer, H. V., Jr.

    1993-01-01

    Meteoritic impacts under oxidizing surface conditions occur on both earth and Mars. Oxidative alteration of impact melt sheets is reported at several terrestrial impact structures including Manicouagan, West Clearwater Lake, and the Ries Basin. A number of studies have advocated that a significant fraction of Martian soil may consist of erosional products of oxidatively altered impact melt sheets. If so, the signature of the Fe-bearing mineralogies formed by the process may be present in visible and near infrared reflectivity data for the Martian surface. Of concern is what mineral assemblages form in impact melt sheets produced under oxidizing conditions and what their spectral signatures are. Spectral and Moessbauer data for 19 powder samples of impact melt rock from Manicouagan Crater are reported. Results show for naturally occurring materials that composite hematite-pyroxene bands have minima in the 910-nm region. Thus many of the anomalous Phobos-2 spectra, characterized by a shallow band minimum in the near-IR whose position varies between approximately 850 and 1000 nm, can be explained by assemblages whose endmembers (hematite and pyroxene) are accepted to be present on Mars. Furthermore, results show that a mineralogically diverse suite of rocks can be generated at essentially constant composition, which implies that variations in Martian surface mineralogy do not necessarily imply variations in chemical composition.

  4. Hematite at Meridiani Planum and Gusev Crater as identified by the Moessbauer Spectrometer MIMOS II

    NASA Technical Reports Server (NTRS)

    Klingelhoefer, G.; Morris, R. V.; Rodionov, D.; Schroeder, C.; de Souza, P. A.; Yen, A.; Renz, F.; Wdowiak, T.

    2006-01-01

    The Moessbauer (MB) spectrometers on the MER rovers Opportunity and Spirit, which landed on Mars in January 2004, have identified the iron-containing mineral hematite (a-Fe2O3) at both landing sites. On Earth, hematite can occur either by itself or with other iron oxides as massive deposits, in veins , and as particles dispersed through a silicate or other matrix material. Hematite particle size can range from nanophase (superparamagnetic) to multidomain and particle shape ranges from equant to acicular to platy. Fine-grained hematite is red in color and is a pigmenting agent. Coarse-grained hematite can be spectrally neutral (gray) at visible wavelengths. Substitutional impurities, particularly Al, are common in hematite. Chemically pure, coarse-grained, and well-crystalline hematite has a magnetic transition (the Morin transition) at 260 K. Moessbauer spectra, recorded as a function of temperature, provide a way to characterize Martian hematite with respect to some of the physical and chemical characteristics. At Meridiani Planum besides the iron-sulfate mineral jarosite also the Fe-oxide hematite has been identified by the Moessbauer spectrometer, mainly in three distinct types of reservoir: - outcrop matrix material dominated by the mineral jarosite in the MB spectrum, certain basaltic soils, and mm-sized spherules dubbed blueberries. Moessbauer spectra of each reservoir yield a distinct set of hyperfine parameters for hematite, suggesting different degrees of crystallinity and particle size. The hematite found by MB instrument MIMOS II in the outcrop material shows the Morin transition at relatively high temperatures (ca. 250 K) which is an indication of pure and well-crystallized hematite. The source of the hematite in the Blueberries as identified by Moessbauer spectroscopy, and also by MiniTES, is not known. These spherules, covering nearly the whole landing site area (Eagle crater, plains, Endurance crater), may be concretions formed in the outcrop

  5. Analysis of Moessbauer Data from Mars: A Database and Artificial Neural Network for Identification of Iron-bearing Phases

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; deSouza, P. A.; Morris, R. V.; Klingelhoefer, G.

    2003-01-01

    The exploration of the planet Mars is one of the major goals within the Solar system exploration programs of the US-American space agency NASA and the European Space Agency ESA. In particular the search for water and life and understanding of the history of the surface and atmosphere will be the major tasks of the upcoming space missions to Mars. The miniaturized Moessbauer spectrometer MIMOS II has been selected for the NASA Mars-Exploration-Rover twin-mission to Mars in 2003 and the ESA 2003 Mars-Express Beagle 2 mission. Reduced in size and weight, in comparison to ordinary laboratory setup, the sensor head just weights approximately 400 g, with a volume of (50x50x90) cu mm, and holds two gamma-ray sources: the stronger for experiments and the weaker for calibrations. The collimator (in sample direction) also shields the primary radiation off the detectors. Around the drive four detectors are mounted. The detectors are made of Si-PIN-photodiodes in chip form (100 sq mm, thickness of 0.5 mm). The control unit is located in a separate electronics board. This board is responsible for the power supply, generation of the drive's velocity reference signal, read of the detector pulses to record the spectrum, data storage and communication with the host computer. After more than four decades from the discovery of the Moessbauer effect, more than 400 minerals were studied at different temperatures. Their Moessbauer parameters were reported in the literature, and have been recently collected in a data bank. Previous Mars-missions, namely Viking and Mars Pathfinder, revealed Si, Al, Fe, Mg, Ca, K, Ti, S and Cl to be the major constituents in soil and rock elemental composition of the red planet. More than 200 minerals already studied by Moessbauer spectroscopy contain significant amounts of these elements. A considerable number of Moessbauer studies were also carried out on meteorites and on Moon samples. Looking backward in the studies of the whole Moessbauer community

  6. Moessbauer and adhesion study of ion beam-modified Fe-PTFE interfaces

    NASA Astrophysics Data System (ADS)

    Ingemarsson, P. Anders; Ericsson, Tore; Wappling, Roger; Possnert, Goran

    Conversion electron Moessbauer spectroscopy was used to study ion beam-induced effects at Fe-PTFE thin film interfaces and to relate these effects to accompanying modifications in adhesion. Irradiation with 16 MeV S-32(3+) ions to doses in the range between 5 x 10 to the 11th and 2 x 10 to the 14th ions/sq cm was carried out before or after deposition of thin Fe-57 layers. For both pre- and post-bombardment, a substantial adhesion enhancement was observed. Associated with this were significant changes in the Moessbauer spectra indicating the formation of Fe-C and Fe-F compounds. This compound formation can be associated with the observed improvement in thin film adhesion.

  7. Internal friction and Moessbauer study of C{endash}Cr associates in MANET steel

    SciTech Connect

    Gondi, P.; Gupta, R.; Montanari, R.; Principi, G.; Tata, M.E.

    1997-02-01

    Internal friction and Moessbauer techniques have been used to investigate the structure of C{endash}Cr associates and the arrangement of Fe atoms near them in the Cr martensitic steel MANET subjected to different thermal treatments. After slow rate cooling from the austenitic field, the Moessbauer spectra exhibit, besides the complex magnetic pattern of martensite, a low intensity single attributed to the presence of a Cr-rich b.c.c. phase. In correspondence, the internal friction curves show, among others, a Snoek-type peak due to an elastic processes involving C{endash}Cr associates with 6 Cr atoms. To explain the experimental results a simple structure model is suggested. {copyright} {ital 1997 Materials Research Society.}

  8. Bulk and thin films of FeTe: A Moessbauer study

    NASA Technical Reports Server (NTRS)

    Escue, W. T.; Aggarwal, K.; Mendiratta, R. G.

    1977-01-01

    Studies of bulk and thin films of FeTe using Moessbauer spectroscopy showed that FeTe has one noncubic Fe (+2) site which is 3d2 4s 4p3 hybridized. The presence of dangling bands was indicated in spectra of FeTe thin films. The films showed a tendency of texture formation. The substrate was observed to influence the film structure and nature of bonds in films.

  9. Inelastic scattering in condensed matter with high intensity Moessbauer radiation. Final technical report, December 1, 1989--November 30, 1992

    SciTech Connect

    Yelon, W.B.; Schupp, G.

    1993-02-01

    The QUEGS facility at MURR has produced a number of new results and demonstrated the range of potential applications of high resolution, high intensity Moessbauer scattering. This work has been carried out by both MU and Purdue researchers and includes published results on Na, W, pentadecane, polydimethylsiloxane and other systems, manuscripts submitted on alkali halides (Phys. Rev. B) and accurate Moessbauer lineshape measurements (Phys. Rev. C), and manuscripts in preparation on glycerol, NiAl and Moessbauer spectra obtained by modulating a scattering crystal. Recently, new collaborations have been initiated which will substantially enhance our efforts. These are with W. Steiner (Vienna), G. Coddens (Saclay), and R. D. Taylor (Los Alamos). Steiner is experienced with Fe-57 Moessbauer scattering, while Coddens specializes in quasielastic neutron scattering; both of these areas naturally complement our work. R. D. Taylor has pioneered Moessbauer spectroscopy from the time of its discovery and has already made important contributions to our study of lattice dynamics and superconductivity for lead alloyed with small quantities of tin. At the same time, a significant instrument upgrade is underway, funded in part by the DOE-URIP program.

  10. Hematite at Meridiani Planum and Gusev Crater as identified by the Moessbauer Spectrometer MIMOS II

    NASA Astrophysics Data System (ADS)

    Klingelhoefer, G.; Morris, R. V.; Rodionov, D.; Schroeder, C.; de Souza, P. A.; Yen, A.; Renz, F.; Wdowiak, T.

    2004-12-01

    The Moessbauer (MB) spectrometers on the MER rovers Opportunity and Spirit, which landed on Mars in January 2004, have identified the iron-containing mineral hematite (a-Fe2O3) at both landing sites. On Earth, hematite can occur either by itself or with other iron oxides as massive deposits, in veins , and as particles dispersed through a silicate or other matrix material. Hematite particle size can range from nanophase (superparamagnetic) to multidomain and particle shape ranges from equant to acicular to platy. Fine-grained hematite is red in color and is a pigmenting agent. Coarse-grained hematite can be spectrally neutral (gray) at visible wavelengths. Substitutional impurities, particularly Al, are common in hematite. Chemically pure, coarse-grained, and well-crystalline hematite has a magnetic transition (the Morin transition) at ~260 K. Moessbauer spectra, recorded as a function of temperature, provide a way to characterize Martian hematite with respect to some of the physical and chemical characteristics. At Meridiani Planum besides the iron-sulfate mineral jarosite also the Fe-oxide hematite has been identified by the Moessbauer spectrometer, mainly in three distinct types of reservoir: - outcrop matrix material dominated by the mineral jarosite in the MB spectrum, certain basaltic soils, and mm-sized spherules dubbed blueberries. Moessbauer spectra of each reservoir yield a distinct set of hyperfine parameters for hematite, suggesting different degrees of crystallinity and particle size. The hematite found by MB instrument MIMOS II in the outcrop material shows the Morin transition at relatively high temperatures (ca. 250 K) which is an indication of pure and well-crystallized hematite. The source of the hematite in the `Blueberries' as identified by Moessbauer spectroscopy, and also by MiniTES, is not known. These spherules, covering nearly the whole landing site area (Eagle crater, plains, Endurance crater), may be concretions formed in the outcrop

  11. XRD and {sup 119}Sn Moessbauer spectroscopy characterization of SnSe obtained from a simple chemical route

    SciTech Connect

    Bernardes-Silva, Ana Claudia . E-mail: anaclaudiabs2000@yahoo.com.br; Mesquita, A.F.; Moura de Neto, E.; Porto, A.O. . E-mail: arilzaporto@yahoo.com.br; Ardisson, J.D.; Lameiras, F.S.

    2005-09-01

    Crystalline tin selenide semiconductor was synthesized by a chemical route. Selenium powder reacted with potassium boronhydride, giving a soluble selenium species potassium seleniumhydride. The reaction of potassium seleniumhydride with tin chloride produced crystalline tin selenide, which was characterized by X-ray diffraction, {sup 119}Sn Moessbauer spectroscopy and scanning electronic microscopy. The material was thermally treated, in nitrogen flow, at 300 and 600 deg. C for 2 h and the particle size evolution was studied by X-ray diffraction. The X-ray diffraction and {sup 119}Sn Moessbauer results showed that a mixture of tin oxides and orthorhombic tin selenide was obtained.

  12. The Miniaturized Moessbauer Spectrometers MIMOS II on MER: Four Years of Operation - A Summary

    NASA Technical Reports Server (NTRS)

    Fleischer, I.; Klingelhoefer, G.; Morris, R. V.; Rodionov, D.; Blumers, M.; Bernhardt, B.; Schroeder, C.; Ming, D. W.; Yen, A. S.; Cohen, B. A.; McCoy, T. J.; Mittlefehldt, D. W.; Schmidt, M. E.; Girones Lopez, J.; Studlek, G.; Brueckner, J.; Gellert, R.; d'Uston, C.

    2008-01-01

    The two Miniaturized Moessbauer Spectrometers (MIMOS II) on board the two Mars Exploration Rovers Spirit and Opportunity have now been collecting important scientific data for more than four years. The spectrometers provide information about Fe-bearing mineral phases and determine Fe oxidation states. The total amount of targets analized exceeds 600, the total integration time exceeds 260 days for both rovers. Since landing, more than five half-lives of the Co-57 MB sources have past (intensity at the time of landing approx. 150 mCi). Current integration times are about 50 hours in order to achieve reasonable statistics as opposed to 8 hours at the beginning of the mission. In total, 13 different mineral phases were detected: Olivine, pyroxene, hematite, magnetite and nanophase ferric oxide were detected at both landing sites. At Gusev, ilmenite, goethite, a ferric sulfate phase and a yet unassigned phase (in the rock Fuzzy Smith) were detected. At Meridiani, jarosite, metallic iron in meteoritic samples (kamacite), troilite, and an unassigned ferric phase were detected. Jarosite and goethite are of special interest, as these minerals are indicators for water activity. In this abstract, an overview of Moessbauer results will be given, with a focus on data obtained since the last martian winter. The MER mission has proven that Moessbauer spectroscopy is a valuable tool for the in situ exploration of extraterrestrial bodies and for the study of Febearing samples. The experience gained through the MER mission makes MIMOS II a obvious choice for future missions to Mars and other targets. Currently, MIMOS II is on the scientific payload of two approved future missions: Phobos Grunt (Russian Space Agency; 2009) and ExoMars (European Space Agency; 2013).

  13. Combined backscatter Moessbauer spectrometer/x ray fluorescence analyzer (BaMS/XRF) for extraterrestrial surfaces

    NASA Technical Reports Server (NTRS)

    Shelfer, T. D.; Wills, E. L.; Agresti, D. G.; Pimperl, M. M.; Shen, M. H.; Morris, R. V.; Nguyen, T.

    1993-01-01

    We have designed and tested a prototype combined backscatter Moessbauer spectrometer and x-ray fluorescence analyzer (BaMS/XRF). A space qualified instrument based on this design would be suitable for in-situ use on planetary missions to the surfaces of the Moon (Artemis and lunar outpost), Mars (MESUR), asteroids, or other solid solar system objects. The BaMS/XRF instrument is designed to be capable of concurrent sample analyses for the mineralogy of iron-bearing phases and elemental composition without the need for sample preparation.

  14. Investigations of Iron Minerals Formed by Dissimilatory Alkaliphilic Bacterium with {sup 57}Fe Moessbauer Spectroscopy

    SciTech Connect

    Chistyakova, N. I.; Rusakov, V. S.; Shapkin, A. A.; Zhilina, T. N.; Zavarzina, D. G.; Kohout, J.

    2010-07-13

    Anaerobic alkaliphilic bacterium of Geoalkalibacter ferrihydriticus type (strain Z-0531), isolated from a bottom sediment sample from the weakly mineralized soda Lake Khadyn, have been analyzed. The strain uses the amorphous Fe(III)-hydroxide (AFH) as an electron acceptor and acetate CH{sub 3}COO{sup -} as an electron donor. Moessbauer investigations of solid phase samples obtained during the process of the bacterium growth were carried out at room temperature, 77.8 K, 4.2 K without and with the presence of an external magnetic field (6 T) applied perpendicular to the {gamma}-bebam.

  15. Magnetic properties and Moessbauer analyses of glass from the K-T boundary, Beloc, Haiti

    NASA Technical Reports Server (NTRS)

    Senftle, F. E.; Thorpe, A. N.; May, L.; Barkatt, A.; Adel-Hadadi, M. A.; Marbury, G. S.; Izett, G.; Sigurdsson, H.; Maurasse, F. J.-M. R.

    1993-01-01

    The experimental magnetic susceptibility, the temperature-independent component of the magnetic susceptibility, the magnetization, and the Curie constant have been measured for a number of specimens of glass from the K-T boundary found at Beloc, Haiti, and the results are compared with those of similar measurements of tektites. Because the Fe(3+)/Fe(2+) ratio is needed to calculate the magnetic parameters, Moessbauer spectroscopic measurements were also made. The data were consistent with the classification of the Beloc glasses as tektites.

  16. Moessbauer spectra of olivine-rich achondrites - Evidence for preterrestrial redox reactions

    NASA Technical Reports Server (NTRS)

    Burns, R. G.; Martinez, S. L.

    1991-01-01

    Moessbauer spectral measurements at 4.2 K were made on several ureilites and the two shergottites found in Antarctica, as well as two ureilite falls, three SNC meteorite falls, and two finds in order to distinguish products of preterrestrial redox reactions from phases formed during oxidative weathering on the earth. The spectra indicated that several ureilites contain major proportions of metallic iron, much of which resulted from preterrestrial carbon-induced reduction of ferrous iron in the outermost 10-100 microns of olivine grains in contact with carbonaceous material in the ureilites. The cryptocrystalline nature of these Fe inclusions in olivine renders the metal extremely vulnerable to aerial oxidation, even in ureilites collected as falls. It is inferred that the nanophase ferric oxides or oxyhydroxides identified in Brachina and Lafayette were produced by terrestrial weather of olivines before the meteorites were found. The absence of goethite in two olivine-bearing Antarctic shergottites suggests that the 2 percent ferric iron determined in their Moessbauer spectra also originated from oxidation on Mars.

  17. Electronic structure properties of neptunium intermetallics under pressure from Moessbauer spectroscopy

    NASA Astrophysics Data System (ADS)

    Kalvius, G. M.; Potzel, W.; Zwirner, S.; Gal, J.; Nowik, I.

    1994-10-01

    Electronic structure properties of neptunium intermetallics obtained by the 60 keV Moessbauer resonance in Np-237 in the pressure range up to 9 GPa and at temperatures from 1.5 K to about 150 K together with X-ray determinations of the bulk modulus are discussed. Samples of the NaCl compounds NpX, the Laves phases NpX2 and the AuCu3 materials NpX3 as well as the tetragonal series NpX2S2 have been studied. The volume coefficients of magnetic moment and magnetic transition temperature allow the classification in terms of 5f bandwidth arising either from 5f-5f overlap or hybridization with ligand s, p, or d electrons. The pressure-temperature magnetic phase diagram of some of these compounds has also been investigated. In NpGa3 and NpIn3 we find a preference for ferromagnetic order under reduced volume. Finally we address the question of crystal field interactions and show that even in a somewhat delocalized case (NpAl2) they are decisive in determining the high pressure Moessbauer spectra.

  18. An East to West Mineralogical Trend in Mars Exploration Rover Spirit Moessbauer Spectra of Home Plate

    NASA Technical Reports Server (NTRS)

    Schroder, C.; Di, K.; Morris, R. V.; Klingelhofer, G.; Li, R.

    2008-01-01

    Home Plate is a light-toned plateau approx.90 m in diameter within the Inner Basin of the Columbia Hills in Gusev crater on Mars. It is the most extensive exposure of layered bedrock encountered by Spirit to date, and it is composed of clastic rocks of moderately altered alkali basalt composition, enriched in some highly volatile elements. Textural observations suggest an explosive origin and geochemical observations favor volcanism, probably a hydrovolcanic explosion [1]. Since it first arrived at Home Plate on sol 744, Spirit has circumnavigated the plateau (Fig. 1) and is now, since sol 1410, resting at its Winter Haven 3 location at the north end of Home Plate. Results: The MER Moessbauer spectrometers determine Fe oxidation states, identify Fe-bearing mineral phases and quantify the distribution of Fe among oxidation states and mineral phases [2]. Moessbauer spectra of Home Plate bedrock were obtained in five different locations from nine different targets (Fig. 1): Barnhill Ace, Posey Manager, and James Cool Papa Bell Stars at the northwest side of Home Plate; Pesapallo, June Emerson, and Elizabeth Emery on the east side; Texas Chili on the south side; Pecan Pie on the west side; and Chanute on the north side.

  19. Multilevel relaxation model for describing the Moessbauer spectra of nanoparticles in a magnetic field

    SciTech Connect

    Chuev, M. A.

    2012-04-15

    A theory is developed for the Moessbauer absorption spectra of an ensemble of single-domain particles in a magnetic field. This theory is based on the generalization of a relaxation model with a quantummechanical description of the stationary states of a particle and on the formalism of Liouville operators for describing the hyperfine interaction for a hyperfine field changing in both the magnitude and direction for various stationary states. The general scheme of calculating relaxation Moessbauer spectra in terms of a standard stochastic approach is substantially optimized using operations with block matrices and a unique tridiagonalization of high-rank non-Hermitian matrices with a simple nonorthogonal transformation in the calculation procedure. The resulting model can easily be implemented on a personal computer. It considers the physical mechanisms of formation of a hyperfine structure in a spectrum of nanoparticles in a real situation and self-consistently describes the qualitative features of the nontrivial evolution of spectra with the temperature and the magnetic-field direction and strength, which has been detected in {sup 57}Fe nucleus experiments performed on magnetic nanoparticles for half a century.

  20. Fe-Bearing Phases Identified by the Moessbauer Spectrometers on the Mars Exploration Rovers: An Overview

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; Klingelhoefer, G.; Rodionov, D.; Yen, A.; Gellert, R.

    2006-01-01

    The twin Mars Exploration Rovers Spirit and Opportunity have explored the martian surface at Gusev Crater (GC) and Meridiani Planum (MP), respectively, for about two Earth years. The Moessbauer (MB) spectrometers on both rovers have analyzed an aggregate of 200 surface targets and have returned to Earth information on the oxidation state of iron, the mineralogical composition of Febearing phases, and the distribution of Fe among oxidation states and phases at the two landing sites [1-7]. To date, 15 component subspectra (10 doublets and 5 sextets) have been identified and most have been assigned to mineralogical compositions. Two subspectra are assigned to phases (jarosite and goethite) that are marker minerals for aqueous processes because they contain hydroxide anion in their structures. In this paper, we give an overview of the Febearing phases identified and their distributions at Gusev crater and Meridiani Planum.

  1. Fe-Bearing Phases Indentified by the Moessbauer Spectrometers on the Mars Exploration Rovers: An Overview

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; Klingelhoefer, G.; Ming, D. W.; Schroeder, C.; Rodionov, D.; Yen, A.; Gellert, R.

    2006-01-01

    The twin Mars Exploration Rovers Spirit and Opportunity have explored the martian surface at Gusev Crater (GC) and Meridiani Planum (MP), respectively, for about two Earth years. The Moessbauer (MB) spectrometers on both rovers have analyzed an aggregate of approx.200 surface targets and have returned to Earth information on the oxidation state of iron, the mineralogical composition of Fe-bearing phases, and the distribution of Fe among oxidation states and phases at the two landing sites [1-7]. To date, 15 component subspectra (10 doublets and 5 sextets) have been identified and most have been assigned to mineralogical compositions. Two subspectra are assigned to phases (jarosite and goethite) that are marker minerals for aqueous processes because they contain hydroxide anion in their structures. In this paper, we give an overview of the Febearing phases identified and their distributions at Gusev crater and Meridiani Planum.

  2. Moessbauer study of amorphous (FeTM){sub 80}B{sub 20}

    SciTech Connect

    Orue, I.; Plazaola, F.; Fernandez-Gubieda, M.L.; Gutierrez, J.; Barandiaran, J.M.

    1994-03-01

    As-cast ferromagnetic amorphous alloys of nominal composition (FeTM){sub 80}B{sub 20} have been studied by Moessbauer Spectroscopy, being TM one transition metal atom, Ni, Cr, Mo or Pd. A detailed analysis of the isomer shift, IS, and hyperfine field distribution, HFD, at Fe sites is reported in order to achieve some conclusions about the Chemical Short Range Order and the electronic structure in these alloys. HFD changes found in (FeNi)B for Ni rich concentrations suggest the existence of Fe atoms strongly interacting with Ni. Small amounts of Cr and Mo shift the HFD to lower values of hyperfine field, B{sub hf}, while Pd enhances the B{sub hf}.

  3. Moessbauer analysis of Lewisville, Texas, archaeological site lignite and hearth samples. Environmental geology notes

    SciTech Connect

    Shiley, R.H.; Hughes, R.E.; Cahill, R.A.; Konopka, K.L.; Hinckley, C.C.

    1985-01-01

    The Lewisville site, located in Denton County on the Trinity River north of Dallas, Texas, was thought to provide evidence of the earliest human activity in the western hemisphere. Radiocarbon dates of 37,000 to 38,000 B.P. determined for the site in the late 1950s conflicted with the presence of a Clovis point, which would fix the age of the site between 11,000 and 11,500 B.P. It was hypothesized (Johnson, 1982) that Clovis people were burning lignite from nearby outcrops: lignite in hearth residues would give older than actual ages by radiocarbon dating. X-ray diffraction and instrumental neutron-activation analysis proved inconclusive; however, Moessbauer spectroscopy indicated that hematite, a pyrite combustion product, was present in the ash. From this evidence the authors conclude that there is some support for the hypothesis.

  4. Chemostratigraphy and Fe Mineralogy of the Victoria Crater Duck Bay Section: Opportunity APXS and Moessbauer Results

    NASA Technical Reports Server (NTRS)

    Mittlefehldt, D. W.; Schroeder, C.; Gellert, R.; Klingelhoefer, G.; Jolliff, B. L.; Morris, R. V.

    2008-01-01

    Meridiani Planum is a vast plain of approximately horizontally bedded sedimentary rocks composed of mixed and reworked basaltic and evaporitic sands containing secondary, diagenetic minerals [e.g., 1-5]. Because bedding planes are subparallel to topography, investigation of contiguous stratigraphy requires examining exposures in impact craters. Early in the mission (sols 130-317), Opportunity was commanded to do detailed study of exposed outcrops in Endurance crater, including the contiguous Karatepe section at the point of ingress. Just over 1000 sols later and roughly 7 km to the south, the rover is being commanded to do a similar study of the Duck Bay section of Victoria crater. Here we report on the preliminary results from the Alpha Particle X-ray Spectrometer (APXS) and Moessbauer instruments.

  5. Development of the Fast Scintillation Detector with Programmable High Voltage Adjustment Suitable for Moessbauer Spectroscopy

    SciTech Connect

    Prochazka, R.; Frydrych, J.; Pechousek, J.

    2010-07-13

    This work is focused on a development of a compact fast scintillation detector suitable for Moessbauer spectroscopy (low energy X-ray/{gamma}-ray detection) where high counting rates are inevitable. Optimization of this part was necessary for a reliable function, better time resolution and to avoid a detector pulses pile-up effect. The pile-up effect decreases the measurement performance, significantly depends on the source activity and also on the pulse duration. Our new detection unit includes a fast scintillation crystal YAP:Ce, an R6095 photomultiplier tube, a high voltage power supply socket C9028-01 assembly, an AD5252 digital potentiometer with an I2C interface and an AD8000 ultra fast operation preamplifier. The main advantages of this solution lie in a short pulse duration (less than 200 ns), stable operation for high activities, programmable gain of the high voltage supply and compact design in the aluminum housing.

  6. Mineralogy at Gusev Crater and Meridiani Planum from the Moessbauer Spectrometers on the Mars Exploration Rovers

    NASA Technical Reports Server (NTRS)

    Morris, Richard V.; Klingelhoefer, Goestar

    2006-01-01

    The Moessbauer spectrometers on the twin MER rovers Spirit and Opportunity have provided significant new information on the distribution of iron among its oxidation states, the identification of the mineralogical composition of iron-bearing phases, and the distribution of iron among those phases for rock and soil at Gusev Crater and Meridiani Planum. The plains of Gusev Crater are dominated by olivine-bearing basalt (approximately Fo(60)) and Fe(3+)/Fe(total)=0.1 - 0.5. The oxide mineral generally present is magnetite. In contrast, initial results for the Columbia Hills are consistent with the presence of hematite and a ferrous iron phase, possibly pyroxene. Gusev spectra also have a ferric doublet (not jarosite) that is tentatively associated with nano-phase ferric oxide. A wider diversity of material is present at Meridiani Planum. Significantly, jarosite-bearing outcrop is present throughout the region, with good exposures in impact craters such as Eagle and Endurance (Fe(3+)/Fe (total) approx. 0.9). The Moessbauer identification of jarosite (a hydroxyl-bearing sulfate mineral) is evidence for aqueous, acid-sulfate processes on Mars. Hematite is observed within the outcrop matrix and in the spheroidal particles (Blueberries) found within the outcrop and as a surface lag. An isolated rock (Bounce Rock) was the only sample at either landing site whose iron-bearing phase was dominated by pyroxene. The basaltic sand in the central portion of Eagle crater, in the intercrater plains, and between slabs of outcrop at both Eagle and Endurance craters is olivine-bearing basalt. The widespread occurrence of olivine-bearing basalt at both MER landing sites implies that physical, rather than chemical, weathering processes dominate at the surface of contemporary Mars.

  7. Engineering Design Handbook: Recoilless Rifle Weapon Systems.

    DTIC Science & Technology

    1976-01-15

    the extra area, the skin friction is increased. For complete internal expansion by Although many nozzles use a divergence 6-17 6 ’•-,,>,••"••’"Y:"I...Basis ted Shoe Maclinery Corp., Beverly, for Design of Tube Sheets of Triangular Mass., Contract DA-19-020-ORD-1847, la yout ", Tro, s. ASME, April 195 2

  8. Identification of Iron-Bearing Phases on the Martian Surface and in Martian Meteorites and Analogue Samples by Moessbauer Spectroscopy

    NASA Technical Reports Server (NTRS)

    Klingelhoefer, G.; Agresti, D. G.; Schroeder, C.; Rodionov, D.; Yen, A.; Ming, Doug; Morris, Richard V.

    2007-01-01

    The Moessbauer spectrometers on the Mars Exploration Rovers (MER) Spirit (Gusev Crater) and Opportunity (Meridiani Planum) have each analyzed more than 100 targets during their ongoing missions (>1050 sols). Here we summarize the Fe-bearing phases identified to date and compare the results to Moessbauer analyses of martian meteorites and lunar samples. We use lunar samples as martian analogues because some, particularly the low-Ti Apollo 15 mare basalts, have bulk chemical compositions that are comparable to basaltic martian meteorites [1,2]. The lunar samples also provide a way to study pigeonite-rich samples. Pigeonite is a pyroxene that is not common in terrestrial basalts, but does often occur on the Moon and is present in basaltic martian meteorites

  9. Design and Construction of an Autonomous Low-Cost Pulse Height Analyzer and a Single Channel Analyzer for Moessbauer Spectroscopy

    SciTech Connect

    Velasquez, A.A.; Trujillo, J.M.; Morales, A.L.; Tobon, J.E.; Gancedo, J.R.; Reyes, L.

    2005-04-26

    A multichannel analyzer (MCA) and a single channel-analyzer (SCA) for Moessbauer spectrometry application have been designed and built. Both systems include low-cost digital and analog components. A microcontroller manages, either in PHA or MCS mode, the data acquisition, data storage and setting of the pulse discriminator limits. The user can monitor the system from an external PC through the serial port with the RS232 communication protocol. A graphic interface made with the LabVIEW software allows the user to adjust digitally the lower and upper limits of the pulse discriminator, and to visualize as well as save the PHA spectra in a file. The system has been tested using a 57Co radioactive source and several iron compounds, yielding satisfactory results. The low cost of its design, construction and maintenance make this equipment an attractive choice when assembling a Moessbauer spectrometer.

  10. Moessbauer and Electron Microprobe Studies of Density Separates of Martian Nakhlite Mil03346: Implications for Interpretation of Moessbauer Spectra Acquired by the Mars Exploration Rovers

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; McKay, G. A.; Agresti, D. G.; Li, Loan

    2008-01-01

    Martian meteorite MIL03346 is described as an augite-rich cumulate rock with approx.80%, approx.3%, and approx.21% modal phase proportions of augite (CPX), olivine and glassy mesostasis, respectively, and is classified as a nakhlite [1]. The Mossbauer spectrum for whole rock (WR) MIL 03346 is unusual for Martian meteorites in that it has a distinct magnetite subspectrum (7% subspectral area) [2]. The meteorite also has products of pre-terrestrial aqueous alteration ("iddingsite") that is associated primarily with the basaltic glass and olivine. The Mossbauer spectrometers on the Mars Exploration Rovers have measured the Fe oxidation state and the Fe mineralogical composition of rocks and soils on the planet s surface since their landing in Gusev Crater and Meridiani Planum in January, 2004 [3,4]. The MIL 03346 meteorite provides an opportunity to "ground truth" or refine Fe phase identifications. This is particularly the case for the so-called "nanophase ferric oxide" (npOx) component. NpOx is a generic name for a ferric rich product of oxidative alteration. On Earth, where we can take samples apart and study individual phases, examples of npOx include ferrihydrite, schwertmannite, akagaaneite, and superparamagnetic (small particle) goethite and hematite. It is also possible for ferric iron to be associated to some unknown extent with igneous phases like pyroxene. We report here an electron microprobe (EMPA) and Moessbauer (MB) study of density separates of MIL 03346. The same separates were used for isotopic studies by [5]. Experimental techniques are described by [6,7].

  11. Moessbauer study on K/sub 2/Fe/sub 2/(CO)/sub 8/ in an external magnetic field

    SciTech Connect

    Arkhipov, I.L.; Kireev, N.V.; Stukan, R.A.; Yunusov, S.M.

    1988-03-01

    We consider in more detail what changes occur in the Moessbauer parameters when apical and equatorial CO groups are replaced by Fe(CO)/sub 4//sup =/ in the trigonal bipyramidal Fe(CO)/sub 5/ molecule. We use Bancroft's concept of the partial contributions to the quadrupole splitting (QS). The main difference between the HFS parameters for the Moessbauer spectra for the possible structures will be a marked difference in the asymmetry parameters. Here /eta/ can be determined for 1/2 /yields/ 3/2 transitions if there is combined hyperfine magnetic and quadrupole interaction. In a diamagnetic (K/sub 2/Fe/sub 2/(CO)/sub 8/), such combined interaction can occur only from the use of external magnetic fields. The Moessbauer spectra were recorded in an Oxford Instruments cryostat having a superconducting solenoid at 4.2 K without a field or with a longitudinal field of 4.6 T. The spectra show that the EFG tensor for K/sub 2/Fe/sub 2/(CO)/sub 8/ is axially symmetric (/eta/ 0) and that the sign of QS is positive.

  12. Fractional randomness

    NASA Astrophysics Data System (ADS)

    Tapiero, Charles S.; Vallois, Pierre

    2016-11-01

    The premise of this paper is that a fractional probability distribution is based on fractional operators and the fractional (Hurst) index used that alters the classical setting of random variables. For example, a random variable defined by its density function might not have a fractional density function defined in its conventional sense. Practically, it implies that a distribution's granularity defined by a fractional kernel may have properties that differ due to the fractional index used and the fractional calculus applied to define it. The purpose of this paper is to consider an application of fractional calculus to define the fractional density function of a random variable. In addition, we provide and prove a number of results, defining the functional forms of these distributions as well as their existence. In particular, we define fractional probability distributions for increasing and decreasing functions that are right continuous. Examples are used to motivate the usefulness of a statistical approach to fractional calculus and its application to economic and financial problems. In conclusion, this paper is a preliminary attempt to construct statistical fractional models. Due to the breadth and the extent of such problems, this paper may be considered as an initial attempt to do so.

  13. Moessbauer and Positron Annihilation Spectroscopy Applied to WWER-1000 RPV Steels

    SciTech Connect

    Slugen, V.; Lipka, J.; Zeman, A.; Debarberis, L.

    2005-04-26

    Moessbauer spectroscopy (MS) and Positron annihilation spectroscopy (PAS) were applied in the evaluation of the microstructure parameters and degradation processes of nuclear reactor pressure vessel (RPV) steel surveillance specimens. Study was oriented to the material investigation of Russian WWER-1000 steels (15Kh2MNFAA and 12Kh2N2MAA) with higher Ni content (1.26 wt.% in base metal and 1.7 wt.% in weld). For comparison, the WWER-440 weld metal (Sv10KhMFT) without Ni was measured too. Specimens were studied in as received form, after irradiation in LVR-15 experimental reactor to the neutron fluence F(E>0.5 MeV) = 1.47x1024 m-2s-1 and after annealing process in vacuum at 475 deg. C/2h. Changes due to different chemical composition and due to irradiation were registered using MS. Post-irradiation thermal treatment and annealing of defects was well detected by different PAS techniques. Results confirm the hypothesis that Ni affects size (decrease) and distribution (more homogeneous) of the Cu- and P-rich clusters and MxCx carbides.

  14. Coal liquefaction process streams characterization and evaluation: Investigation of the forms of sulfur in five Wilsonville resid samples by XAFS and moessbauer spectroscopy

    SciTech Connect

    Huffman, G.P.; Huggins, F.E.; Shah, N. . Consortium for Fossil Fuel Science)

    1992-11-01

    This study demonstrated the feasibility of using XAFS and Moessbauer spectroscopy for the examination of distillation resid materials derived from direct coal liquefaction. The least-squares analysis of the XANES region of the K-shell XAFS spectra was shown to be technique which can be used to determine the sulfur forms in coal liquefaction-derived resid samples. The large amount of pyrrhotite in the resid samples (71 to 99% [plus minus]10% of the total sulfur) interfered with the precise quantitative analysis of the organic sulfur. However, a spectral subtraction routine was successfully used to provide semi-quantitative results for sulfur species other than the pyrrhotite. Moessbauer spectroscopy, considered a more accurate method than XAFS for the quantitative analysis of inorganic iron-sulfur species (pyrite, pyrrhotite, iron sulfates), was successfully used to speciate these materials in the coal liquefaction resids. Further application of XAFS and Moessbauer spectroscopy as process development tools appears justified by these results.

  15. Coal liquefaction process streams characterization and evaluation: Investigation of the forms of sulfur in five Wilsonville resid samples by XAFS and moessbauer spectroscopy

    SciTech Connect

    Huffman, G.P.; Huggins, F.E.; Shah, N.

    1992-11-01

    This study demonstrated the feasibility of using XAFS and Moessbauer spectroscopy for the examination of distillation resid materials derived from direct coal liquefaction. The least-squares analysis of the XANES region of the K-shell XAFS spectra was shown to be technique which can be used to determine the sulfur forms in coal liquefaction-derived resid samples. The large amount of pyrrhotite in the resid samples (71 to 99% {plus_minus}10% of the total sulfur) interfered with the precise quantitative analysis of the organic sulfur. However, a spectral subtraction routine was successfully used to provide semi-quantitative results for sulfur species other than the pyrrhotite. Moessbauer spectroscopy, considered a more accurate method than XAFS for the quantitative analysis of inorganic iron-sulfur species (pyrite, pyrrhotite, iron sulfates), was successfully used to speciate these materials in the coal liquefaction resids. Further application of XAFS and Moessbauer spectroscopy as process development tools appears justified by these results.

  16. 57Fe- and 119Sn-Moessbauer Studies of Tin Doped Chromium Iron Oxides of Composition {alpha}-Cr2-xFexO3

    SciTech Connect

    Helgason, Oern; Berry, Frank J.; Ren Xiaolin; Moyo, Thomas

    2005-04-26

    Tin-doped iron chromium oxides of composition {alpha}-Cr2-xFexO3 prepared by the calcination of precipitates adopt the corundum-related structure. 57Fe Moessbauer spectroscopy shows the materials to be composed of small superparamagnetic particles and no evidence for a Morin transition was observed above 80K. The supertransferred hyperfine magnetic field at the tin site is shown by 119Sn Moessbauer spectroscopy to be less than that experienced in tin-doped {alpha}-Fe2O3.

  17. Iron Mineralogy and Aqueous Alteration on Mars from the MER Moessbauer Spectrometers. Chapter 15

    NASA Technical Reports Server (NTRS)

    Morris, Richard V.; Klingelhoefer, Goestar

    2007-01-01

    The twin Mars Exploration Rovers Spirit (Gusev crater) and Opportunity (Meridiani Planum) used MIMOS II Moessbauer spectrometers to analyze martian surface materials in the first application of extraterrestrial Moessbauer spectroscopy. The instruments acquired spectra that identified the speciation of Fe according to oxidation state, coordination state, and mineralogical composition and provided quantitative information about the distribution of Fe among oxidation states, coordination states, and Fe-bearing phases. A total of 12 unique Fe-bearing phases were identified: Fe(2+) in olivine, pyroxene, and ilmenite; Fe(2+) and Fe(3+) in magnetite and chromite; Fe(3+) in nanophase ferric oxide (npOx), hematite, goethite, jarosite, an unassigned Fe3+ sulfate, and an unassigned Fe(3+) phase associated with jarosite; and Fe(0) in kamacite. Weakly altered basalts at Gusev crater (SO3 = 2.5 +/- 1.4 wt.% and Fe(3+)/Fe(sub T) = 0.24 +/- 0.11) are widespread on the Gusev plains and occur in less abundance on West Spur and Husband Hill in the Columbia Hills. Altered low-S rocks (SO3 = 5.2 +/- 2.0 wt.% and Fe(3+)/Fe(sub T) = 0.63 +/- 0.18) are the most common type of rock in the Columbia Hills. Ilm-bearing, weakly altered basalts were detected only in the Columbia Hills, as was the only occurrence of chromite in an altered low-S rock named Assemblee. Altered high-S rocks (SO3 > 14.2 wt.% and Fe(3+)/Fe(sub T) = 0.83 +/- 0.05) are the outcrop rocks of the ubiquitous Burns formation at Meridiani Planum. Two Fe(0)-bearing rocks at Meridiani Planum (Barberton and Heat Shield Rock) are meteorites. Laguna Class soil is weakly altered (SO3 = 6 +/- 2 wt.% and Fe(3+)/Fe(sub T) = 0.29 +/- 0.08) and widely distributed at both Gusev crater and Meridiani Planum, implying efficient global mixing processes or a global distribution of precursor rocks with comparable Fe mineralogical compositions. Paso Robles Class soil is heavily altered (SO3 approx. 31 wt.% and Fe(3+)/Fe(sub T) = 0.83 +/- 0

  18. Moessbauer study of iron-carbide growth and Fischer-Tropsch activity

    SciTech Connect

    Rao, K.R.P.M.; Huggins, F.E.; Huffman, G.P.

    1995-12-31

    There is a need to establish a correlation between the Fischer-Tropsch (FT) activity of an iron-based catalyst and the catalyst phase during FT synthesis. The nature of iron phases formed during activation and FT synthesis is influenced by the gas used for activation. Moessbauer investigations of iron-based catalysts subjected to pretreatment in gas atmospheres containing mixtures of CO, H{sub 2}, and He have been carried out. Studies on UCI 1185-57 catalyst indicate that activation of the catalyst in CO leads to the formation of 100% magnetite and the magnetite formed gets rapidly converted to at least 90% of x-Fe{sub 5}C{sub 2} during activation. The x-Fe{sub 5}C{sub 2} formed during activation gets partly (= 25%) converted back to Fe{sub 3}O{sub 4} during FT synthesis and both x-Fe{sub 5}C{sub 2} and Fe{sub 3}O{sub 4} reach constant values. On the other hand, activation of the catalyst in synthesis gas leads to formation of Fe{sub 3}O{sub 4} and which is slowly converted to x-Fe{sub 5}C{sub 2} and e-Fe{sub 2.2}C during activation, and both carbide phases increase slowly during FT synthesis. FT synthesis activity is found to give rise to {approx} 70% (H2+CO) conversion in the case of CO activated catalyst as compared to {approx} 20% (H2+CO) conversion in the case of synthesis gas-activated catalyst.

  19. Moessbauer Mineralogical Evidence for Aqueous Processes at Gusev Crater and Meridiani Planum

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; Klingelhoefer, G.

    2006-01-01

    The Moessbauer spectrometers on the MER rovers have measured the relative abundances of iron with respect to both oxidation state and iron-bearing phase at Gusev Crater (Spirit rover) and Meridiani Planum (Opportunity rover). The assemblage of phases indicates aqueous alteration processes at both landing sites. Although the rock and soil of the Gusev Crater plains are dominated by Fe(2+) in olivine-bearing basalt (approx.Fo60), a Fe(3+)-rich component (nanophase ferric oxide, np-Ox) has significant abundance in surface soils (13-28% of total Fe) and in the surface coatings (rinds) of certain rocks (39%) but not in rock interiors exposed by grinding (5-6%). The mode of occurrence of np-Ox implies that it is the product of oxidative alteration of Fe(2+) silicate and oxide phases in the presence of H2O. The ubiquitous presence of sulfur in soil and in rock coatings, as determined by the MER-A APXS instrument, suggests that the alteration occurred under acid-sulfate conditions, so that both hydrolytic and sulfatic reactions are viable. A possible source for the weathering agents is volcanic emanations rich in H2O and SO2. Generally, rocks in the Columbia Hills are significantly more altered than those in the Gusev plains, with a higher proportion of Fe(3+) oxide phases compared to Fe(2+) silicate phases. This mineralogical dichotomy implies a difference in the timing, rate, duration, and/or mechanism of alteration for basaltic material in the Gusev plains compared to basaltic material in the Columbia Hills. It is possible, for example, that the basaltic material in the Columbia Hills underwent aqueous alteration in a paleoclimate that favored nearly complete alteration and that the basaltic material of the Gusev plains will not achieve the degree of alteration exhibited by the Columbia Hills under current martian surface conditions.

  20. Moessbauer Spectroscopy for Lunar Resource Assessment: Measurement of Mineralogy and Soil Maturity

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; Agresti, D. G.; Shelfer, T. D.; Pimperl, M. M.; Shen, M.-H.; Gibson, M. A.; Wills, E. L.

    1992-01-01

    First-order assessment of lunar soil as a resource includes measurement of its mineralogy and maturity. Soils in which the mineral ilmenite is present in high concentrations are desirable feedstock for the production of oxygen at a lunar base. The maturity of lunar soils is a measure of their relative residence time in the upper 1 mm of the lunar surface. Increasing maturity implies increasing load of solar wind species (e.g., N, H, and He-3), decreasing mean grain size, and increasing glass content. All these physicochemical properties that vary in a regular way with maturity are important parameters for assessing lunar soil as a resource. For example, He-3 can be extracted and potentially used for nuclear fusion. A commonly used index for lunar soil maturity is I(sub s)/FeO, which is the concentration of fine-grained metal determined by ferromagnetic resonance (I(sub s)) normalized to the total iron content (as FeO). I(sub s)/FeO has been measured for virtually every soil returned by the Apollo and Luna missions to the Moon. Because the technique is sensitive to both oxidation state and mineralogy, iron Moessbauer spectroscopy (FeMS) is a viable technique for in situ lunar resource assessment. Its utility for mineralogy is apparent from examination of published FeMS data for lunar samples. From the data published, it can be inferred that FeMS data can also be used to determine soil maturity. The use of FeMS to determine mineralogy and maturity and progress on development of a FeMS instrument for lunar surface use are discussed.

  1. Understanding Multiplication of Fractions.

    ERIC Educational Resources Information Center

    Sweetland, Robert D.

    1984-01-01

    Discussed the use of Cuisenaire rods in teaching the multiplication of fractions. Considers whole number times proper fraction, proper fraction multiplied by proper fraction, mixed number times proper fraction, and mixed fraction multiplied by mixed fractions. (JN)

  2. Iron Moessbauer spectroscopy: Superparamagnetism in hydrothermal vents and the search for evidence of past life on Mars

    NASA Technical Reports Server (NTRS)

    Agresti, David G.; Wdowiak, Thomas J.

    1992-01-01

    In view of the demonstrated value of Iron Moessbauer Spectroscopy (FeMS) in the study of extraterrestrial iron and the fact that, after silicon and oxygen, iron is the most abundant element on the surface of Mars, we proposed, and have under development, a backscatter Moessbauer spectrometer with x ray fluorescence capability (BaMS/XRF) for use on Mars as a geophysical prospecting instrument. Specifically, we have proposed BaMS/XRF as part of the geochemistry instrumentation on NASA's Mars Environment Survey (MESUR) mission. BaMS/XRF will have applications in: (1) the study of past environments through the examination of sedimentary material; (2) the study of the contemporary Martian environment; and (3) the study of iron-containing minerals of possible biogenic origin. Development of a reference library from a geophysical point of view for putative Martian surface materials at appropriate temperatures is now underway. We carried out preliminary optical reflectance and FeMS measurements on mineral products (iron oxyhydroxides) of deep-sea hydrothermal activity. Various aspects of this investigation are presented.

  3. Local environment of iron in heavy ion-irradiated amorphous magnetic oxides by Moessbauer and x-ray absorption spectroscopy

    SciTech Connect

    Studer, F.; Houpert Ch. ); Toulemonde, M. ) Dartyge E. )

    1991-04-01

    Moessbauer and X-ray absorption spectroscopies of some crystallized iron oxides, Fe{sub 2}O{sub 3}, FePO{sub 4}, Fe{sub 3}PO{sub 7}, and SrMn{sub 1.85}Fe{sub 0.15}O{sub 2.5}, the garnet Y{sub 3}Fe{sub 5}O{sub 12}, and the barium hexaferrite BaFe{sub 12}O{sub 19} have been undertaken in order to look at the local order around iron in Y{sub 3}Fe{sub 5}O{sub 12} and BaFe{sub 12}O{sub 19} materials amorphized by irradiation with high energy (27 MeV/n) xenon ions accelerated by GANIL. Simulations of the Moessbauer spectra suggested the presence of fivefold coordinated iron in the amorphous irradiated compounds with a distribution of magnetic interactions due to the variations of the number of iron second neighbors. The XANES spectra at the Fe-K edge confirmed the fivefold coordination of iron in the amorphous ferrites, show that the local structure around iron appears to be similar although the original structures were different, and appear close to the one observed in the Fe{sub 3}PO{sub 7} compound in which iron stands in a trigonal bipyramidal environment.

  4. Determination of the Moessbauer parameters of rare-earth nitroprussides: Evidence for new light-induced magnetic excited state (LIMES) in nitroprussides

    SciTech Connect

    Rusanov, V.; Stankov, S.; Ahmedova, A.; Trautwein, A.X.

    2009-05-15

    Nitroprussides of the rare-earth elements and some mixed rare-earth-sodium nitroprussides are studied by Moessbauer spectroscopy at ambient and lower temperatures. The high precision Moessbauer measurements reveal fine changes in the electronic configurations of the nitroprusside anions. A small increase of the quadrupole splitting reveals charge polarization effects in the nitroprusside anion caused by the oblate or prolate shape of the rare-earth ion and the lanthanide contraction. Despite the very large magnetic moment of holmium a magnetic phase transition is not observed down to 300 mK. The population of the metastable states SI and SII are evidenced in europium and scandium nitroprussides, and most likely they can be populated in all rare-earth nitroprussides. No distinct correlation between the Moessbauer parameters and the decay temperatures T{sub c} of the metastable states are found. In a very thin surface layer strong color change, which remains stable at room temperature, is detected. A quadrupole doublet with Moessbauer parameters typical for Fe(III), low spin S=1/2 state is related to a new colored photoproduct. The photoproduct is called light-induced magnetic excited state (LIMES) and explained with a photochemical redox reaction, which changes the valence, spin, and magnetic state of 4f-3d bimetallic complexes. - Graphical abstract: Rare-earth nitroprussides are studied by Moessbauer spectroscopy. Population of metastable states in a thin surface layer, and another state which remains stable at room temperature, are detected. The latter is a photoproduct which is called light-induced magnetic excited state (LIMES) and explained with a photochemical redox reaction, which changes the valence, spin, and magnetic state of 4f-3d bimetallic complexes.

  5. Mystery Fractions

    ERIC Educational Resources Information Center

    Bhattacharyya, Sonalee; Namakshi, Nama; Zunker, Christina; Warshauer, Hiroko K.; Warshauer, Max

    2016-01-01

    Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

  6. Pitch Fractionation.

    DTIC Science & Technology

    1981-12-15

    13 3. Solvent Fractionation Experiments .................................... 15 4. Fourier Transform Infrared Spectra for A240 Petrolem Pitch AG 12...34 and Mesophase Pitch AG 164B ............................... 21 5. Fourier Transform Infrared Spectra ................................... 23 6...compared by Fourier transform infrared (FTIR) analysis using a Digilab Model FTS 14 spectrophotometer (Rockwell International, Anaheim, California

  7. Moessbauer study of iron-carbide growth and Fischer-Tropsch activity

    SciTech Connect

    Rao, K.R.P.M.; Huggins, F.E.; Huffman, G.P.

    1995-12-31

    There is a need to establish a correlation between the Fischer-Tropsch (FT) activity of an iron-based catalyst and the catalyst phase during FT synthesis. The nature of iron phases formed during activation and FT synthesis is influenced by the nature of the gas and pressure apart from other parameters like temperature, flow rate etc., used for activation. Moessbauer investigations of iron-based catalysts subjected to pretreatment at two different pressures in gas atmospheres containing mixtures of CO, H{sub 2}, and He have been carried out. Studies on UCI 1185-57 (64%Fe{sub 2}O{sub 3}/5%CuO/1%K{sub 2}O/30% Kaolin) catalyst indicate that activation of the catalyst in CO at 12 atms. leads to the formation of 100% magnetite and the magnetite formed gets rapidly converted to at least 90% of {chi}-Fe{sub 5}C{sub 2} during activation. The FT activity was found to be good at 70-80% of (H{sub 2}+CO) conversion. On the other hand, activation. The FT activity was found to be good at 70-80% of (H{sub 2}+CO) conversion. On the other hand, activation of the catalyst in synthesis gas at 12 atms. leads to formation of Fe{sub 3}O{sub 4} and it gets sluggishly converted to {chi}-Fe{sub 5}C{sub 2} and {epsilon}-Fe{sub 2.2}C during activation and both continue to grow slowly during FT synthesis. FT activity is found to be poor. Pretreatment of the catalyst, 100fe/3.6Si/0.71K at a low pressure of 1 atms. in syngas gave rise to the formation of {chi}-Fe{sub 5}C{sub 2} and good FT activity. On the other hand, pretreatment of the catalyst, 100Fe/3.6Si/0.71K at a relatively high pressure of 12 atms. in syngas did not give rise to the formation any carbide and FT activity was poor.

  8. Fraction Reduction through Continued Fractions

    ERIC Educational Resources Information Center

    Carley, Holly

    2011-01-01

    This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

  9. Isotope fractionation

    NASA Astrophysics Data System (ADS)

    Bell, Peter M.

    A rash of new controversy has emerged around the subject of mass-independent isotope fractionation effects, particularly in the case of the oxygen isotopes. To be sure, the controversy has been around for awhile, but it has been given new impetus by the results of a recent study by Mark H. Thiemens and John E. Heidenreich III of the University of California, San Diego (Science, March 4, 1983).Gustav Arrhenius has been trying to convince the planetary science community that chemical effects in isotope fractionation processes could explain observations in meteorites that appear to be outside of the traditionally understood mass-dependent fractionations (G. Arrhenius, J . L. McCrumb, and N. F. Friedman, Astrophys. Space Sci, 65, 297, 1974). Robert Clayton had made the basic observations of oxygen in carbonaceous chondrites that the slope of the δ17 versus δ18 line was 1 instead of the slope of ½ characteristic of terrestrial rocks and lunar samples (Ann. Rev. Nucl. Part. Sci., 28, 501, 1978). The mass-independent effects were ascribed to the apparent contribution of an ancient presolar system component of O16.

  10. Moessbauer and magnetic study of Mn, Zr and Cd substituted W-type hexaferrites prepared by co-precipitation

    SciTech Connect

    Iqbal, Muhammad Javed; Khan, Rafaqat Ali; Mizukami, Shigemi; Miyazaki, Terunobu

    2011-11-15

    Highlights: {yields} Zr and Cd ions substitute tetrahedral 4e and 4f{sub IV} sites while Mn ions occupy octahedral 6g and 4f sites. {yields} Doping of W-type hexaferrites with Mn, Zr and Cd improves the values of M{sub s} and M{sub r}. {yields} The enhancement of magnetic characteristic togetherwith the formation of rice shaped W-type hexaferrites nanoparticles is promising for imaging and sensing devices. {yields} The synthesized materials are suitable for magnetic data storage with high density. -- Abstract: BaCo{sub 2-x}Mn{sub x}Fe{sub 16-2y}(Zr-Cd){sub y}O{sub 27} (x = 0-0.5 and y = 0-1.0) hexaferrite nanocrystallites of average sizes in the range of 33-42 nm are synthesized by the chemical co-precipitation method. The synthesized materials are characterized using different techniques including X-ray diffraction (XRD), energy dispersive X-ray florescence (ED-XRF), scanning electron microscope (SEM), Moessbauer spectrometer and vibrating-sample magnetometer (VSM). Based on analysis of the data obtained from Moessbauer spectral studies, doping is believed to have occurred preferably in the vicinity of 12k sub-lattice, i.e. f{sub IV} (4e, 4f{sub IV}), 2b (6g, 4f) and 2d site. Variations in the saturation magnetization (77.1-60.9 emu g{sup -1}), remanent magnetization (22.08-31.23 emu g{sup -1}) and coercivity (1570.1-674.7 Oe) exhibit tunable behavior with dopant content and therefore can be useful for application in various magnetic devices.

  11. Characterization of magnetite in silico-aluminous fly ash by SEM, TEM, XRD, magnetic susceptibility, and Moessbauer spectroscopy

    SciTech Connect

    Gomes, S.; Francois, M.; Abdelmoula, M.; Refait, P.; Pellissier, C.; Evrard, O.

    1999-11-01

    Spinel magnetite contained in a silico-aluminous fly ash (originating from la Maxe's power plant, near Metz in the east of France) issued from bituminous coal combustion has been studied by scanning and transmission electron microscopy linked with energy dispersive spectroscopy. X-ray diffraction, susceptibility measurements, and Moessbauer spectroscopy. The results show that in this magnetite Mg is strongly substituted for Fe and the chemical formula is closer to MgFe{sub 2}O{sub 4} than Fe{sub 3}O{sub 4}. Magnetite also contains Mn, Ca, and Si elements, but at a lower proportion. The results are compatible with the chemical formula Fe{sub 2.08}Mg{sub 0.75}Mn{sub 0.11}Ca{sub 0.04}Si{sub 0.02}O{sub 4} and crystallochemical formula [Fe{sup 2{minus}}{sub 0.92}Ca{sup 2+}{sub 0.06}Si{sup 4+}{sub 0.02}]{sup tetra}[Fe{sup 3+}Fe{sup 2+}{sub 0.16}Mg{sup 2+}{sub 0.73}Mn{sup 2+}{sub 0.11}]{sup octa}O{sub 4}, showing the cation distribution on octahedral and tetrahedral sites of the spinel structure. The reason Mg element is not incorporated in soluble surface salt and in glass composition of the silico-aluminous fly ashes is now understood.

  12. The Incredible Diversity of Fe-bearing Phases at Gusev Crater, Mars, According to the Mars Exploration Rover Moessbauer Spectrometer

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; Klingelhoefer, G.; Schroeder, C.; Rodionov, D. S.; Ming, D. W.; Yen, A.

    2006-01-01

    The Mars Exploration Rover (MER) Spirit landed on the plains of Gusev Crater on 4 January 2004. One primary scientific objective for the mission is to characterize the mineralogical and elemental composition of surface materials, searching for evidence of water and clues for assessing past and current climates and their suitability for life [1]. The role of the Moessbauer (MB) spectrometer on Spirit is to provide quantitative information about the distribution of Fe among its oxidation and coordination states, identification of Fe-bearing phases, and relative distribution of Fe among those phases. The speciation and distribution of Fe in Martian rock and soil constrains the primary rock types, redox conditions under which primary minerals crystallized, the extent of alteration and weathering, the type of alteration and weathering products, and the processes and environmental conditions for alteration and weathering. In this abstract, we discuss the incredible diversity of Fe-bearing phases detected by Spirit s MB instrument during its first 540 sols of exploration at Gusev crater [2,3].

  13. Moessbauer Analysis of Fe94-xNb6Bx (x = 9, 14, 20) Alloys Developed by Mechanical Alloying

    SciTech Connect

    Bruna, P.

    2005-04-26

    The alloys were prepared by milling elemental powders in a planetary ball mill. XRD analysis of the powders indicate that a nanocrystalline heterogeneous bcc alloy was obtained. DSC study of the thermal stability of the powders obtained indicate that some grain growth and reordering of the structure was obtained at temperatures as low as 350 deg. C up to 600 deg. C. Room temperature Transmission Moessbauer spectroscopy from the as milled alloys as well as from the annealed alloys was performed to determine the structure, homogeneity and how the structure changed after annealing at 600 deg. C. The results indicate that the as milled alloys are mainly a crystalline bcc alloy containing most of the Fe, Nb and B. A small amount of a disordered/amorphous phase is also formed for the three alloys. Annealing of the to B richer alloys results in the diffusion of most of the B outside the alloy structure and the crystallization of Fe2B and {alpha}-Fe. Annealing the heterogeneous as-milled powders enhances the separation of Fe rich ({alpha}-Fe ), B rich (Fe2B) and Nb rich regions in the two richer in B alloys studied. On the contrary, the alloy x=9 does not change significantly during annealing.

  14. Combined Backscatter Moessbauer Spectrometer and X Ray Fluorescence analyzer (BaMS/XRF) for planetary surface materials

    NASA Technical Reports Server (NTRS)

    Agresti, D. G.; Shelfer, T. D.; Pimperl, M. M.; Wills, E. L.; Morris, R. V.

    1991-01-01

    A backscatter Moessbauer spectrometer (BaMS) with included x ray fluorescence (XRF) capability for the Mars Environment Survey (MESUR) Mission, which has been proposed by NASA for 1998, is being developed. The instrument will also be suitable for other planetary missions such as those to the Moon, asteroids, and other solid solar-system objects. The BaMS would be unique for MESUR in providing information about iron mineralogy in rocks, clays, and other surface materials, including relative proportions of iron-bearing minerals. It requires no sample preparation and can identify all the normal oxidation states of iron (3+, 2+, 0). Thus, BaMS is diagnostic for weathering and other soil-forming processes. Backscatter design allows the addition of XRF elemental analysis with little or no modification. The BaMS/XRF instrument complements the thermal analyzer with evolved gas analyzer (TA-EGA) and the alpha-proton x-ray spectrometer (APXS) proposed (along with BaMS) for geochemical analysis on MESUR.

  15. Equilibrium Iron Isotope Fractionation Factors of Minerals: Reevaluation from the Data of Nuclear Inelastic Resonant X-ray Scattering and Mossbauer Spectroscopy

    SciTech Connect

    Polyakov, Dr. V. B.; Clayton, R. N.; Horita, Juske; Mineev, S. D.

    2007-01-01

    We have critically reevaluated equilibrium iron isotope fractionation factors for oxide and sulfide minerals using recently acquired data obtained by Moessbauer spectroscopy and inelastic nuclear resonant X-ray scattering (INRXS) synchrotron radiation. Good agreement was observed in the iron {beta}-factors of metallic iron ({alpha}-Fe) and hematite calculated using both Moessbauer- and INRXS-derived data, which supports the validity and reliability of the calculations. Based on this excellent agreement, we suggest the use of the present data on the iron {beta}-factors of hematite as a reference. The previous Moessbauer-derived iron {beta}-factor for magnetite has been modified significantly based on the Fe-sublattice density of states obtained from the INRXS experiments. This resolves the disagreement between naturally observed iron isotope fractionation factors for mineral pairs involving magnetite and those obtained from the calculated {beta}-factors. The correctness of iron {beta}-factor for pyrite has been corroborated by the good agreement with experimental data of sulfur isotope geothermometers of pyrite-galena and pyrite-sphalerite. A good correlation between the potential energy of the cation site, the oxidation state of iron and the iron {beta}-factor value has been established. Specifically, ferric compounds, which have a higher potential energy of iron than ferrous compounds, have higher {beta}-factors. A similar dependence of b-factors on the oxidation state and potential energy could be extended to other transition metals. Extremely low values of INRXS-derived iron {beta}-factors for troilite and Fe{sub 3}S significantly widen the range of iron b-factors for covalently bonded compounds.

  16. Constraints on the oxidation state of the mantle: An electrochemical and sup 57 Fe Moessbauer study of mantle-derived ilmenites

    SciTech Connect

    Virgo, D.; Luth, R.W. ); Moats, M.A.; Ulmer, G.C. )

    1988-07-01

    Ilmenite samples from four kimberlite localities were studied using electrochemical, Moessbauer spectroscopic, and microprobe analytical techniques in order to infer the oxidation state of their source regions in the mantle. The values of Fe{sup 3+}/{Sigma}Fe calculated from analyses, using three different electron microanalytical instruments assuming ilmenite stoichiometry, are consistently higher than those derived from the Moessbauer data, by as much as 100%. Furthermore, the range in Fe{sup 3+}/{Sigma}Fe calculated using the analyses from different instruments and/or different correction schemes is nearly as large. Thus Fe{sup 3+}/{Sigma}Fe calculated from microprobe analyses should be taken with caution, even if the precision appears high. {sup 57}Fe Moessbauer spectroscopy on the electrochemical experiment run products demonstrates that Fe{sup 3+}/{Sigma}Fe is significantly lower than it is for the natural C-bearing ilmenites. In contrast, the ilmenite that lacked C did not change Fe{sup 3+}/{Sigma}Fe during the electrochemical experiment. Examination of the reduced samples with SEM established that the natural, single-phase ilmenites exsolved during the electrochemical experiment to form ilmenite{sub ss} + spinel{sub ss}. The initial, reduced trends in the electrochemical experiments for the C-bearing ilmenites are attributed to disequilibrium interactions between the decomposing sample and the evolved gas in the electrochemical cell and do not represent the quenched mantle memory nor the intrinsic f{sub O{sub 2}} of the sample prior to reduction. Furthermore, the oxidized f{sub O{sub 2}} trend is interpreted, for the carbon-bearing samples, are representing the f{sub O{sub 2}} of the ilmenite{sub ss} + spinel{sub ss} assemblage and not the intrinsic f{sub o{sub 2}} of the mantle-derived ilemnite{sub ss}.

  17. Moessbauer spectroscopy and magnetic characteristics of Zn{sub 1-x}Co{sub x}Fe{sub 2}O{sub 4} (x = 0-1) nanoparticles

    SciTech Connect

    Ghasemi, Ali; Sepelak, Vladimir; Shirsath, Sagar E.; Liu Xiaoxi; Morisako, Akimitsu

    2011-04-01

    Zn{sub 1-x}Co{sub x}Fe{sub 2}O{sub 4} (x = 0-1 in a step of 0.2) nanoparticles with different range of particle size including 5-10 nm and 200-250 nm have been prepared by sol-gel process. Moessbauer spectra at room temperature indicated that, with increasing cobalt content, there is a transition from paramagnetic to magnetically ordered-ferrimagnetic state. Magnetic properties were measured at 300 and 10 K using a Quantum Design MPMS-5S SQUID magnetometer. It was found that with an increase in cobalt content the saturation magnetization and coercivity increase.

  18. Mineralogy of SNC Meteorite EET79001 by Simultaneous Fitting of Moessbauer Backscatter Spectra

    NASA Technical Reports Server (NTRS)

    Morris, Richard V.; Agresti, D. G.

    2010-01-01

    We have acquired M ssbauer spectra for SNC meteorite EET79001 with a MIMOS II backscatter M ssbauer spectrometer [1] similar to those now operating on Mars as part of the Mars Exploration Rover (MER) missions. We are working to compare the Fe mineralogical composition of martian meteorites with in-situ measurements on Mars. Our samples were hand picked from the >1 mm size fraction of saw fines on the basis of lithology, color, and grain size (Table 1). The chips were individually analyzed at approx.300K by placing them on a piece of plastic that was in turn supported by the contact ring of the instrument (oriented vertically). Tungsten foil was used to mask certain areas from analysis. As shown in Figure 1, a variety of spectra was obtained, each resulting from different relative contributions of the Fe-bearing minerals present in the sample. Because the nine samples are reasonably mixtures of the same Fe-bearing phases in variable proportions, the nine spectra were fit simultaneously (simfit) with a common model, adjusting parameters to a single minimum chi-squared convergence criterion [2]. The starting point for the fitting model and values of hyperfine parameters was the work of Solberg and Burns [3], who identified olivine, pyroxene, and ferrous glass as major, and ilmenite and a ferric phase as minor (<5%), Fe-bearing phases in EET79001.

  19. Fractional vector calculus and fractional Maxwell's equations

    SciTech Connect

    Tarasov, Vasily E.

    2008-11-15

    The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered.

  20. Initialized Fractional Calculus

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    2000-01-01

    This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

  1. Moessbauer spectroscopy study of the aging and tempering of high nitrogen quenched Fe-N alloys: Kinetics of formation of Fe{sub 16}N{sub 2} nitride by interstitial ordering in martensite

    SciTech Connect

    Fall, I.; Genin, J.M.R. |

    1996-08-01

    The distribution of nitrogen atoms in austenite and during the different stages of aging and tempering of martensite is studied by Moessbauer spectroscopy, X-ray diffraction, and transmission electron microscopy (TEM). Transmission Moessbauer spectroscopy (TMS) and conversion electron Moessbauer spectroscopy (CEMS) are used for studying the austenite phase where the distribution of nitrogen atoms is found to depend on the nitriding method, gas nitriding in the authors` case, or ion implantation. Conversion electron Moessbauer spectroscopy, which concerns a depth predominantly less than 200 nm, reveals a nitrogen atom distribution different from that found in the bulk by TMS. The identification and kinetics of the stages of aging and tempering of martensite are followed by TMS measurements, and the phase characterization is confirmed by X-ray diffraction and TEM. The major stages are the early ordering of nitrogen atoms, which leads to small coherent precipitates of {alpha}-Fe{sub 16}N{sub 2}; the passage by thickening to semicoherent precipitates of {alpha}-Fe{sub 16}N{sub 2}; the dissolution of {alpha}-Fe{sub 16}N{sub 2} with the concomitant formation of {gamma}-Fe{sub 4}N; and the decomposition of retained austenite by tempering. The three first stages correspond to activation energies of 95, 126, and 94 kJ/mole, respectively, consistent with the nitrogen diffusion for the first and third stages and the dislocation pipe diffusion of iron for the second.

  2. Tempered fractional calculus

    SciTech Connect

    Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

    2015-07-15

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

  3. Determination of the Lamb-Moessbauer factors of LiFePO{sub 4} and FePO{sub 4} for electrochemical in situ and operando measurements in Li-ion batteries

    SciTech Connect

    Aldon, L.

    2010-01-15

    {sup 57}Fe Moessbauer spectroscopy is a powerful tool to investigate redox reactions during in electrochemical lithium insertion/extraction processes. Electrochemical oxidation of LiFe{sup II}PO{sub 4} (triphylite) in Li-ion batteries results in Fe{sup III}PO{sub 4} (heterosite). LiFePO{sub 4} was synthesized by solid state reaction at 800 deg. C under Ar flow from Li{sub 2}CO{sub 3}, FeC{sub 2}O{sub 4}.2H{sub 2}O and NH{sub 4}H{sub 2}PO{sub 4} precursors in stoichiometric composition. FePO{sub 4} was prepared from chemical oxidation of LiFePO{sub 4} using bromine as oxidative agent. For both materials a complete {sup 57}Fe Moessbauer study as a function of the temperature has been carried out. The Debye temperatures are found to be theta{sub M}=336 K for LiFePO{sub 4} and theta{sub M}=359 K for FePO{sub 4}, leading to Lamb-Moessbauer factors f{sub 300K}=0.73 and 0.77, respectively. These data will be useful for a precise estimation of the relative amounts of each species in a mixture. - Graphical abstract: Relative amount of FePO{sub 4} obtained by Moessbauer and electrochemical data. We have corrected Moessbauer spectral intensities with our f factor of both LiFePO{sub 4} and FePO{sub 4}. Open (filled) squares correspond to values obtained during charging (discharging) process. The dashed line, given as a guideline for the eye, corresponds to the ideal case were amounts deduced from different experimental measurements are equal.

  4. Fraction Sense: Foundational Understandings.

    PubMed

    Fennell, Francis Skip; Karp, Karen

    2016-08-09

    The intent of this commentary is to identify elements of fraction sense and note how the research studies provided in this special issue, in related but somewhat different ways, validate the importance of such understandings. Proficiency with fractions serves as a prerequisite for student success in higher level mathematics, as well as serving as a gateway to many occupations and varied contexts beyond the mathematics classroom. Fraction sense is developed through instructional opportunities involving fraction equivalence and magnitude, comparing and ordering fractions, using fraction benchmarks, and computational estimation. Such foundations are then extended to operations involving fractions and decimals and applications involving proportional reasoning. These components of fraction sense are all addressed in the studies provided in this issue, with particular consideration devoted to the significant importance of the use of the number line as a central representational tool for conceptually understanding fraction magnitude.

  5. TEMPERED FRACTIONAL CALCULUS

    PubMed Central

    MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA

    2014-01-01

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series. PMID:26085690

  6. YPdSn and YPd{sub 2}Sn: Structure, {sup 89}Y solid state NMR and {sup 119}Sn Moessbauer spectroscopy

    SciTech Connect

    Hoeting, Christoph; Eckert, Hellmut; Langer, Thorsten; Schellenberg, Inga; Poettgen, Rainer

    2012-06-15

    The stannides YPdSn and YPd{sub 2}Sn were synthesized by high-frequency melting of the elements in sealed tantalum tubes. Both structures were refined on the basis of single crystal X-ray diffractometer data: TiNiSi type, Pnma, a=715.4(1), b=458.8(1), c=789.1(1) pm, wR2=0.0461, 510 F{sup 2} values, 20 variables for YPdSn and MnCu{sub 2}Al type, Fm3 Macron m, a=671.44(8), wR2=0.0740, 55 F{sup 2} values, 5 parameters for YPd{sub 2}Sn. The yttrium atoms in the new stannide YPdSn are coordinated by two tilted Pd{sub 3}Sn{sub 3} hexagons (ordered AlB{sub 2} superstructure). In the Heusler phase YPd{sub 2}Sn each yttrium atom has octahedral tin coordination and additionally eight palladium neighbors. The cubic site symmetry of yttrium is reflected in the {sup 119}Sn Moessbauer spectrum which shows no quadrupole splitting. In contrast, YPdSn shows a single signal at {delta}=1.82(1) mm/s subjected to quadrupole splitting of {Delta}E{sub Q}=0.93(1) mm/s. Both compounds have been characterized by high-resolution {sup 89}Y solid state NMR spectroscopy, which indicates the presence of strong Knight shifts. The spectrum of YPd{sub 2}Sn is characterized by an unusually large linewidth, suggesting the presence of a Knight shift distribution reflecting local disordering effects. The range of {sup 89}Y Knight shifts of several binary and ternary intermetallic yttrium compounds is briefly discussed. - Graphical abstract: YPdSn and YPd{sub 2}Sn: Structure, {sup 89}Y solid state NMR and {sup 119}Sn Moessbauer spectroscopy. Highlights: Black-Right-Pointing-Pointer Synthesis and structure of ternary stannides YPdSn and YPd{sub 2}Sn. Black-Right-Pointing-Pointer {sup 119}Sn Moessbauer spectroscopic investigation of YPdSn and YPd{sub 2}Sn. Black-Right-Pointing-Pointer {sup 89}Y solid state NMR of intermetallics.

  7. DIY Fraction Pack.

    ERIC Educational Resources Information Center

    Graham, Alan; Graham, Louise

    2003-01-01

    Describes a very successful attempt to teach fractions to year 5 pupils based on pupils making their own fraction pack. Children decided for themselves how to make the fractional slices used in the activity using colored cardboard sheets and templates of a paper circle consisting of 24 equal slices. (Author/NB)

  8. Pitch fractionation. Technical report

    SciTech Connect

    Weinberg, V.L.; White, J.L.

    1981-12-15

    Petroleum pitch (Ashland A240) has been subjected to thermal treatment and solvent fractionation to produce refined pitches to be evaluated as impregnants for carbon-carbon composites. The solvent fractions were obtained by sequential Soxhlet extraction with solvents such as hexane, cyclohexane, toluene, and pyridine. The most severe thermal treatment produced a mesophase pitch (approximately 50% mesophase); an appreciable portion of the mesophase was soluble in strong solvents. There were substantial differences in chemical composition and in pyrolysis behavior of the fractions. As the depth of fraction increased, the pyrolysis yield and bloating increased, and the microstructure of the coke became finer until glassy microconstituents were formed in the deepest fractions.

  9. Innovative instrumentation for mineralogical and elemental analyses of solid extraterrestrial surfaces: The Backscatter Moessbauer Spectrometer/X Ray Fluorescence analyzer (BaMS/XRF)

    NASA Technical Reports Server (NTRS)

    Shelfer, T. D.; Morris, Richard V.; Nguyen, T.; Agresti, D. G.; Wills, E. L.

    1994-01-01

    We have developed a four-detector research-grade backscatter Moessbauer spectrometer (BaMS) instrument with low resolution x-ray fluorescence analysis (XRF) capability. A flight-qualified instrument based on this design would be suitable for use on missions to the surfaces of solid solar-system objects (Moon, Mars, asteroids, etc.). Target specifications for the flight instrument are as follows: mass less than 500 g; volumes less than 300 cu cm; and power less than 2 W. The BaMS/XRF instrument would provide data on the oxidation state of iron and its distribution among iron-bearing mineralogies and elemental composition information. This data is a primary concern for the characterization of extraterrestrial surface materials.

  10. Moessbauer Effect Study of Bi2O3. Na2O. B2O3. Fe2O3 Glass System

    SciTech Connect

    Salah, S.H.; Kashif, I.; Salem, S.M.; Mostafa, A.G.; El-Manakhly, K.A.

    2005-04-26

    Sodium-tetra-borate host glass containing both bismuth and iron cations were prepared obeying the composition (Na2B4O7)0.75 (Fe2O3)0.25-x (Bi2O3)x [where x = 0.0, 0.05, 0.10, 0.15, 0.20, and 0.25 mol.%]. X-ray diffraction indicated that all samples were in a homogeneous glassy phase. Moessbauer effect results showed that all iron ions appeared as Fe3+ ions occupying tetrahedral coordination state. The covalency of the Fe-O bond increased as bismuth oxide was gradually increased. IR measurements indicated the presence of some non-bridging oxygens and confirmed that iron ions occupy the tetrahedral coordination state. It was found also that, as Bi2O3 was gradually increased both magnetic susceptibility and specific volume decreased, while both density and molar volume increased.

  11. Structure and oscillational motion of /sup 57/Fe atoms in interstitial sites in Al as determined from interference of Moessbauer. gamma. radiation

    SciTech Connect

    Pauling, L.

    1981-12-01

    The first excited site of the /sup 57/Fe atom entrapped in an interstitial site in aluminum, as reported by W. Petry, G. Vogl, and W. Mansel (Phys. Rev. Lett. 45, 1862 (1980)) from a Moessbauer spectroscopic study of a single crystal, is analyzed by consideration of the value of the Hooke's law constant of the Fe-Al bonds obtained from the values for elemental Fe and Al. The eight wavefunctions for the eightfold nearly degenerate excited state are described as 2s1p1d1f hybrids of three-dimensional harmonic oscillator wavefunctions relative to the center of the undistorted Al/sub 6/ octahedron or as localized 1s functions relative to the center of the distorted octahedron. These considerations provide a qualitative understanding of the observations on this system.

  12. Dividing Fractions: A Pedagogical Technique

    ERIC Educational Resources Information Center

    Lewis, Robert

    2016-01-01

    When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…

  13. FRACTIONAL PEARSON DIFFUSIONS.

    PubMed

    Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

    2013-07-15

    Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

  14. FRACTIONAL PEARSON DIFFUSIONS

    PubMed Central

    Leonenko, Nikolai N.; Meerschaert, Mark M.

    2013-01-01

    Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change. PMID:23626377

  15. Can Kindergartners Do Fractions?

    ERIC Educational Resources Information Center

    Cwikla, Julie

    2014-01-01

    Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems (Empson…

  16. An Appetite for Fractions

    ERIC Educational Resources Information Center

    Wilkerson, Trena L.; Bryan, Tommy; Curry, Jane

    2012-01-01

    This article describes how using candy bars as models gives sixth-grade students a taste for learning to represent fractions whose denominators are factors of twelve. Using paper models of the candy bars, students explored and compared fractions. They noticed fewer different representations for one-third than for one-half. The authors conclude…

  17. On fractional programming

    SciTech Connect

    Bajona-Xandri, C.; Martinez-Legaz, J.E.

    1994-12-31

    This paper studies the minimax fractional programming problem, assuming quasiconvexity of the objective function, under the lower subdifferentiability viewpoint. Necessary and sufficient optimality conditions and dual properties are found. We present applications of this theory to find the Pareto efficient solutions of a multiobjective fractional problem and to solve several economic models.

  18. (Carbon isotope fractionation inplants)

    SciTech Connect

    O'Leary, M.H.

    1990-01-01

    The objectives of this research are: To develop a theoretical and experimental framework for understanding isotope fractionations in plants; and to develop methods for using this isotope fractionation for understanding the dynamics of CO{sub 2} fixation in plants. Progress is described.

  19. Fractional dissipative standard map.

    PubMed

    Tarasov, Vasily E; Edelman, M

    2010-06-01

    Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term memory. The memory effect in the fractional maps means that their present state of evolution depends on all past states with special forms of weights. Already a small deviation of the order of derivative from the integer value corresponding to the regular dissipative standard map (small memory effects) leads to the qualitatively new behavior of the corresponding attractors. The fractional dissipative standard maps are used to demonstrate a new type of fractional attractors in the wide range of the fractional orders of derivatives.

  20. Fractional calculus in bioengineering.

    PubMed

    Magin, Richard L

    2004-01-01

    Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

  1. Fractional market dynamics

    NASA Astrophysics Data System (ADS)

    Laskin, Nick

    2000-12-01

    A new extension of a fractality concept in financial mathematics has been developed. We have introduced a new fractional Langevin-type stochastic differential equation that differs from the standard Langevin equation: (i) by replacing the first-order derivative with respect to time by the fractional derivative of order μ; and (ii) by replacing “white noise” Gaussian stochastic force by the generalized “shot noise”, each pulse of which has a random amplitude with the α-stable Lévy distribution. As an application of the developed fractional non-Gaussian dynamical approach the expression for the probability distribution function (pdf) of the returns has been established. It is shown that the obtained fractional pdf fits well the central part and the tails of the empirical distribution of S&P 500 returns.

  2. Catalytic reforming of naphtha fractions

    SciTech Connect

    Bishop, K.C.; Vorhis, F.H.

    1980-09-16

    Production of motor gasoline and a btx-enriched reformate by fractionating a naphtha feedstock into a mid-boiling btxprecursor fraction, a relatively high-boiling fraction and a relatively low-boiling fraction; catalytically reforming the btxprecursor fraction in a first reforming zone; combining the relatively high-boiling and low-boiling fractions and catalytically reforming the combined fractions in a second reforming zone.

  3. Intracellular Cadmium Isotope Fractionation

    NASA Astrophysics Data System (ADS)

    Horner, T. J.; Lee, R. B.; Henderson, G. M.; Rickaby, R. E.

    2011-12-01

    Recent stable isotope studies into the biological utilization of transition metals (e.g. Cu, Fe, Zn, Cd) suggest several stepwise cellular processes can fractionate isotopes in both culture and nature. However, the determination of fractionation factors is often unsatisfactory, as significant variability can exist - even between different organisms with the same cellular functions. Thus, it has not been possible to adequately understand the source and mechanisms of metal isotopic fractionation. In order to address this problem, we investigated the biological fractionation of Cd isotopes within genetically-modified bacteria (E. coli). There is currently only one known biological use or requirement of Cd, a Cd/Zn carbonic anhydrase (CdCA, from the marine diatom T. weissfloggii), which we introduce into the E. coli genome. We have also developed a cleaning procedure that allows for the treating of bacteria so as to study the isotopic composition of different cellular components. We find that whole cells always exhibit a preference for uptake of the lighter isotopes of Cd. Notably, whole cells appear to have a similar Cd isotopic composition regardless of the expression of CdCA within the E. coli. However, isotopic fractionation can occur within the genetically modified E. coli during Cd use, such that Cd bound in CdCA can display a distinct isotopic composition compared to the cell as a whole. Thus, the externally observed fractionation is independent of the internal uses of Cd, with the largest Cd isotope fractionation occurring during cross-membrane transport. A general implication of these experiments is that trace metal isotopic fractionation most likely reflects metal transport into biological cells (either actively or passively), rather than relating to expression of specific physiological function and genetic expression of different metalloenzymes.

  4. Thermodynamics in Fractional Calculus

    NASA Astrophysics Data System (ADS)

    Meilanov, R. P.; Magomedov, R. A.

    2014-11-01

    A generalization of thermodynamics in the formalism of fractional-order derivatives is given. Results of the traditional thermodynamics of Carnot, Clausius, and Helmholtz are obtained in the particular case where the exponent of a fractional-order derivative is equal to unity. A one-parametric "fractal" equation of state is obtained with account of the second virial coefficient. The application of the resulting equation of state in the case of the gas argon is considered.

  5. Symmetric continued fractions

    SciTech Connect

    Panprasitwech, Oranit; Laohakosol, Vichian; Chaichana, Tuangrat

    2010-11-11

    Explicit formulae for continued fractions with symmetric patterns in their partial quotients are constructed in the field of formal power series. Similar to the work of Cohn in 1996, which generalized the so-called folding lemma to {kappa}-fold symmetry, the notion of {kappa}-duplicating symmetric continued fractions is investigated using a modification of the 1995 technique due to Clemens, Merrill and Roeder.

  6. Chromatographic methods of fractionation.

    PubMed

    Friesen, A D

    1987-01-01

    Chromatography's functional versatility, separation efficiency, gentle non-denaturing separating process and ease of automation and scale-up make it attractive for industrial scale protein purification. The Winnipeg Rh Institute's new Plasma Fractionation facility is an example of the use of chromatography for the large scale purification of plasma protein fractions. The fractionation facility has a capacity to process 800 litres of plasma per batch into blood clotting factor VIII and IX, albumin and intravenous immune serum globulin (i.v. ISG). Albumin and i.v. ISG are purified using ion exchange columns of DEAE-Sepharose (230 litre size), DEAE-Biogel (150 litre size) and CM-Sepharose (150 litre size). The chromatographic process is automated using a Modicon 584 Programmable Logic Controller to regulate valves, pumps and sensors which control plasma flow during fractionation. The stainless steel tanks and piping are automatically cleaned-in-place. The high degree of automation and cleaning provides efficient operation and sanitary processing. Chromatographic methods (DEAE-Sepharose and metal chelation) are also being used at the pilot scale to purify the human blood products superoxide dismutase and hemoglobin from outdated red blood cells. Characterization of the protein fractions produced by chromatography has shown them to be of equal or higher quality than fractions produced by other techniques.

  7. Fractional laser skin resurfacing.

    PubMed

    Alexiades-Armenakas, Macrene R; Dover, Jeffrey S; Arndt, Kenneth A

    2012-11-01

    Laser skin resurfacing (LSR) has evolved over the past 2 decades from traditional ablative to fractional nonablative and fractional ablative resurfacing. Traditional ablative LSR was highly effective in reducing rhytides, photoaging, and acne scarring but was associated with significant side effects and complications. In contrast, nonablative LSR was very safe but failed to deliver consistent clinical improvement. Fractional LSR has achieved the middle ground; it combined the efficacy of traditional LSR with the safety of nonablative modalities. The first fractional laser was a nonablative erbium-doped yttrium aluminum garnet (Er:YAG) laser that produced microscopic columns of thermal injury in the epidermis and upper dermis. Heralding an entirely new concept of laser energy delivery, it delivered the laser beam in microarrays. It resulted in microscopic columns of treated tissue and intervening areas of untreated skin, which yielded rapid reepithelialization. Fractional delivery was quickly applied to ablative wavelengths such as carbon dioxide, Er:YAG, and yttrium scandium gallium garnet (2,790 nm), providing more significant clinical outcomes. Adjustable laser parameters, including power, pitch, dwell time, and spot density, allowed for precise determination of percent surface area, affected penetration depth, and clinical recovery time and efficacy. Fractional LSR has been a significant advance to the laser field, striking the balance between safety and efficacy.

  8. Magnetite in Martian Meteorite Mil 03346 and Gusev Adirondack Class Basalt: Moessbauer Evidence for Variability in the Oxidation State of Adirondack Lavas

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; McKay, G. A.; Ming, D. W.; Klingelhoefer, G.; Schroeder, C.; Rodionov, D.; Yen, A.

    2006-01-01

    The Moessbauer spectrometers on the Mars Exploration Rovers Spirit (Gusev crater) and Opportunity (Meridiani Planum) have returned information on the oxidation state of iron, the mineralogical composition of Fe-bearing phases, and the distribution of Fe among oxidation states and phases [1,2,3]. To date, 100 and 85 surface targets have been analyzed by the Spirit and Opportunity spectrometers, respectively. Twelve component subspectra (8 doublets and 4 sextets) have been identified and most have been assigned to mineralogical compositions [4]. Two sextet subspectra result from the opaque and strongly magnetic mineral magnetite (Fe3O4 for the stoichiometric composition), one each for the crystallographic sites occupied by tetrahedrally-coordinated Fe3+ and by octahedrally-coordinated Fe3+ and Fe2+. At Gusev crater, the percentage of total Fe associated with magnetite for rocks ranges from 0 to 35% (Fig. 1) [3]. The range for soils (5 to 12% of total Fe from Mt, with one exception) is narrower. The ubiquitous presence of Mt in soil firmly establishes the phase as the strongly magnetic component in martian soil

  9. Characterization of carbonitrided and oxidized layers on low-carbon steel by conversion electron Moessbauer spectrometry, X-ray diffractometry, and X-ray photoelectron spectrometry

    SciTech Connect

    Kurosawa, K.; Li, H.L.; Ujihira, Y.; Nomura, K.

    1999-03-01

    The structures of low-carbon steel oxidized in an aqueous saline bath at 403 K and a fused salt bath at 673 K after carbonitriding were studied using conversion electron Moessbauer spectrometry (CEMS), x-ray diffractometry (XRD), and x-ray photoelectron spectrometry (XPS). Only a doublet peak caused by poor crystallinity of iron oxyhydroxides (FeOOH) or fine particles of iron oxides such as magnetite (Fe{sub 3}O{sub 4}) and maghemite ({gamma}-Fe{sub 2}O{sub 3}) was detected in the CEMS spectra of the surface of the carbonitrided steel oxidized in the aqueous saline bath. Corrosion resistance of the carbonitrided specimens was increased by oxidizing. The oxidized layers produced in the aqueous saline bath were superior to those produced in the fused salt bath as a result of pores in the carbonitrided zone being filled with finer particles of iron oxides and the production of tight, thick oxide layers of amorphous iron oxyhydroxides or fine iron oxides. Deformation of iron nitride ({gamma}{prime}-Fe{sub 4}N) crystals in the carbonitrided zone could not be detected by oxidizing in the aqueous saline bath but were detected in the fused salt bath at 673 K.

  10. Identifying Fractions on Number Lines.

    ERIC Educational Resources Information Center

    Bright, George W.; And Others

    1988-01-01

    This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. The instruction primarily concerned representing fractions and ordering fractions on number lines. (Author/PK)

  11. Release Fraction Evaluation

    SciTech Connect

    Bamberger, Judith A.; Glissmeyer, John A.

    2004-01-01

    This document presents results of experiments conducted to measure release fractions during certain tank retrieval processes. The tests were performed in a 1/4 scale model of a waste storage tank. The retrieval processes simulated were: (1) Discharging liquid or slurry from the mouth of a vertically oriented two-in. Schedule 40 pipe. The discharging material was in free-fall from the mouth of the pipe near the top of the tank into a liquid or slurry pool at the bottom of the tank. (2) The jet from a 9/16-in.-diameter nozzle transferring liquid or slurry waste from one side of the tank to the other. The discharging liquid was aimed at the opposite side of the tank from the nozzle and either impacted the tank wall or fell into a liquid or slurry pool in the bottom of the tank. (3) A high pressure fan jet of liquid striking a steel plate or simulated waste from a stand-off distance of a few inches. For each process, a water-soluble fluorescent dye was added to the liquid fraction as a tracer. Kaolin clay was used to represent the solids. The tank was covered and there was no forced ventilation in the tank during the tests. Six air samples were collected during each test. The air samples were collected at fixed positions in the tank. The air sample filters were dried and weighed to determine the solids collection. The fluorescent dye was then leached from each filter and quantified with a fluorometer to determine the collection of liquid. Samples of the slurry and liquid simulants were also collected to determine the quantities of simulant used in each test. To calculate the release fraction, the quantity collected on each air sample was adjusted for the fraction of the tank volume sampled and divided by the quantity of material exposed in the simulation. The method was not as sensitive for the solids content as it was for the liquid content, but in those instances where a solids release fraction was determined, it was in relatively good agreement with that of the

  12. FRACTIONAL CRYSTALLIZATION FEED ENVELOPE

    SciTech Connect

    HERTING DL

    2008-03-19

    Laboratory work was completed on a set of evaporation tests designed to establish a feed envelope for the fractional crystallization process. The feed envelope defines chemical concentration limits within which the process can be operated successfully. All 38 runs in the half-factorial design matrix were completed successfully, based on the qualitative definition of success. There is no feed composition likely to be derived from saltcake dissolution that would cause the fractional crystallization process to not meet acceptable performance requirements. However, some compositions clearly would provide more successful operation than other compositions.

  13. Momentum fractionation on superstrata

    SciTech Connect

    Bena, Iosif; Martinec, Emil; Turton, David; Warner, Nicholas P.

    2016-05-11

    Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in highdegree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Lastly, our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.

  14. Momentum fractionation on superstrata

    DOE PAGES

    Bena, Iosif; Martinec, Emil; Turton, David; ...

    2016-05-11

    Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in highdegree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifoldmore » singularities. Upon taking the AdS3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Lastly, our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.« less

  15. Sweet Work with Fractions

    ERIC Educational Resources Information Center

    Vinogradova, Natalya; Blaine, Larry

    2013-01-01

    Almost everyone loves chocolate. However, the same cannot be said about fractions, which are loved by markedly fewer. Middle school students tend to view them with wary respect, but little affection. The authors attempt to sweeten the subject by describing a type of game involving division of chocolate bars. The activity they describe provides a…

  16. Field-Flow Fractionation.

    ERIC Educational Resources Information Center

    Caldwell, Karin D.

    1988-01-01

    Describes a technique for separating samples that range over 15 orders of magnitude in molecular weight. Discusses theory, apparatus, and sample preparation techniques. Lists several types of field-flow fractionation (FFF) and their uses: sedimentation FFF, thermal FFF, flow FFF, electrical FFF, and steric FFF. (ML)

  17. Fraction collector for electrophoresis

    NASA Technical Reports Server (NTRS)

    Bier, M.

    1977-01-01

    Rotating-tube electrophoresis apparatus employs rotating jet of eluting buffer to reduce effects of convection during separation. Designed for separation of microorganisms and biological species, system combines gravity/gradient compensating of lumen with buffer flush at fraction outlet to increase separation efficiency.

  18. Young Children's Notations for Fractions

    ERIC Educational Resources Information Center

    Brizuela, Barbara M.

    2006-01-01

    This paper focuses on the kinds of notations young children make for fractional numbers. The extant literature in the area of fractional numbers acknowledges children's difficulties in conceptualizing fractional numbers. Some of the research suggests possibly delaying an introduction to conventional notations for algorithms and fractions until…

  19. Creating, Naming, and Justifying Fractions

    ERIC Educational Resources Information Center

    Siebert, Daniel; Gaskin, Nicole

    2006-01-01

    For students to develop meaningful conceptions of fractions and fraction operations, they need to think of fractions in terms other than as just whole-number combinations. In this article, we suggest two powerful images for thinking about fractions that move beyond whole-number reasoning. (Contains 5 figures.)

  20. Arbitrage with fractional Gaussian processes

    NASA Astrophysics Data System (ADS)

    Zhang, Xili; Xiao, Weilin

    2017-04-01

    While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.

  1. Testing fractional action cosmology

    NASA Astrophysics Data System (ADS)

    Shchigolev, V. K.

    2016-08-01

    The present work deals with a combined test of the so-called Fractional Action Cosmology (FAC) on the example of a specific model obtained by the author earlier. In this model, the effective cosmological term is proportional to the Hubble parameter squared through the so-called kinematic induction. The reason of studying this cosmological model could be explained by its ability to describe two periods of accelerated expansion, that is in agreement with the recent observations and the cosmological inflation paradigm. First of all, we put our model through the theoretical tests, which gives a general conception of the influence of the model parameters on its behavior. Then, we obtain some restrictions on the principal parameters of the model, including the fractional index, by means of the observational data. Finally, the cosmography parameters and the observational data compared to the theoretical predictions are presented both analytically and graphically.

  2. Fractional lattice charge transport

    PubMed Central

    Flach, Sergej; Khomeriki, Ramaz

    2017-01-01

    We consider the dynamics of noninteracting quantum particles on a square lattice in the presence of a magnetic flux α and a dc electric field E oriented along the lattice diagonal. In general, the adiabatic dynamics will be characterized by Bloch oscillations in the electrical field direction and dispersive ballistic transport in the perpendicular direction. For rational values of α and a corresponding discrete set of values of E(α) vanishing gaps in the spectrum induce a fractionalization of the charge in the perpendicular direction - while left movers are still performing dispersive ballistic transport, the complementary fraction of right movers is propagating in a dispersionless relativistic manner in the opposite direction. Generalizations and the possible probing of the effect with atomic Bose-Einstein condensates and photonic networks are discussed. Zak phase of respective band associated with gap closing regime has been computed and it is found converging to π/2 value. PMID:28102302

  3. Floquet Fractional Chern Insulators

    NASA Astrophysics Data System (ADS)

    Grushin, Adolfo G.; Gómez-León, Álvaro; Neupert, Titus

    2014-04-01

    We show theoretically that periodically driven systems with short range Hubbard interactions offer a feasible platform to experimentally realize fractional Chern insulator states. We exemplify the procedure for both the driven honeycomb and the square lattice, where we derive the effective steady state band structure of the driven system by using the Floquet theory and subsequently study the interacting system with exact numerical diagonalization. The fractional Chern insulator state equivalent to the 1/3 Laughlin state appears at 7/12 total filling (1/6 filling of the upper band). The state also features spontaneous ferromagnetism and is thus an example of the spontaneous breaking of a continuous symmetry along with a topological phase transition. We discuss light-driven graphene and shaken optical lattices as possible experimental systems that can realize such a state.

  4. Fractional Trajectories: Decorrelation Versus Friction

    DTIC Science & Technology

    2013-07-27

    from the integration of fractional differential equations in time. In Section 2 we provide a general demonstration of the new perspective on fractional ...section we demonstrate the equivalence between a fractional trajectory that is the solution of a Caputo fractional differential equation , and the... fractional differential equation dα dtα V(t) = OV(t), (1) where 0 < α < 1 and O is an operator, either linear or nonlinear, acting on the vector V(t

  5. Iron isotope fractionation in sulfides: constraints on mechanisms of sulfide formations in hydrothermal and magmatic systems.

    NASA Astrophysics Data System (ADS)

    Polyakov, Veniamin; Soultanov, Dilshod

    2010-05-01

    Data on non-traditional stable isotope fractionations (e.g., Fe, Cu) provide further insight into mechanisms of sulfide mineralization. Correct interpretation of these data is impossible without knowledge on equilibrium isotopic fractionation factors of sulfides. We present data on iron isotope fractionation factors (β-factors) of chalcopyrite (CuFeS2) and mackinawite (FeS). Iron β-factors for chalcopyrite were derived from synchrotron experimental data on inelastic nuclear resonant x-ray scattering (INRXS) [1] using the method described elsewhere [2,3]. The β-factors for mackinawite were found from the Moessbauer second-order Doppler shift data [4] by the method presented in [5]. The temperature dependence of the iron β-factors are fitted by following third-order polynomials: 103lnβcpy = 0.82560x - 0.01298x2 + 0.0005246x3 103lnβmcw = 0.2542x - 0.0001847x2 + 2.072×103x3 where x=106/T2 Using these data along with β-factors for pyrite and troilite [3,6], we compared iron isotope fractionation between pyrite and chalcopyrite in hydrothermal and magmatic conditions. Rouxel et al. [7] studied iron isotope of seafloor of hydrothermal vents in detail. They found that pyrite is enriched in light iron isotope relative to chalcopyrite in the case of black smoker Bio 9. This result evidences absence of iron isotope equilibrium between pyrite and chalcopyrite, because in equilibrium pyrite is enriched in heavy iron isotope (βpy > βcpy). Quantitatively, iron isotope fractionation between chalcolpyrite and pyrite is very close to equilibrium iron isotope fractionation between chalcolpyrite and FeS phase (mackinawite or troilite). This agrees the mechanism of pyrite formation through intermidient FeS phase if to assume isotopic equilibrium between the FeS phase and dissolved iron and no isotopic effect in the final stage of conversion FeS to FeS2 (pyrite). Another iron isotope fractionation was observed between pyrite and chalcopyrite in the case of the Cu-Au porphyry

  6. Fractional Galilean symmetries

    NASA Astrophysics Data System (ADS)

    Hosseiny, Ali; Rouhani, Shahin

    2016-09-01

    We generalize the differential representation of the operators of the Galilean algebras to include fractional derivatives. As a result a whole new class of scale invariant Galilean algebras are obtained. The first member of this class has dynamical index z = 2 similar to the Schrödinger algebra. The second member of the class has dynamical index z = 3 / 2, which happens to be the dynamical index Kardar-Parisi-Zhang equation.

  7. New Dry Fractionation Methods

    NASA Technical Reports Server (NTRS)

    McKay, David S.; Cooper, Bonnie L.

    2010-01-01

    This slide presentation describes new fractionation methods that are used to create dust that is respirable for testing the effects of inhalation of lunar dust in preparation for future manned lunar exploration. Because lunar dust is a very limited commodity, a method that does not result in loss of the material had to be developed. The dust separation system that is described incorporates some traditional methods, while preventing the dust from being contaminated or changed in reactivity properties while also limiting losses.

  8. Model Fractional Chern Insulators

    NASA Astrophysics Data System (ADS)

    Behrmann, Jörg; Liu, Zhao; Bergholtz, Emil J.

    2016-05-01

    We devise local lattice models whose ground states are model fractional Chern insulators—Abelian and non-Abelian topologically ordered states characterized by exact ground state degeneracies at any finite size and infinite entanglement gaps. Most saliently, we construct exact parent Hamiltonians for two distinct families of bosonic lattice generalizations of the Zk parafermion quantum Hall states: (i) color-entangled fractional Chern insulators at band filling fractions ν =k /(C +1 ) and (ii) nematic states at ν =k /2 , where C is the Chern number of the lowest band. In spite of a fluctuating Berry curvature, our construction is partially frustration free: the ground states reside entirely within the lowest band and exactly minimize a local (k +1 ) body repulsion term by term. In addition to providing the first known models hosting intriguing states such as higher Chern number generalizations of the Fibonacci anyon quantum Hall states, the remarkable stability and finite-size properties make our models particularly well suited for the study of novel phenomena involving, e.g., twist defects and proximity induced superconductivity, as well as being a guide for designing experiments.

  9. [Ablative and fractional lasers].

    PubMed

    Beylot, C; Grognard, C; Michaud, T

    2009-10-01

    The use of pulsed or scanning Carbon Dioxide, and pulsed Erbium-YAG lasers allows the programmable and reproducible photocoagulation of thin layers of the epidermis and superficial dermis. Thermal damage depends on the type of laser and is greater with CO(2) lasers. The degree of neocollagenesis is proportional to the thermal damage and is better with CO(2) lasers. Their main indication is the correction of photoaged facial skin but they can also be used for corrective dermatology, e.g. for scars and genodermatosis. Results are highly satisfactory but the technique is invasive and the patient experiences a social hindrance of around two weeks. Fractionated techniques treat 25% of the defective skin area at each session in noncontiguous microzones; four sessions are therefore necessary to treat the entire cutaneous surface. The treatment is given under topical anesthesia and is much less invasive, particularly with nonablative fractional laser treatment in which photothermolysis does not penetrate below the epidermis and/or the effects are slight, with no or very little social isolation. However, the results are much less satisfactory than the results of ablative laser and there is no firming effect. Other zones than the face can be treated. With the fractional CO(2) and Erbium ablative lasers, which have multiplied over the past 2 years, the much wider impacts cause perforation of the epidermis and there is a zone of ablation by laser photovaporization, with a zone of thermal damage below. The results are better in correcting photoaging of the face, without, however, achieving the efficacy of ablative lasers, which remain the reference technique. However, the effects are not insignificant, requiring at least 5 days of social isolation.

  10. Fractional channel multichannel analyzer

    DOEpatents

    Brackenbush, Larry W.; Anderson, Gordon A.

    1994-01-01

    A multichannel analyzer incorporating the features of the present invention obtains the effect of fractional channels thus greatly reducing the number of actual channels necessary to record complex line spectra. This is accomplished by using an analog-to-digital converter in the asynscronous mode, i.e., the gate pulse from the pulse height-to-pulse width converter is not synchronized with the signal from a clock oscillator. This saves power and reduces the number of components required on the board to achieve the effect of radically expanding the number of channels without changing the circuit board.

  11. Fractional channel multichannel analyzer

    DOEpatents

    Brackenbush, L.W.; Anderson, G.A.

    1994-08-23

    A multichannel analyzer incorporating the features of the present invention obtains the effect of fractional channels thus greatly reducing the number of actual channels necessary to record complex line spectra. This is accomplished by using an analog-to-digital converter in the asynchronous mode, i.e., the gate pulse from the pulse height-to-pulse width converter is not synchronized with the signal from a clock oscillator. This saves power and reduces the number of components required on the board to achieve the effect of radically expanding the number of channels without changing the circuit board. 9 figs.

  12. Solvent Fractionation of Lignin

    SciTech Connect

    Chatterjee, Sabornie; Saito, Tomonori

    2014-01-01

    Lignin is a highly abundant source of renewable carbon that can be considered as a valuable sustainable source of biobased materials. The major issues for the commercial production of value added high performance lignin products are lignin s physical and chemical heterogenities. To overcome these problems, a variety of procedures have been developed to produce pure lignin suitable for high performace applications such as lignin-derived carbon materials. However, most of the isolation procedures affect lignin s properties and structure. In this chapter, a short review of the effect of solvent fractionation on lignin s properties and structure is presented.

  13. Assessment of the optimum degree of Sr{sub 3}Fe{sub 2}MoO{sub 9} electron-doping through oxygen removal: An X-ray powder diffraction and {sup 57}Fe Moessbauer spectroscopy study

    SciTech Connect

    Lopez, Carlos A.; Viola, Maria del C.; Pedregosa, Jose C.; Mercader, Roberto C.

    2010-10-15

    We describe the preparation and structural characterization by X-ray powder diffraction (XRPD) and Moessbauer spectroscopy of three electron-doped perovskites Sr{sub 3}Fe{sub 2}MoO{sub 9-{delta}} with Fe/Mo = 2 obtained from Sr{sub 3}Fe{sub 2}MoO{sub 9}. The compounds were synthesized by topotactic reduction with H{sub 2}/N{sub 2} (5/95) at 600, 700 and 800 {sup o}C. Above 800 {sup o}C the Fe/Mo ratio changes from Fe/Mo = 2-1 < Fe/Mo < 2. The structural refinements of the XRPD data for the reduced perovskites were carried out by the Rietveld profile analysis method. The crystal structure of these phases is cubic, space group Fm3-bar m, with cationic disorder at the two different B sites that can be populated in variable proportions by the Fe atoms. The Moessbauer spectra allowed determining the evolution of the different species formed after the treatments at different temperatures and confirm that Fe ions in the samples reduced at 600, 700 and 800 {sup o}C are only in the high-spin Fe{sup 3+} electronic state.

  14. Body Fractions: A Physical Approach to Fraction Learning

    ERIC Educational Resources Information Center

    Mills, Judith

    2011-01-01

    Many students experience great difficulty understanding the meaning of fractions. For many students who have spent their early mathematics lessons focusing on counting (whole) numbers, recognising that there are many numbers between those whole numbers called fractional numbers, is quite revolutionary. The foundation of understanding fractions is…

  15. Ejection Fraction Heart Failure Measurement

    MedlinePlus

    ... Thromboembolism Aortic Aneurysm More Ejection Fraction Heart Failure Measurement Updated:Feb 15,2017 The ejection fraction (EF) is an important measurement in determining how well your heart is pumping ...

  16. Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

    PubMed

    Pu, Yi-Fei; Yi, Zhang; Zhou, Ji-Liu

    2016-07-14

    This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.

  17. How Weird Are Weird Fractions?

    ERIC Educational Resources Information Center

    Stuffelbeam, Ryan

    2013-01-01

    A positive rational is a weird fraction if its value is unchanged by an illegitimate, digit-based reduction. In this article, we prove that each weird fraction is uniquely weird and initiate a discussion of the prevalence of weird fractions.

  18. The random continued fraction transformation

    NASA Astrophysics Data System (ADS)

    Kalle, Charlene; Kempton, Tom; Verbitskiy, Evgeny

    2017-03-01

    We introduce a random dynamical system related to continued fraction expansions. It uses random combinations of the Gauss map and the Rényi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces, as well as the dynamical properties of the system.

  19. Fractional diffusion on bounded domains

    DOE PAGES

    Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

    2015-03-13

    We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

  20. Numerical approaches to fractional calculus and fractional ordinary differential equation

    NASA Astrophysics Data System (ADS)

    Li, Changpin; Chen, An; Ye, Junjie

    2011-05-01

    Nowadays, fractional calculus are used to model various different phenomena in nature, but due to the non-local property of the fractional derivative, it still remains a lot of improvements in the present numerical approaches. In this paper, some new numerical approaches based on piecewise interpolation for fractional calculus, and some new improved approaches based on the Simpson method for the fractional differential equations are proposed. We use higher order piecewise interpolation polynomial to approximate the fractional integral and fractional derivatives, and use the Simpson method to design a higher order algorithm for the fractional differential equations. Error analyses and stability analyses are also given, and the numerical results show that these constructed numerical approaches are efficient.

  1. Fractional chemotaxis diffusion equations.

    PubMed

    Langlands, T A M; Henry, B I

    2010-05-01

    We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.

  2. Soot Volume Fraction Imaging

    NASA Technical Reports Server (NTRS)

    Greenberg, Paul S.; Ku, Jerry C.

    1994-01-01

    A new technique is described for the full-field determination of soot volume fractions via laser extinction measurements. This technique differs from previously reported point-wise methods in that a two-dimensional array (i.e., image) of data is acquired simultaneously. In this fashion, the net data rate is increased, allowing the study of time-dependent phenomena and the investigation of spatial and temporal correlations. A telecentric imaging configuration is employed to provide depth-invariant magnification and to permit the specification of the collection angle for scattered light. To improve the threshold measurement sensitivity, a method is employed to suppress undesirable coherent imaging effects. A discussion of the tomographic inversion process is provided, including the results obtained from numerical simulation. Results obtained with this method from an ethylene diffusion flame are shown to be in close agreement with those previously obtained by sequential point-wise interrogation.

  3. Functional fractionation of platelets.

    PubMed

    Haver, V M; Gear, A R

    1981-02-01

    Studies of platelet populations suggest that they are heterogeneous in size, age, and metabolic parameters. In an attempt to correlate these parameters with efficiency of aggregation, a new technique, functional fractionation, was developed. Platelet populations are separated by their differential reactivity to aggregating agents. For example, low doses of ADP (0.1 to 0.7 microM) are added to stirred PRP, after which gentle centrifugation is used to remove aggregates from single unreacted platelets. The loose aggregates can be readily dispersed for comparison of the physical or biochemical properties of the reacted versus unreacted platelets. It was found that reactive platelets were larger (6.5 micrometer3) than unreacted platelets (5.51 micrometer3). No significant difference in density existed between the two populations, and no release of [14C]serotonin from prelabeled platelets occurred during functional fractionation. Scanning and transmission electron microscopy confirmed the size difference and revealed that in both populations platelets were structurally intact with a normal discoid shape and no significant difference in organelle content. Human platelets most reactive to ADP were also enriched in glycogen (3.6-fold), ATP (1.6-fold), and ADP (twofold), compared with less reactive cells. These "reactive" cells took up more 51[Cr] and contained 1.9 times more surface sialic acid. In an in vivo aging experiment, rats were injected with 75[Se]methionine. Shortly after labeling (1 day), the most reactive platelets possessed the highest amount of 75[Se]. These results reveal that functionally active platelets, which are also larger, are more active metabolically than less reactive platelets, possess a higher negative surface charge, and may be a younger population.

  4. Fraction Reduction in Membrane Systems

    PubMed Central

    Zhang, Hong

    2014-01-01

    Fraction reduction is a basic computation for rational numbers. P system is a new computing model, while the current methods for fraction reductions are not available in these systems. In this paper, we propose a method of fraction reduction and discuss how to carry it out in cell-like P systems with the membrane structure and the rules with priority designed. During the application of fraction reduction rules, synchronization is guaranteed by arranging some special objects in these rules. Our work contributes to performing the rational computation in P systems since the rational operands can be given in the form of fraction. PMID:24772037

  5. Fractionally charged skyrmions in fractional quantum Hall effect.

    PubMed

    Balram, Ajit C; Wurstbauer, U; Wójs, A; Pinczuk, A; Jain, J K

    2015-11-26

    The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.

  6. Fractionally charged skyrmions in fractional quantum Hall effect

    SciTech Connect

    Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.

    2015-11-26

    The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.

  7. Fractional variational calculus in terms of Riesz fractional derivatives

    NASA Astrophysics Data System (ADS)

    Agrawal, O. P.

    2007-06-01

    This paper presents extensions of traditional calculus of variations for systems containing Riesz fractional derivatives (RFDs). Specifically, we present generalized Euler-Lagrange equations and the transversality conditions for fractional variational problems (FVPs) defined in terms of RFDs. We consider two problems, a simple FVP and an FVP of Lagrange. Results of the first problem are extended to problems containing multiple fractional derivatives, functions and parameters, and to unspecified boundary conditions. For the second problem, we present Lagrange-type multiplier rules. For both problems, we develop the Euler-Lagrange-type necessary conditions which must be satisfied for the given functional to be extremum. Problems are considered to demonstrate applications of the formulations. Explicitly, we introduce fractional momenta, fractional Hamiltonian, fractional Hamilton equations of motion, fractional field theory and fractional optimal control. The formulations presented and the resulting equations are similar to the formulations for FVPs given in Agrawal (2002 J. Math. Anal. Appl. 272 368, 2006 J. Phys. A: Math. Gen. 39 10375) and to those that appear in the field of classical calculus of variations. These formulations are simple and can be extended to other problems in the field of fractional calculus of variations.

  8. Accessible solitons of fractional dimension

    SciTech Connect

    Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi

    2016-05-15

    We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.

  9. Trigonometric Integrals via Partial Fractions

    ERIC Educational Resources Information Center

    Chen, H.; Fulford, M.

    2005-01-01

    Parametric differentiation is used to derive the partial fractions decompositions of certain rational functions. Those decompositions enable us to integrate some new combinations of trigonometric functions.

  10. Fractional-time quantum dynamics.

    PubMed

    Iomin, Alexander

    2009-08-01

    Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schrödinger equation (SE), which differs from the standard SE by the fractional time derivative: partial differential/partial differentialt --> partial differential(alpha)/partial differentialt(alpha). It is shown that for alpha=1/2 the fractional SE is isospectral to a comb model. An analytical expression for the Green's functions of the systems are obtained. The semiclassical limit is discussed.

  11. Fractional random walk lattice dynamics

    NASA Astrophysics Data System (ADS)

    Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.

    2017-02-01

    We analyze time-discrete and time-continuous ‘fractional’ random walks on undirected regular networks with special focus on cubic periodic lattices in n  =  1, 2, 3,.. dimensions. The fractional random walk dynamics is governed by a master equation involving fractional powers of Laplacian matrices {{L}\\fracα{2}}} where α =2 recovers the normal walk. First we demonstrate that the interval 0<α ≤slant 2 is admissible for the fractional random walk. We derive analytical expressions for the transition matrix of the fractional random walk and closely related the average return probabilities. We further obtain the fundamental matrix {{Z}(α )} , and the mean relaxation time (Kemeny constant) for the fractional random walk. The representation for the fundamental matrix {{Z}(α )} relates fractional random walks with normal random walks. We show that the matrix elements of the transition matrix of the fractional random walk exihibit for large cubic n-dimensional lattices a power law decay of an n-dimensional infinite space Riesz fractional derivative type indicating emergence of Lévy flights. As a further footprint of Lévy flights in the n-dimensional space, the transition matrix and return probabilities of the fractional random walk are dominated for large times t by slowly relaxing long-wave modes leading to a characteristic {{t}-\\frac{n{α}} -decay. It can be concluded that, due to long range moves of fractional random walk, a small world property is emerging increasing the efficiency to explore the lattice when instead of a normal random walk a fractional random walk is chosen.

  12. Unwrapping Students' Ideas about Fractions

    ERIC Educational Resources Information Center

    Lewis, Rebecca M.; Gibbons, Lynsey K.; Kazemi, Elham; Lind, Teresa

    2015-01-01

    Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to…

  13. Rational Exponentials and Continued Fractions

    ERIC Educational Resources Information Center

    Denny, J. K.

    2012-01-01

    Using continued fraction expansions, we can approximate constants, such as pi and e, using an appropriate integer n raised to the power x[superscript 1/x], x a suitable rational. We review continued fractions and give an algorithm for producing these approximations.

  14. Understanding Magnitudes to Understand Fractions

    ERIC Educational Resources Information Center

    Gabriel, Florence

    2016-01-01

    Fractions are known to be difficult to learn and difficult to teach, yet they are vital for students to have access to further mathematical concepts. This article uses evidence to support teachers employing teaching methods that focus on the conceptual understanding of the magnitude of fractions.

  15. Radiating subdispersive fractional optical solitons

    NASA Astrophysics Data System (ADS)

    Fujioka, J.; Espinosa, A.; Rodríguez, R. F.; Malomed, B. A.

    2014-09-01

    It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.

  16. Radiating subdispersive fractional optical solitons

    SciTech Connect

    Fujioka, J. Espinosa, A.; Rodríguez, R. F.; Malomed, B. A.

    2014-09-01

    It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.

  17. A new fractional wavelet transform

    NASA Astrophysics Data System (ADS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-03-01

    The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.

  18. Fractional active disturbance rejection control.

    PubMed

    Li, Dazi; Ding, Pan; Gao, Zhiqiang

    2016-05-01

    A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ωo and controller bandwidth ωc on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme.

  19. Fractionally charged skyrmions in fractional quantum Hall effect

    DOE PAGES

    Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; ...

    2015-11-26

    The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeemanmore » energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.« less

  20. Recalcitrant dissolved organic carbon fractions.

    PubMed

    Hansell, Dennis A

    2013-01-01

    Marine dissolved organic carbon (DOC) exhibits a spectrum of reactivity, from very fast turnover of the most bioavailable forms in the surface ocean to long-lived materials circulating within the ocean abyss. These disparate reactivities group DOC by fractions with distinctive functions in the cycling of carbon, ranging from support of the microbial loop to involvement in the biological pump to a hypothesized major source/sink of atmospheric CO(2) driving paleoclimate variability. Here, the major fractions constituting the global ocean's recalcitrant DOC pool are quantitatively and qualitatively characterized with reference to their roles in carbon biogeochemistry. A nomenclature for the fractions is proposed based on those roles.

  1. Australia's Next Top Fraction Model

    ERIC Educational Resources Information Center

    Gould, Peter

    2013-01-01

    Peter Gould suggests Australia's next top fraction model should be a linear model rather than an area model. He provides a convincing argument and gives examples of ways to introduce a linear model in primary classrooms.

  2. Xenon fractionation in porous planetesimals

    NASA Technical Reports Server (NTRS)

    Zahnle, Kevin; Pollack, James B.; Kasting, James F.

    1990-01-01

    The distinctively fractionated Xe on Mars and earth may have its root in a common source from which both planets accreted. Beginning with Ozima and Nakazawa's (1980) hypothesis that terrestrial Xe fractionation was caused by gravitational separation of adsorbed solar nebular gases inside large porous planetesimals, it is pointed out that Xe would have been trapped as the planetesimal grew and pores were squeezed shut by lithostatic pressure. It is shown that enough fractionated Xe to supply the earth could have been trapped this way. The degree of fractionation is controlled by the lithostatic pressure at the pore-closing front and so would have been roughly the same for all large planetesimals. The predicted degree of fractionation agrees well with that preserved in terrestrial and Martian Xe. Relative to Xe, this source is strongly depleted in other noble gases. In contrast to the original Ozima and Nakazawa hypothesis, the present hypothesis predicts the observed fractionation, and it allows planetary accretion to occur after the dissipation of the solar nebula.

  3. Xenon fractionation in porous planetesimals.

    PubMed

    Zahnle, K; Pollack, J B; Kasting, J F

    1990-01-01

    The distinctively fractionated Xe on Mars and Earth may have its root in a common source from which both planets accreted. We begin with Ozima and Nakazawa's hypothesis that terrestrial Xe fractionation was caused by gravitational separation of adsorbed solar nebular gases inside large porous planetesimals. We point out that Xe would have been trapped as the planetesimal grew and pores were squeezed shut by lithostatic pressure. We show that enough fractionated Xe to supply the Earth could have been trapped this way. The degree of fractionation is controlled by the lithostatic pressure at the pore-closing front and so would have been roughly the same for all large planetesimals. The predicted degree of fractionation agrees well with that preserved in terrestrial and martian Xe. Relative to Xe, this source is strongly depleted in other noble gases. In contrast to the original Ozima and Nakazawa hypothesis, our hypothesis predicts the observed fractionation, and it allows planetary accretion to occur after the dissipation of the solar nebula. The required planetesimals are large, representing a class of object now extinct in the solar system.

  4. Fractional characteristic times and dissipated energy in fractional linear viscoelasticity

    NASA Astrophysics Data System (ADS)

    Colinas-Armijo, Natalia; Di Paola, Mario; Pinnola, Francesco P.

    2016-08-01

    In fractional viscoelasticity the stress-strain relation is a differential equation with non-integer operators (derivative or integral). Such constitutive law is able to describe the mechanical behavior of several materials, but when fractional operators appear, the elastic and the viscous contribution are inseparable and the characteristic times (relaxation and retardation time) cannot be defined. This paper aims to provide an approach to separate the elastic and the viscous phase in the fractional stress-strain relation with the aid of an equivalent classical model (Kelvin-Voigt or Maxwell). For such equivalent model the parameters are selected by an optimization procedure. Once the parameters of the equivalent model are defined, characteristic times of fractional viscoelasticity are readily defined as ratio between viscosity and stiffness. In the numerical applications, three kinds of different excitations are considered, that is, harmonic, periodic, and pseudo-stochastic. It is shown that, for any periodic excitation, the equivalent models have some important features: (i) the dissipated energy per cycle at steady-state coincides with the Staverman-Schwarzl formulation of the fractional model, (ii) the elastic and the viscous coefficients of the equivalent model are strictly related to the storage and the loss modulus, respectively.

  5. Delayed coker fractionator advanced control

    SciTech Connect

    Jaisinghani, R.; Minter, B. ); Tica, A.; Puglesi, A.; Ojeda, R. )

    1993-08-01

    In a delayed coking process, as coke drum switches are made, rapid changes occur in both the fractionator feed rate and composition. With conventional control, it is not unusual to see long transient behavior of large swings in both quality and flowrates of coker gas oils. This can extract a heavy economic toll, not only in coker operation, but in the operation of downstream units as the upset is propagated. An advanced process control application (APC) was recently implemented on the coker fractionator at the Yacimentos Petroliferos Fiscales (YPF), Lujan de Cuyo Refinery, in Mendoza, Argentina. This coker fractionator control design was unique as it handled two different operating objectives: control of product qualities via tower temperature profile during normal operation and control of gas oil product flow ratio during drum switch. This combination of control objectives in one multivariable predictive control program was achieved by including special logic to decouple the individual tuning requirements. Also, additional logic was included to unambiguously detect and identify drum switch and drum steam out as discrete events within 30 seconds of their actual occurrence. These discrete events were then used as disturbance variables to minimize fractionator transient behavior. As a performance measure, the overhead temperature was controlled within 2 C to 2.5 C of its target, gas oil flows were stabilized during drum switches and steam generation via pump around was maximized. Overall, implementing advanced control for the delayed coker fractionator resulted in substantial benefits from product quality control, product flow control and minimized energy consumption.

  6. Dominoes as Fractions: Misconceptions and Understandings.

    ERIC Educational Resources Information Center

    Ward, Robin A.

    1999-01-01

    Presents an activity in which students must arrange five fractions represented by dominoes in ascending order and justify their reasons for the ordering. Representing common fractions with dominoes helps identify students' misconceptions about fractions. (ASK)

  7. REFractions: The Representing Equivalent Fractions Game

    ERIC Educational Resources Information Center

    Tucker, Stephen I.

    2014-01-01

    Stephen Tucker presents a fractions game that addresses a range of fraction concepts including equivalence and computation. The REFractions game also improves students' fluency with representing, comparing and adding fractions.

  8. On Fractional Model Reference Adaptive Control

    PubMed Central

    Shi, Bao; Dong, Chao

    2014-01-01

    This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology. PMID:24574897

  9. Fractional Schrödinger equation.

    PubMed

    Laskin, Nick

    2002-11-01

    Some properties of the fractional Schrödinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrödinger equation we find the energy spectra of a hydrogenlike atom (fractional "Bohr atom") and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schrödinger equations.

  10. Understanding Partitive Division of Fractions.

    ERIC Educational Resources Information Center

    Ott, Jack M.; And Others

    1991-01-01

    Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

  11. Fractions, trees and unfinished business

    NASA Astrophysics Data System (ADS)

    Shraiman, Boris

    In this talk, mourning the loss of a teacher and a dear friend, I would like to share some unfinished thoughts loosely connecting - via Farey fraction trees - Kadanoff's study of universality of quasi-periodic route to chaos with the effort to understand universal features of genealogical trees.

  12. Optimization in fractional aircraft ownership

    NASA Astrophysics Data System (ADS)

    Septiani, R. D.; Pasaribu, H. M.; Soewono, E.; Fayalita, R. A.

    2012-05-01

    Fractional Aircraft Ownership is a new concept in flight ownership management system where each individual or corporation may own a fraction of an aircraft. In this system, the owners have privilege to schedule their flight according to their needs. Fractional management companies (FMC) manages all aspects of aircraft operations, including utilization of FMC's aircraft in combination of outsourced aircrafts. This gives the owners the right to enjoy the benefits of private aviations. However, FMC may have complicated business requirements that neither commercial airlines nor charter airlines faces. Here, optimization models are constructed to minimize the number of aircrafts in order to maximize the profit and to minimize the daily operating cost. In this paper, three kinds of demand scenarios are made to represent different flight operations from different types of fractional owners. The problems are formulated as an optimization of profit and a daily operational cost to find the optimum flight assignments satisfying the weekly and daily demand respectively from the owners. Numerical results are obtained by Genetic Algorithm method.

  13. Math Fair: Focus on Fractions

    ERIC Educational Resources Information Center

    Mokashi, Neelima A.

    2009-01-01

    This article depicts the rewarding experience of creating mathematical environments for kindergarten and elementary students by focusing on one of the most important and often difficult-to-grasp concepts (fractions) through play methods incorporated into a math fair. The basic concept of a math fair is threefold: (1) to create preplanned,…

  14. Staircase and Fractional Part Functions

    ERIC Educational Resources Information Center

    Amram, Meirav; Dagan, Miriam; Ioshpe, Michael; Satianov, Pavel

    2016-01-01

    The staircase and fractional part functions are basic examples of real functions. They can be applied in several parts of mathematics, such as analysis, number theory, formulas for primes, and so on; in computer programming, the floor and ceiling functions are provided by a significant number of programming languages--they have some basic uses in…

  15. Fractional quantum Hall effect revisited

    NASA Astrophysics Data System (ADS)

    Jacak, J.; Łydżba, P.; Jacak, L.

    2015-10-01

    The topology-based explanation of the fractional quantum Hall effect (FQHE) is summarized. The cyclotron braid subgroups crucial for this approach are introduced in order to identify the origin of the Laughlin correlations in 2D (two-dimensional) Hall systems. Flux-tubes and vortices for composite fermions in their standard constructions are explained in terms of cyclotron braids. The derivation of the hierarchy of the FQHE is proposed by mapping onto the integer effect within the topology-based approach. The experimental observations of the FQHE supporting the cyclotron braid picture are reviewed with a special attention paid to recent experiments with a suspended graphene. The triggering role of a carrier mobility for organization of the fractional state in Hall configuration is emphasized. The prerequisites for the FQHE are indicated including topological conditions substantially increasing the previously accepted set of physical necessities. The explanation of numerical studies by exact diagonalizations of the fractional Chern insulator states is formulated in terms of the topology condition applied to the Berry field flux quantization. Some new ideas withz regard to the synthetic fractional states in the optical lattices are also formulated.

  16. Pythagorean Approximations and Continued Fractions

    ERIC Educational Resources Information Center

    Peralta, Javier

    2008-01-01

    In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

  17. Isotopic Fractionation in Interstellar Chemistry

    NASA Technical Reports Server (NTRS)

    Charnley, Steven

    2009-01-01

    Isotopically fractionated material is found in many solar system objects, including meteorites and comets. It is thought, in some cases, to trace interstellar material that was incorporated into the solar sys tem without undergoing significant processing. In this poster, we sho w the results of several models of the nitrogen, oxygen, and carbon f ractionation in proto-stellar cores.

  18. Fractional diffusion: recovering the distributed fractional derivative from overposed data

    NASA Astrophysics Data System (ADS)

    Rundell, W.; Zhang, Z.

    2017-03-01

    There has been considerable recent study in ‘subdiffusion’ models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one such is to realize that the order of the fractional derivative is related to the time scales of the underlying diffusion process. This raises the question of what order α of derivative should be taken and if a single value actually suffices. This has led to models that combine a finite number of these derivatives each with a different fractional exponent {αk} and different weighting value c k to better model a greater possible range of time scales. Ultimately, one wants to look at a situation that combines derivatives in a continuous way—the so-called distributional model with parameter μ ≤ft(α \\right) . However all of this begs the question of how one determines this ‘order’ of differentiation. Recovering a single fractional value has been an active part of the process from the beginning of fractional diffusion modeling and if this is the only unknown then the markers left by the fractional order derivative are relatively straightforward to determine. In the case of a finite combination of derivatives this becomes much more complex due to the more limited analytic tools available for such equations, but recent progress in this direction has been made, (Li et al 2015 Appl. Math. Comput. 257 381–97, Li and Yamamoto 2015 Appl. Anal. 94 570–9). This paper considers the full distributional model where the order is viewed as a function μ ≤ft(α \\right) on the interval (0, 1]. We show existence, uniqueness and regularity for an initial-boundary value problem including an important representation theorem in the case of a single spatial variable. This is then used in the inverse problem of recovering the distributional coefficient μ ≤ft(α \\right) from a time trace of the solution and a uniqueness result is

  19. {sup 57}Fe Moessbauer and x-ray magnetic circular dichroism study of magnetic compensation of the rare-earth sublattice in Nd{sub 2-x}Ho{sub x}Fe{sub 14}B compounds

    SciTech Connect

    Chaboy, J.; Piquer, C.; Plugaru, N.; Bartolome, F.; Laguna-Marco, M. A.

    2007-10-01

    We present here a study of the magnetic properties of the Nd{sub 2-x}Ho{sub x}Fe{sub 14}B series. The macroscopic properties of these compounds evolve continuously from those of Nd{sub 2}Fe{sub 14}B to those of Ho{sub 2}Fe{sub 14}B as Ho gradually replaces Nd. The system shows a compensation of the rare-earth sublattice magnetization for a critical concentration, x{sub c}=0.55, that is reflected into the anomalous behavior of both macroscopic and microscopic magnetic probes. The combined analysis of magnetization, {sup 57}Fe Moessbauer spectroscopy and Fe K-edge x-ray magnetic circular dichroism (XMCD) measurements suggests that the origin of the anomalous magnetic behavior found at x{sub c}=0.55 is mainly due to the Ho sublattice. Moreover, the analysis of the Fe K-edge XMCD signals reveal the presence of a rare-earth contribution, reflecting the coupling of the rare-earth and Fe magnetic moments, which can lead to the possibility of disentangling the magnetic behavior of both Fe and R atoms using a single absorption edge.

  20. Improving Children's Knowledge of Fraction Magnitudes

    ERIC Educational Resources Information Center

    Fazio, Lisa K.; Kennedy, Casey A.; Siegler, Robert S.

    2016-01-01

    We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards' suggestions for teaching fractions, would improve children's fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played "Catch…

  1. 12 CFR 5.67 - Fractional shares.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... fair price upon the fraction not being issued through its sale, or the purchase of the additional fraction required for a full share, if there is an established and active market in the national bank's stock; (c) Remit the cash equivalent of the fraction not being issued to those to whom fractional...

  2. A fractional Dirac equation and its solution

    NASA Astrophysics Data System (ADS)

    Muslih, Sami I.; Agrawal, Om P.; Baleanu, Dumitru

    2010-02-01

    This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.

  3. Using Number Sense to Compare Fractions

    ERIC Educational Resources Information Center

    Bray, Wendy S.; Abreu-Sanchez, Laura

    2010-01-01

    One mathematical focus for third graders is to develop deep understanding of fractions and fraction equivalence, including comparing fractions through use of models and reasoning strategies. Before reading further, consider how you might solve the following problem: Which fraction is greater, 14/24 or 17/36? The initial impulse of many adults is…

  4. Evaluating fractionated space systems - Status

    NASA Astrophysics Data System (ADS)

    Cornford, S.; Jenkins, S.; Wall, S.; Cole, B.; Bairstow, B.; Rouquette, N.; Dubos, G.; Ryan, T.; Zarifian, P.; Boutwell, J.

    DARPA has funded a number of teams to further refine its Fractionated Spacecraft vision. Several teams, including this team led by JPL, have been tasked to develop a tool for the evaluation of the Business case for a fractionated system architecture. This evaluation is to understand under what conditions and constraints the fractionated architecture make more sense (in a cost/benefit sense) than the traditional monolithic paradigm. Our approach to this evaluation is to generate and evaluate a variety of trade space options. These options include various sets of stimuli, various degrees of fractionation and various subsystem element properties. The stimuli include many not normally modeled such as technology obsolescence, funding profile changes and changes in mission objectives during the mission itself. The degrees of fractionation enable various traditional subsystem elements to be distributed across different free flyers which then act in concert as needed. This will enable key technologies to be updated as need dictates and availability allows. We have described our approach in a previous IEEE Aerospace conference paper but will briefly summarize here. Our approach to generate the Business Case evaluation is to explicitly model both the implementation and operation phases for the life cycle of a fractionated constellation. A variety of models are integrated into the Phoenix ModelCenter framework and are used to generate various intermediate data which is aggregated into the Present Strategic Value (PSV). The PSV is essentially the value (including the value of the embedded real options) minus the cost. These PSVs are calculated for a variety of configurations and scenarios including variations of various stimuli or uncertainties (e.g. supply chain delays, launch vehicle failures and orbital debris events). There are various decision options (e.g. delay, accelerate, cancel) which can now be exercised for each stimulus. We can compute the PSV for the various comb

  5. Fractional variational calculus and the transversality conditions

    NASA Astrophysics Data System (ADS)

    Agrawal, O. P.

    2006-08-01

    This paper presents the Euler-Lagrange equations and the transversality conditions for fractional variational problems. The fractional derivatives are defined in the sense of Riemann-Liouville and Caputo. The connection between the transversality conditions and the natural boundary conditions necessary to solve a fractional differential equation is examined. It is demonstrated that fractional boundary conditions may be necessary even when the problem is defined in terms of the Caputo derivative. Furthermore, both fractional derivatives (the Riemann-Liouville and the Caputo) arise in the formulations, even when the fractional variational problem is defined in terms of one fractional derivative only. Examples are presented to demonstrate the applications of the formulations.

  6. Test Operations Procedure (TOP) 4-2-013 Commodity Engineering Test Procedures, Recoilless Rifle Ammunition

    DTIC Science & Technology

    2009-09-22

    to prevent air born dust from invalidating the test. Alternatively, cover the area with an impenetrable barrier such as a large plastic sheet...81 4.10.1 Fungus ...................................................................................... 81 4.10.2...and Y coordinate of each impact relative to the aim point. (7) Meteorological conditions including wind, temperature, humidity, and air density

  7. Complexity and the Fractional Calculus

    DTIC Science & Technology

    2013-01-01

    Paolo Grigolini,, Mauro Bologna,, Bruce West 611102 c. THIS PAGE The public reporting burden for this collection of information is estimated to...dx.doi.org/10.1155/2013/498789 Research Article Complexity and the Fractional Calculus Pensri Pramukkul,1 Adam Svenkeson,1 Paolo Grigolini,1 Mauro ...8. PERFORMING ORGANIZATION REPORT NUMBER 19a. NAME OF RESPONSIBLE PERSON 19b. TELEPHONE NUMBER Paolo Grigolini Pensri Pramukkul, Adam Svenkeson

  8. FRACTIONAL DYNAMICS AT MULTIPLE TIMES

    PubMed Central

    Meerschaert, Mark M.; Straka, Peter

    2013-01-01

    A continuous time random walk (CTRW) imposes a random waiting time between random particle jumps. CTRW limit densities solve a fractional Fokker-Planck equation, but since the CTRW limit is not Markovian, this is not sufficient to characterize the process. This paper applies continuum renewal theory to restore the Markov property on an expanded state space, and compute the joint CTRW limit density at multiple times. PMID:23378670

  9. Electrochemically controlled iron isotope fractionation

    NASA Astrophysics Data System (ADS)

    Black, Jay R.; Young, Edward D.; Kavner, Abby

    2010-02-01

    Variations in the stable isotope abundances of transition metals have been observed in the geologic record and trying to understand and reconstruct the physical/environmental conditions that produced these signatures is an area of active research. It is clear that changes in oxidation state lead to large fractionations of the stable isotopes of many transition metals such as iron, suggesting that transition metal stable isotope signatures could be used as a paleo-redox proxy. However, the factors contributing to these observed stable isotope variations are poorly understood. Here we investigate how the kinetics of iron redox electrochemistry generates isotope fractionation. Through a combination of electrodeposition experiments and modeling of electrochemical processes including mass-transport, we show that electron transfer reactions are the cause of a large isotope separation, while mass transport-limited supply of reactant to the electrode attenuates the observed isotopic fractionation. Furthermore, the stable isotope composition of electroplated transition metals can be tuned in the laboratory by controlling parameters such as solution chemistry, reaction overpotential, and solution convection. These methods are potentially useful for generating isotopically-marked metal surfaces for tracking and forensic purposes. In addition, our studies will help interpret stable isotope data in terms of identifying underlying electron transfer processes in laboratory and natural samples.

  10. Fractional statistical potential in graphene

    NASA Astrophysics Data System (ADS)

    Ardenghi, J. S.

    2017-03-01

    In this work the fractional statistics is applied to an anyon gas in graphene to obtain the special features that the arbitrary phase interchange of the particle coordinates introduce in the thermodynamic properties. The electron gas is constituted by N anyons in the long wavelength approximation obeying fractional exclusion statistics and the partition function is analyzed in terms of a perturbation expansion up to first order in the dimensionless constant λ / L being L the length of the graphene sheet and λ = βℏvF the thermal wavelength. By considering the correct permutation expansion of the many-anyons wavefunction, taking into account that the phase changes with the number of inversions in each permutation, the statistical fermionic/bosonic potential is obtained and the intermediate statistical behavior is found. It is shown that "extra" fermonic and bosonic particles states appears and this "statistical particle" distribution depends on N. Entropy and specific heat is obtained up to first order in λ / L showing that the results obtained differs from those obtained in different approximation to the fractional exclusion statistics.

  11. Improving Children's Knowledge of Fraction Magnitudes.

    PubMed

    Fazio, Lisa K; Kennedy, Casey A; Siegler, Robert S

    2016-01-01

    We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards' suggestions for teaching fractions, would improve children's fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played Catch the Monster with Fractions, a game in which they estimated fraction locations on a number line and received feedback on the accuracy of their estimates. The intervention lasted less than 15 minutes. In our initial study, children showed large gains from pretest to posttest in their fraction number line estimates, magnitude comparisons, and recall accuracy. In a more rigorous second study, the experimental group showed similarly large improvements, whereas a control group showed no improvement from practicing fraction number line estimates without feedback. The results provide evidence for the effectiveness of interventions emphasizing fraction magnitudes and indicate how psychological theories and research can be used to evaluate specific recommendations of the Common Core State Standards.

  12. On fractional Langevin equation involving two fractional orders

    NASA Astrophysics Data System (ADS)

    Baghani, Omid

    2017-01-01

    In numerical analysis, it is frequently needed to examine how far a numerical solution is from the exact one. To investigate this issue quantitatively, we need a tool to measure the difference between them and obviously this task is accomplished by the aid of an appropriate norm on a certain space of functions. For example, Sobolev spaces are indispensable part of theoretical analysis of partial differential equations and boundary integral equations, as well as are necessary for the analysis of some numerical methods for the solving of such equations. But most of articles that appear in this field usually use ‖.‖∞ in the space of C[a, b] which is very restrictive. In this paper, we introduce a new norm that is convenient for the fractional and singular differential equations. Using this norm, the existence and uniqueness of initial value problems for nonlinear Langevin equation with two different fractional orders are studied. In fact, the obtained results could be used for the classical cases. Finally, by two examples we show that we cannot always speak about the existence and uniqueness of solutions just by using the previous methods.

  13. Conformable Fractional Nikiforov—Uvarov Method

    NASA Astrophysics Data System (ADS)

    Karayer, H.; Demirhan, D.; Büyükkılıç, F.

    2016-07-01

    We introduce conformable fractional Nikiforov—Uvarov (NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schrödinger equation (SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods—Saxon potential, and Hulthen potential.

  14. FRACTIONATING COLUMN PRODUCT COLLECTOR CONTROL

    DOEpatents

    Paxson, G.D. Jr.

    1964-03-10

    Means for detecting minute fluid products from a chemical separation column and for advancing a collector tube rack in order to automatically separate and collect successive fractionated products are described. A charge is imposed on the forming drops at the column orifice to create an electric field as the drop falls in the vicinity of a sensing plate. The field is detected by an electrometer tube coupled to the plate causing an output signal to actuate rotation of a collector turntable rack, thereby positioning new collectors under the orifice. The invention provides reliable automatic collection independent of drop size, rate of fall, or chemical composition. (AEC)

  15. Trends in whey protein fractionation.

    PubMed

    El-Sayed, Mayyada M H; Chase, Howard A

    2011-08-01

    Whey is a by-product of cheese manufacture that is normally treated as a waste. However, it contains a mixture of proteins with important nutritional and biological attributes. To extract these valuable proteins, whey fractionation has been developed using three main techniques; namely chromatographic (e.g., ion-exchange and hydrophobic adsorption), membrane (e.g., traditional pressure-driven and electro-separation)-, or combined methods. Recently, new promising techniques have been introduced such as aqueous two-phase separation (ATPS) and magnetic fishing. This article reviews the use of these techniques together with an evaluation of their performance regarding the yield and purity of two major proteins in whey.

  16. Immersed Boundary Fractional Step Method

    NASA Astrophysics Data System (ADS)

    Taira, Kunihiko

    2005-11-01

    We present a new formulation of the immersed boundary method for incompressible flow over moving rigid bodies. Like many existing techniques we introduce a set of interpolation points on the surface at which the no-slip boundary condition is satisfied by including a (regularized) force in the momentum equations. By introducing interpolation and regularization operators and grouping pressure and force unknowns together, the discretized Navier-Stokes equations with the immersed boundary method can be formulated with an identical structure to the traditional fractional step method, but with a modified Poisson equation whose unknowns are both the pressure and the boundary force. The method highlights the analogous roles of pressure and boundary forcing as Lagrange multipliers in order to satisfy the divergence free and no-slip constraints, respectively. The overall method is found to be a simple addition to an existing fractional step code and the extended Poisson equation is solved efficiently with the conjugate gradient method. We demonstrate convergence and present results for two-dimensional flows with a variety of moving rigid bodies.

  17. Staircase and fractional part functions

    NASA Astrophysics Data System (ADS)

    Amram, Meirav; Dagan, Miriam; Ioshpe, Michael; Satianov, Pavel

    2016-10-01

    The staircase and fractional part functions are basic examples of real functions. They can be applied in several parts of mathematics, such as analysis, number theory, formulas for primes, and so on; in computer programming, the floor and ceiling functions are provided by a significant number of programming languages - they have some basic uses in various programming tasks. In this paper, we view the staircase and fractional part functions as a classical example of non-continuous real functions. We introduce some of their basic properties, present some interesting constructions concerning them, and explore some intriguing interpretations of such functions. Throughout the paper, we use these functions in order to explain basic concepts in a first calculus course, such as domain of definition, discontinuity, and oddness of functions. We also explain in detail how, after researching the properties of such functions, one can draw their graph; this is a crucial part in the process of understanding their nature. In the paper, we present some subjects that the first-year student in the exact sciences may not encounter. We try to clarify those subjects and show that such ideas are important in the understanding of non-continuous functions, as a part of studying analysis in general.

  18. Dean flow fractionation of chromosomes

    NASA Astrophysics Data System (ADS)

    Hockin, Matt; Sant, Himanshu J.; Capecchi, Mario; Gale, Bruce K.

    2016-03-01

    Efforts to transfer intact mammalian chromosomes between cells have been attempted for more than 50 years with the consistent result being transfer of sub unit length pieces regardless of method. Inertial microfluidics is a new field that has shown much promise in addressing the fractionation of particles in the 2-20 μm size range (with unknown limits) and separations are based upon particles being carried by curving confined flows (within a spiral shaped, often rectangular flow chamber) and migrating to stable "equilibrium" positions of varying distance from a chamber wall depending on the balance of dean and lift forces. We fabricated spiral channels for inertial microfluidic separations using a standard soft lithography process. The concentration of chromosomes, small contaminant DNA and large cell debris in each outlets were evaluated using microscope (60X) and a flow cytometer. Using Dean Flow Fractionation, we were able to focus 4.5 times more chromosomes in outlet 2 compared to outlet 4 where most of the large debris is found. We recover 16% of the chromosomes in outlet #1- 50% in 2, 23% in 3 and 11% in 4. It should be noted that these estimates of recovery do not capture one piece of information- it actually may be that the chromosomes at each outlet are physically different and work needs to be done to verify this potential.

  19. Ejection Fraction: What Does It Measure?

    MedlinePlus

    ... does the term "ejection fraction" mean? What does it measure? Answers from Rekha Mankad, M.D. Ejection fraction ... percentage of blood leaving your heart each time it contracts. During each heartbeat pumping cycle, the heart ...

  20. Fractional Topological Insulators in Three Dimensions

    SciTech Connect

    Maciejko, Joseph; Zhang Shoucheng; Qi Xiaoliang; Karch, Andreas

    2010-12-10

    Topological insulators can be generally defined by a topological field theory with an axion angle {theta} of 0 or {pi}. In this work, we introduce the concept of fractional topological insulator defined by a fractional axion angle and show that it can be consistent with time reversal T invariance if ground state degeneracies are present. The fractional axion angle can be measured experimentally by the quantized fractional bulk magnetoelectric polarization P{sub 3}, and a 'halved' fractional quantum Hall effect on the surface with Hall conductance of the form {sigma}{sub H}=(p/q)(e{sup 2}/2h) with p, q odd. In the simplest of these states the electron behaves as a bound state of three fractionally charged 'quarks' coupled to a deconfined non-Abelian SU(3) 'color' gauge field, where the fractional charge of the quarks changes the quantization condition of P{sub 3} and allows fractional values consistent with T invariance.

  1. Calcium and titanium isotopic fractionations during evaporation

    NASA Astrophysics Data System (ADS)

    Zhang, Junjun; Huang, Shichun; Davis, Andrew M.; Dauphas, Nicolas; Hashimoto, Akihiko; Jacobsen, Stein B.

    2014-09-01

    Isotope fractionations associated with high temperature evaporation provide important constraints on the physicochemical processes that affected planetary materials at the birth of the solar system. Previous evaporation experiments have focused on isotopic fractionation of moderately to highly volatile elements. Here, we investigate the isotope fractionation behavior of two highly refractory elements, calcium and titanium, during evaporation of perovskite (CaTiO3) in a vacuum furnace. In our experiments, isotope fractionation during evaporation follows the Rayleigh law, but not the commonly used exponential law, with the dominant evaporating species being Ca(g) and TiO2(g). If isotope fractionations in early solar system materials did follow the Rayleigh law, the common practice of using an exponential fractionation law to correct for mass-dependent fractionation in the study of mass-independent fractionations may introduce significant artificial isotope anomalies.

  2. Fractionation of Organosolv Lignin Using Acetone:Water and Properties of the Obtained Fractions

    SciTech Connect

    Sadeghifar, Hasan; Wells, Tyrone; Le, Rosemary Khuu; Sadeghifar, Fatemeh; Yuan, Joshua S.; Jonas Ragauskas, Arthur

    2016-11-07

    In this study, lignin fractions with different molecular weight were prepared using a simple and almost green method from switchgrass and pine organosolv lignin. Different proportions of acetone in water, ranging from 30 to 60%, were used for lignin fractionation. A higher concentration of acetone dissolved higher molecular weight fractions of the lignin. Fractionated organosolv lignin showed different molecular weight and functional groups. Higher molecular weight fractions exhibited more aliphatic and less phenolic OH than lower molecular weight fractions. Lower molecular weight fractions lead to more homogeneous structure compared to samples with a higher molecular weight. In conclusion, all fractions showed strong antioxidant activity.

  3. Moessbauer Mineralogy of Rock, Soil, and Dust at Gusev Crater, Mars: Spirit's Journey through Weakly Altered Olivine Basalt on the Plains and Pervasively Altered Basalt in the Columbia Hills

    NASA Technical Reports Server (NTRS)

    Morris, R. V.; Klingelhoefer, G.; Schroeder, C.; Rodionov, D. S.; Yen, A.; Ming, D. W.; deSouza, P. A., Jr.; Fleischer, I.; Wdowiak, T.; Gellert, R.; Bernhardt, B.; Evlanov, E. N.; Zubkov, B.; Foh, J.; Bonnes, U.; Kankeleit, E.; Guetlich, P.; Renz, F.; Squyres, S. W.; Arvidson, R. E.

    2006-01-01

    The Moessbauer spectrometer on Spirit measured the oxidation state of Fe, identified Fe-bearing phases, and measured relative abundances of Fe among those phases for surface materials on the plains and in the Columbia Hills of Gusev crater. Eight Fe-bearing phases were identified: olivine, pyroxene, ilmenite, magnetite, nanophase ferric oxide (npOx), hematite, goethite, and a Fe(3+)-sulfate. Adirondack basaltic rocks on the plains are nearly unaltered (Fe(3+)/Fe(sub T)<0.2) with Fe from olivine, pyroxene (Ol>Px), and minor npOx and magnetite. Columbia Hills basaltic rocks are nearly unaltered (Peace and Backstay), moderately altered (WoolyPatch, Wishstone, and Keystone), and pervasively altered (e.g., Clovis, Uchben, Watchtower, Keel, and Paros with Fe(3+)/Fe(sub T) approx.0.6-0.9). Fe from pyroxene is greater than Fe from olivine (Ol sometimes absent), and Fe(2+) from Ol+Px is 40-49% and 9-24% for moderately and pervasively altered materials, respectively. Ilmenite (Fe from Ilm approx.3-6%) is present in Backstay, Wishstone, Keystone, and related rocks along with magnetite (Fe from Mt approx. 10-15%). Remaining Fe is present as npOx, hematite, and goethite in variable proportions. Clovis has the highest goethite content (Fe from Gt=40%). Goethite (alpha-FeOOH) is mineralogical evidence for aqueous processes because it has structural hydroxide and is formed under aqueous conditions. Relatively unaltered basaltic soils (Fe(3+)/Fe(sub T) approx. 0.3) occur throughout Gusev crater (approx. 60-80% Fe from Ol+Px, approx. 10-30% from npOx, and approx. 10% from Mt). PasoRobles soil in the Columbia Hills has a unique occurrence of high concentrations of Fe(3+)-sulfate (approx. 65% of Fe). Magnetite is identified as a strongly magnetic phase in Martian soil and dust.

  4. Fast parareal iterations for fractional diffusion equations

    NASA Astrophysics Data System (ADS)

    Wu, Shu-Lin; Zhou, Tao

    2017-01-01

    Numerical methods for fractional PDEs is a hot topic recently. This work is concerned with the parareal algorithm for system of ODEs u‧ (t) + Au (t) = f that arising from semi-discretizations of time-dependent fractional diffusion equations with nonsymmetric Riemann-Liouville fractional derivatives. The spatial semi-discretization of this kind of fractional derivatives often results in a coefficient matrix A with spectrum σ (A)

  5. Stretching Student Teachers' Understanding of Fractions

    ERIC Educational Resources Information Center

    Harvey, Roger

    2012-01-01

    The teaching of fractions in elementary school is known to be challenging. Literature indicates that teachers' and prospective teachers' lack of depth of fraction content knowledge and associated pedagogical knowledge is of concern. This study investigated the fraction content knowledge of prospective teachers and their ability to use that…

  6. Mediants Make (Number) Sense of Fraction Foibles

    ERIC Educational Resources Information Center

    McDowell, Eric L.

    2016-01-01

    By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

  7. Early Predictors of Middle School Fraction Knowledge

    ERIC Educational Resources Information Center

    Bailey, Drew H.; Siegler, Robert S.; Geary, David C.

    2014-01-01

    Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic…

  8. The Richness of Children's Fraction Strategies

    ERIC Educational Resources Information Center

    Kent, Laura B.; Empson, Susan B.; Nielsen, Lynne

    2015-01-01

    In this article, the authors discuss a special type of multiplication-and-division-of-fractions problem that elementary school teachers can use to promote children's understanding of fractional quantities and their relationships. These problems are accessible to students working at different levels of fraction understanding, and they can be solved…

  9. 16 CFR 500.17 - Fractions.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 16 Commercial Practices 1 2010-01-01 2010-01-01 false Fractions. 500.17 Section 500.17 Commercial... LABELING ACT § 500.17 Fractions. (a) SI metric declarations of net quantity of contents of any consumer commodity may contain only decimal fractions. Other declarations of net quantity of contents may...

  10. Locating Fractions on a Number Line

    ERIC Educational Resources Information Center

    Wong, Monica

    2013-01-01

    Understanding fractions remains problematic for many students. The use of the number line aids in this understanding, but requires students to recognise that a fraction represents the distance from zero to a dot or arrow marked on a number line which is a linear scale. This article continues the discussion from "Identifying Fractions on a…

  11. Teaching Fractions. Educational Practices Series-22

    ERIC Educational Resources Information Center

    Fazio, Lisa; Siegler, Robert

    2011-01-01

    Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

  12. Identifying Fractions on a Number Line

    ERIC Educational Resources Information Center

    Wong, Monica

    2013-01-01

    Fractions are generally introduced to students using the part--whole model. Yet the number line is another important representation which can be used to build fraction concepts (Australian Curriculum Assessment and Reporting Authority [ACARA], 2012). Number lines are recognised as key in students' number development not only of fractions, but…

  13. An Alternative Starting Point for Fraction Instruction

    ERIC Educational Resources Information Center

    Cortina, José Luis; Višnovská, Jana; Zúñiga, Claudia

    2015-01-01

    We analyze the results of a study conducted for the purpose of assessing the viability of an alternative starting point for teaching fractions. The alternative is based on Freudenthal's insights about fraction as comparison. It involves portraying the entities that unit fractions quantify as always being apart from the reference unit, instead of…

  14. Few Fractional Order Derivatives and Their Computations

    ERIC Educational Resources Information Center

    Bhatta, D. D.

    2007-01-01

    This work presents an introductory development of fractional order derivatives and their computations. Historical development of fractional calculus is discussed. This paper presents how to obtain computational results of fractional order derivatives for some elementary functions. Computational results are illustrated in tabular and graphical…

  15. Preparing for Algebra by Building Fraction Sense

    ERIC Educational Resources Information Center

    Rodrigues, Jessica; Dyson, Nancy I.; Hansen, Nicole; Jordan, Nancy C.

    2016-01-01

    Fractions are troublesome for many children, especially students with learning difficulties and disabilities in mathematics. To address this serious educational concern, this article recommends the use of number lines to build fraction sense. Math activities that center on the number line build fraction concepts as early as third grade. A number…

  16. Isotopic Fractionation by Gravitational Escape

    NASA Astrophysics Data System (ADS)

    Lammer, H. S. J.

    2003-04-01

    Present natural data bases for abundances of the isotopic compositions of noble gases, carbon and nitrogen inventories can be found in the Sun, the solar wind, meteorites and the planetary atmospheres and crustal reservoirs. Mass distributions in the various volatile reservoirs provide boundary conditions which must be satisfied in modelling the history of the present atmospheres. Such boundary conditions are constraints posed by comparison of isotopic ratios in primordial volatile sources with the isotopic pattern which was found on the planets and their satellites. Observations from space missions and Earth-based spectroscopic telescope observations of Venus, Mars and Saturn's major satellite Titan show that the atmospheric evolution of these planetary bodies to their present states was affected by processes capable of fractionating their elements and isotopes. The isotope ratios of D/H in the atmospheres of Venus and Mars indicate evidence for their planetary water inventories. Venus' H2O content may have been at least 0.3% of a terrestrial ocean. Analysis of the D/H ratio on Mars imply that a global H2O ocean with a depth of ≤ 30 m was lost since the end of hydrodynamic escape. Calculations of the time evolution of the 15N/14N isotope anomalies in the atmospheres of Mars and Titan show that the Martian atmosphere was at least ≥ 20 times denser than at present and that the mass of Titan's early atmosphere was about 30 times greater than its present value. A detailed study of gravitational fractionation of isotopes in planetary atmospheres furthermore indicates a much higher solar wind mass flux of the early Sun during the first half billion years.

  17. Fractional Action Cosmology with Variable Order Parameter

    NASA Astrophysics Data System (ADS)

    El-Nabulsi, Rami Ahmad

    2017-01-01

    Fractional action cosmology with variable order parameter was constructed in this paper. Starting from a fractional weighted action which generalizes the fractional actionlike variational approach, a large number of cosmological dynamical equations are obtained depending on the mathematical type of the fractional order parameter. Through this paper, we selected two independent types which result on a number of cosmological scenarios and we discussed their dynamical consequences. It was observed that the present fractional cosmological formalism holds a large family of solutions and offers new features not found in the standard formalism and in many fundamental research papers.

  18. Correlation Structure of Fractional Pearson Diffusions.

    PubMed

    Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

    2013-09-01

    The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative.

  19. Correlation Structure of Fractional Pearson Diffusions

    PubMed Central

    Leonenko, Nikolai N.; Meerschaert, Mark M.; Sikorskii, Alla

    2013-01-01

    The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative. PMID:24089586

  20. Fractional Action Cosmology with Variable Order Parameter

    NASA Astrophysics Data System (ADS)

    El-Nabulsi, Rami Ahmad

    2017-04-01

    Fractional action cosmology with variable order parameter was constructed in this paper. Starting from a fractional weighted action which generalizes the fractional actionlike variational approach, a large number of cosmological dynamical equations are obtained depending on the mathematical type of the fractional order parameter. Through this paper, we selected two independent types which result on a number of cosmological scenarios and we discussed their dynamical consequences. It was observed that the present fractional cosmological formalism holds a large family of solutions and offers new features not found in the standard formalism and in many fundamental research papers.

  1. Fractionation of Organosolv Lignin Using Acetone:Water and Properties of the Obtained Fractions

    DOE PAGES

    Sadeghifar, Hasan; Wells, Tyrone; Le, Rosemary Khuu; ...

    2016-11-07

    In this study, lignin fractions with different molecular weight were prepared using a simple and almost green method from switchgrass and pine organosolv lignin. Different proportions of acetone in water, ranging from 30 to 60%, were used for lignin fractionation. A higher concentration of acetone dissolved higher molecular weight fractions of the lignin. Fractionated organosolv lignin showed different molecular weight and functional groups. Higher molecular weight fractions exhibited more aliphatic and less phenolic OH than lower molecular weight fractions. Lower molecular weight fractions lead to more homogeneous structure compared to samples with a higher molecular weight. In conclusion, all fractionsmore » showed strong antioxidant activity.« less

  2. Fractions Learning in Children With Mathematics Difficulties.

    PubMed

    Tian, Jing; Siegler, Robert S

    2016-08-04

    Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA peers in fraction understanding and fall further behind during middle school. In contrast, Chinese children, who like the MD children in the United States score in the bottom one third of the distribution in their country, possess reasonably good fraction understanding. We interpret these findings within the framework of the integrated theory of numerical development. By emphasizing the importance of fraction magnitude knowledge for numerical understanding in general, the theory proved useful for understanding differences in fraction knowledge between MD and TA children and for understanding how knowledge can be improved. Several interventions demonstrated the possibility of improving fraction magnitude knowledge and producing benefits that generalize to fraction arithmetic learning among children with MD. The reasonably good fraction understanding of Chinese children with MD and several successful interventions with U.S. students provide hope for the improvement of fraction knowledge among American children with MD.

  3. Stretching student teachers' understanding of fractions

    NASA Astrophysics Data System (ADS)

    Harvey, Roger

    2012-12-01

    The teaching of fractions in elementary school is known to be challenging. Literature indicates that teachers' and prospective teachers' lack of depth of fraction content knowledge and associated pedagogical knowledge is of concern. This study investigated the fraction content knowledge of prospective teachers and their ability to use that knowledge in a novel situation. Prospective teachers who regarded their own fractional content knowledge as weak were recruited to participate in the study. They completed a questionnaire and then participated in a loosely structured teaching experiment in which they were shown how an elastic strip could be used to assist in the development of fraction ideas. Data gained from questionnaires and transcripts of the teaching experiment indicated that using the elastic strip was effective in challenging and enriching the participants' knowledge of equivalent fractions and ordering fractions. The physical nature of the use of the fraction strip required participants to articulate their thoughts to other participants which assisted in making their actions relating to the fraction tasks explicit. The results suggest that the use of the elastic strip, and associated teaching, should be considered as a productive way of assisting prospective teachers to develop their understanding of fractional concepts.

  4. WATER FRACTIONS IN EXTRASOLAR PLANETESIMALS

    SciTech Connect

    Jura, M.; Xu, S. E-mail: sxu@astro.ucla.edu

    2012-01-15

    With the goal of using externally polluted white dwarfs to investigate the water fractions of extrasolar planetesimals, we assemble from the literature a sample that we estimate to be more than 60% complete of DB white dwarfs warmer than 13,000 K, more luminous than 3 Multiplication-Sign 10{sup -3} L{sub Sun }, and within 80 pc of the Sun. When considering all the stars together, we find that the summed mass accretion rate of heavy atoms exceeds that of hydrogen by over a factor of 1000. If so, this sub-population of extrasolar asteroids treated as an ensemble has little water and is at least a factor of 20 drier than CI chondrites, the most primitive meteorites. Furthermore, while an apparent 'excess' of oxygen in a single DB can be interpreted as evidence that the accreted material originated in a water-rich parent body, we show that at least in some cases, there can be sufficient uncertainties in the time history of the accretion rate that such an argument may be ambiguous. Regardless of the difficulty associated with interpreting the results from an individual object, our analysis of the population of polluted DBs provides indirect observational support for the theoretical view that a snow line is important in disks where rocky planetesimals form.

  5. Quantum Spin Liquids and Fractionalization

    NASA Astrophysics Data System (ADS)

    Misguich, Grégoire

    This chapter discusses quantum antiferromagnets which do not break any symmetries at zero temperature - also called "spin liquids" - and focuses on lattice spin models with Heisenberg-like (i.e. SU(2)-symmetric) interactions in dimensions larger than one. We begin by discussing the Lieb-Schultz-Mattis theorem and its recent extension to D > 1 by Hastings (2004), which establishes an important distinction between spin liquids with an integer and with a half-integer spin per unit cell. Spin liquids of the first kind, "band insulators", can often be understood by elementary means, whereas the latter, "Mott insulators", are more complex (featuring "topological order") and support spin-1/2 excitations (spinons). The fermionic formalism (Affleck and Marston, 1988) is described and the effect of fluctuations about mean-field solutions, such as the possible creation of instabilities, is discussed in a qualitative way. In particular, we explain the emergence of gauge modes and their relation to fractionalization. The concept of the projective symmetry group (X.-G. Wen, 2002) is introduced, with the aid of some examples. Finally, we present the phenomenology of (gapped) short-ranged resonating-valence-bond spin liquids, and make contact with the fermionic approach by discussing their description in terms of a fluctuating Z 2 gauge field. Some recent references are given to other types of spin liquid, including gapless ones.

  6. Mineralogical and Geochemical Analyses of Antarctic Lake Sediments: A Reflectance and Moessbauer Spectroscopy Study with Applications for Remote Sensing on Mars

    NASA Technical Reports Server (NTRS)

    Froeschl, Heinz; Lougear, Andre; Trautwein, Alfred X.; Newton, Jason; Doran, Peter T.; Koerner, Wilfried; Koeberl, Christian; Bishop, Janice (Technical Monitor); DeVincenzi, Donald L. (Technical Monitor)

    2000-01-01

    Lakebottom sediments from the Dry Valleys region of Antarctica have been analyzed here in order to study the influence of water chemistry on the mineralogy and geochemistry of these sediments, as well as to evaluate techniques for remote spectral identification of potential biomarker minerals on Mars. Lakes from the Dry Valleys region of Antarctica have been investigated as possible analogs for extinct lake environments on early Mars. Sediment cores were collected in the present study from perennially ice-covered Lake Hoare in the Taylor Valley. These sediments were taken from a core in an oxic region of the lake and another core in an anoxic zone. Differences between the two cores were observed in the sediment color, Fe(II)/Fe(III) ratio, the presence of pyrite, the abundance of Fe, S and some trace elements, and the C, N and S isotope fractionation patterns. The results of visible-infrared reflectance spectroscopy (0.3-25 microns) Mossbauer spectroscopy (77 and 4 K) and X-ray diffraction are combined to determine the mineralogy and composition of these samples. The sediments are dominated by plagioclase, K-feldspar, quartz and pyroxene. Algal mats grow on the bottom of the lake and organic material has been found throughout the cores. Calcite is abundant in some layers of the aerobic core (shallow region) and pyrite is abundant in some layers of the anaerobic core (deep region). Analysis of the spectroscopic features due to organics and carbonates with respect to the abundance of organic C and carbonate contents was performed in order to select optimal spectral bands for remote identification of these components in planetary regoliths. Carbonate bands near 4 and 6.8 microns (approx.2500 and 1500/cm) were detected for carbonate abundances as low as 0.1 wt.% CO2. Organic features at 3.38, 3.42 and 3.51 microns (2960, 2925 and 2850/cm) were detected for organic C abundances as low as 0.06 wt.% C. The d13C trends show a more complex organic history for the anaerobic

  7. Generalized hydrodynamic correlations and fractional memory functions

    NASA Astrophysics Data System (ADS)

    Rodríguez, Rosalio F.; Fujioka, Jorge

    2015-12-01

    A fractional generalized hydrodynamic (GH) model of the longitudinal velocity fluctuations correlation, and its associated memory function, for a complex fluid is analyzed. The adiabatic elimination of fast variables introduces memory effects in the transport equations, and the dynamic of the fluctuations is described by a generalized Langevin equation with long-range noise correlations. These features motivate the introduction of Caputo time fractional derivatives and allows us to calculate analytic expressions for the fractional longitudinal velocity correlation function and its associated memory function. Our analysis eliminates a spurious constant term in the non-fractional memory function found in the non-fractional description. It also produces a significantly slower power-law decay of the memory function in the GH regime that reduces to the well-known exponential decay in the non-fractional Navier-Stokes limit.

  8. Possible isotopic fractionation effects in sputtered minerals

    NASA Technical Reports Server (NTRS)

    Haff, P. K.; Watson, C. C.; Tombrello, T. A.

    1980-01-01

    A model which makes definite predictions for the fractionation of isotopes in sputtered material is discussed. The fractionation patterns are nonlinear, and the pattern for a particular set of isotopes depends on the chemical matrix within which those isotopes are contained. Calculations are presented for all nonmonoisotopic elements contained in the minerals perovskite, anorthite, ackermanite, enstatite, and troilite. All isotopes are fractionated at the level of approximately 4-6 deg/o per atomic mass unit. Oxygen is always positively fractionated (heavier isotopes sputtered preferentially), and heavier elements are generally negatively fractioned (light isotopes sputtered preferentially). The value of Delta (O-18:O-16) is always less by about 1.8 deg/o than a linear extrapolation based upon the calculated delta (O-17:O-16) value would suggest. The phenomenon of both negative and positive fractionation patterns from a single target mineral are used to make an experimental test of the proposed model.

  9. Unpacking the Division Interpretation of a Fraction

    ERIC Educational Resources Information Center

    Poon, Rebecca C.; Lewis, Priscilla Eide

    2015-01-01

    One of the challenges in learning fractions is understanding how and why a fraction can have multiple interpretations. As presented in one textbook, a fraction is "a symbol, such as 2/3, 5/1, or 8/5, used to name a part of a whole, a part of a set, a location on a number line, or a division of whole numbers" (Charles et al. 2012, p.…

  10. Fractional Differential and Integral Inequalities with Applications

    DTIC Science & Technology

    2016-02-14

    nanotechnology . Consider the equation (3.1) ( )(t) = f(, () ) + (, () ), (0) = 0, where 0 < < 1, (, () ), (, ...boundary conditions. References [1] D. Baleanu, Z. B. Guvencs̈ , J.A. T. Machado, New Trends in Nanotechnology and Fractional Calculus Applications...Rivero, J. Trujillo and M. Pilar Velasco, “On Deterministic Fractional Models,” New Trends in Nanotechnology and Fractional Calculus Applications, edited

  11. A dynamic programming approach to adaptive fractionation

    NASA Astrophysics Data System (ADS)

    Ramakrishnan, Jagdish; Craft, David; Bortfeld, Thomas; Tsitsiklis, John N.

    2012-03-01

    We conduct a theoretical study of various solution methods for the adaptive fractionation problem. The two messages of this paper are as follows: (i) dynamic programming (DP) is a useful framework for adaptive radiation therapy, particularly adaptive fractionation, because it allows us to assess how close to optimal different methods are, and (ii) heuristic methods proposed in this paper are near-optimal, and therefore, can be used to evaluate the best possible benefit of using an adaptive fraction size. The essence of adaptive fractionation is to increase the fraction size when the tumor and organ-at-risk (OAR) are far apart (a ‘favorable’ anatomy) and to decrease the fraction size when they are close together. Given that a fixed prescribed dose must be delivered to the tumor over the course of the treatment, such an approach results in a lower cumulative dose to the OAR when compared to that resulting from standard fractionation. We first establish a benchmark by using the DP algorithm to solve the problem exactly. In this case, we characterize the structure of an optimal policy, which provides guidance for our choice of heuristics. We develop two intuitive, numerically near-optimal heuristic policies, which could be used for more complex, high-dimensional problems. Furthermore, one of the heuristics requires only a statistic of the motion probability distribution, making it a reasonable method for use in a realistic setting. Numerically, we find that the amount of decrease in dose to the OAR can vary significantly (5-85%) depending on the amount of motion in the anatomy, the number of fractions and the range of fraction sizes allowed. In general, the decrease in dose to the OAR is more pronounced when: (i) we have a high probability of large tumor-OAR distances, (ii) we use many fractions (as in a hyper-fractionated setting) and (iii) we allow large daily fraction size deviations.

  12. Control of Initialized Fractional-Order Systems

    NASA Technical Reports Server (NTRS)

    Hartly, Tom T.; Lorenzo, Carl F.

    2002-01-01

    Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

  13. Fractionation and utilization of gossypol resin

    SciTech Connect

    Tursunov, A.K.; Dzhailov, A.T.; Fatkhullaev, E.; Sadykov, A.A.

    1985-10-01

    Gossypol resin is formed as a secondary waste product during distillation of fatty acides isolated from cottonseed oil soap stocks; it is insoluble in water but soluble in products of petroleum distillation. For fractionation, gossypol resin was saponified with caustic soda or caustic potash. Using this method, the resin was separated into unsaponifiable (21-24%) and saponifiable (76-79%) parts. Details of the individual fractions of gossypol resin are presented. The unsaponifiable fraction contains hydrocarbons, alcohols, beta-sito-sterol, beta-amyrin, and vitamin E. The fatty acid fraction of the resin is a mixture of fatty acids and lactones.

  14. The derivative of a continued fraction

    SciTech Connect

    Bowman, Kimiko o

    2009-01-01

    The paper considers second order continued fractions associated with (I) the Psi function {psi}(z), (II) the continued fraction component in ln {Gamma}(z) due to Stieltjes. The second order sequences k*{sub s}/k{sub s} provide approximants, some of which are remarkably close. In addition a series form for the convergent {chi}{sub s}={omega}{sub s} associated with a continued fraction provides an expression for the derivatives of a continued fraction. The implementation uses a Maple code for derivatives.

  15. Thermomechanical Fractional Model of TEMHD Rotational Flow

    PubMed Central

    Hamza, F.; Abd El-Latief, A.; Khatan, W.

    2017-01-01

    In this work, the fractional mathematical model of an unsteady rotational flow of Xanthan gum (XG) between two cylinders in the presence of a transverse magnetic field has been studied. This model consists of two fractional parameters α and β representing thermomechanical effects. The Laplace transform is used to obtain the numerical solutions. The fractional parameter influence has been discussed graphically for the functions field distribution (temperature, velocity, stress and electric current distributions). The relationship between the rotation of both cylinders and the fractional parameters has been discussed on the functions field distribution for small and large values of time. PMID:28045941

  16. Developmental Foundations of Children's Fraction Magnitude Knowledge.

    PubMed

    Mou, Yi; Li, Yaoran; Hoard, Mary K; Nugent, Lara D; Chu, Felicia W; Rouder, Jeffrey N; Geary, David C

    2016-01-01

    The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children's mathematical development, and the knowledge of fraction magnitudes influences children's later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8(th) and 9(th) graders' (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9(th) grade algebra achievement. Understanding and fluently identifying the numerator-denominator relation in 7(th) grade emerged as the key predictor of later fraction magnitudes knowledge in both 8(th) and 9(th) grades. Competence at using fraction procedures, knowledge of whole number magnitudes, and the central executive contributed to 9(th) but not 8(th) graders' fraction magnitude knowledge, and knowledge of whole number magnitude contributed to cross-grade gains. The key results suggest fluent processing of numerator-denominator relations presages students' understanding of fractions as magnitudes and that the integration of whole number and fraction magnitudes occurs gradually.

  17. THEORETICAL AND EXPERIMENTAL ASPECTS OF ISOTOPIC FRACTIONATION.

    USGS Publications Warehouse

    O'Neil, James R.

    1986-01-01

    Essential to the interpretation of natural variations of light stable isotope ratios is knowledge of the magnitude and temperature dependence of isotopic fractionation factors between the common minerals and fluids. These fractionation factors are obtained in three ways: (1) Semi-empirical calculations using spectroscopic data and the methods of statistical mechanics. (2) Laboratory calibration studies. (3) Measurements of natural samples whose formation conditions are well-known or highly constrained. In this chapter methods (1) and (2) are evaluated and a review is given of the present state of knowledge of the theory of isotopic fractionation and the fraction that influence the isotopic properties of minerals.

  18. Oxygen isotope fractionation in double carbonates.

    PubMed

    Zheng, Yong-Fei; Böttcher, Michael E

    2016-01-01

    Oxygen isotope fractionations in double carbonates of different crystal structures were calculated by the increment method. Synthesis experiments were performed at 60 °C and 100 °C to determine oxygen and carbon isotope fractionations involving PbMg[CO3]2. The calculations suggest that the double carbonates of calcite structure are systematically enriched in (18)O relative to those of aragonite and mixture structures. Internally consistent oxygen isotope fractionation factors are obtained for these minerals with respect to quartz, calcite and water at a temperature range of 0-1200 °C. The calculated fractionation factors for double carbonate-water systems are generally consistent with the data available from laboratory experiments. The experimentally determined fractionation factors for PbMg[CO3]2, BaMg[CO3]2 and CaMg[CO3]2 against H2O not only fall between fractionation factors involving pure carbonate end-members but are also close to the calculated fractionation factors. In contrast, experimentally determined carbon isotope fractionation factors between PbMg[CO3]2 and CO2 are much closer to theoretical predictions for the cerussite-CO2 system than for the magnesite-CO2 system, similar to the fractionation behavior for BaMg[CO3]2. Therefore, the combined theoretical and experimental results provide insights into the effects of crystal structure and exchange kinetics on oxygen isotope partitioning in double carbonates.

  19. Caputo standard α-family of maps: fractional difference vs. fractional.

    PubMed

    Edelman, M

    2014-06-01

    In this paper, the author compares behaviors of systems which can be described by fractional differential and fractional difference equations using the fractional and fractional difference Caputo standard α-Families of maps as examples. The author shows that properties of fractional difference maps (systems with falling factorial-law memory) are similar to the properties of fractional maps (systems with power-law memory). The similarities (types of attractors, power-law convergence of trajectories, existence of cascade of bifurcations and intermittent cascade of bifurcations type trajectories, and dependence of properties on the memory parameter α) and differences in properties of falling factorial- and power-law memory maps are investigated.

  20. A Fractional Variational Approach to the Fractional Basset-Type Equation

    NASA Astrophysics Data System (ADS)

    Baleanu, Dumitru; Garra, Roberto; Petras, Ivo

    2013-08-01

    In this paper we discuss an application of fractional variational calculus to the Basset-type fractional equations. It is well known that the unsteady motion of a sphere immersed in a Stokes fluid is described by an integro-differential equation involving derivative of real order. Here we study the inverse problem, i.e. we consider the problem from a Lagrangian point of view in the framework of fractional variational calculus. In this way we find an application of fractional variational methods to a classical physical model, finding a Basset-type fractional equation starting from a Lagrangian depending on derivatives of fractional order.

  1. Elemental Modes of Occurrence in an Illinois #6 Coal and Fractions Prepared by Physical Separation Techniques at a Coal Preparation Plant

    SciTech Connect

    Huggins, F.; Seidu, L; Shah, N; Huffman, G; Honaker, R; Kyger, J; Higgins, B; Robertson, J; Pal, S; Seehra, M

    2009-01-01

    In order to gain better insight into elemental partitioning between clean coal and tailings, modes of occurrence have been determined for a number of major and trace elements (S, K, Ca, V, Cr, Mn, Fe, Zn, As, Se, Pb) in an Illinois No.6 coal and fractions prepared by physical separation methods at a commercial coal preparation plant. Elemental modes of occurrence were largely determined directly by XAFS or Moessbauer spectroscopic methods because the concentrations of major minerals and wt.% ash were found to be highly correlated for this coal and derived fractions, rendering correlations between individual elements and minerals ambiguous for inferring elemental modes of occurrence. Of the major elements investigated, iron and potassium are shown to be entirely inorganic in occurrence. Most (90%) of the iron is present as pyrite, with minor fractions in the form of clays and sulfates. All potassium is present in illitic clays. Calcium in the original coal is 80-90% inorganic and is divided between calcite, gypsum, and illite, with the remainder of the calcium present as carboxyl-bound calcium. In the clean coal fraction, organically associated Ca exceeds 50% of the total calcium. This organically-associated form of Ca explains the poorer separation of Ca relative to both K and ash. Among the trace elements, V and Cr are predominantly inorganically associated with illite, but minor amounts (5-15% Cr, 20-30% V) of these elements are also organically associated. Estimates of the V and Cr contents of illite are 420 ppm and 630 ppm, respectively, whereas these elements average 20 and 8 ppm in the macerals. Arsenic in the coal is almost entirely associated with pyrite, with an average As content of about 150 ppm, but some As ({approx} 10%) is present as arsenate due to minor oxidation of the pyrite. The mode of occurrence of Zn, although entirely inorganic, is more complex than normally noted for Illinois basin coals; about 2/3 is present in sphalerite, with lesser

  2. Control of Initialized Fractional-Order Systems

    NASA Technical Reports Server (NTRS)

    Hartley, Tom T.; Lorenzo, Carl F.

    2004-01-01

    Fractional-Order systems, or systems containing fractional derivatives and integrals, have been studied by many in the engineering area. Additionally, very readable discussions, devoted specifically to the subject, are presented by Oldham and Spanier, Miller and Ross, and Pudlubny (1999a). It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional system theory. Of specific interest to electrical engineers are long lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, and chaos. With the growing number of applications, it is important to establish a theory of control for these fractional-order systems, and for the potential use of fractional-order systems as feedback compensators. This topic is addressed in this paper. The first section discusses the control of fractional-order systems using a vector space representation, where initialization is included in the discussion. It should be noted that Bagley and Calico and Padovan and Sawicki both present a fractional state-space representation, which do not include the important historic effects. Incorporation of these effects based on the initialized fractional calculus is presented . The control methods presented in this paper are based on the initialized fractional order system theory. The second section presents an input-output approach. Some of the problems encountered in these sections are: a) the need to introduce a new complex plane to study the dynamics of fractional-order systems, b) the need to properly define the Laplace transform of the fractional derivative, and c) the proper inclusion of the initialization response in the system and control formulation. Following this, the next section generalizes the proportional-plus-integral-control (PI-control) and PID-control (PI-plus- derivative) concepts using fractional integrals. This is then further generalized using general fractional- order

  3. Paper Plate Fractions: The Counting Connection

    ERIC Educational Resources Information Center

    McCoy, Ann; Barnett, Joann; Stine, Tammy

    2016-01-01

    Without a doubt, fractions prove to be a stumbling block for many children. Researchers have suggested a variety of explanations for why this is the case. The introduction of symbolization and operations before the development of conceptual understanding of fractions, a lack of understanding of the role of the numerator and denominator, and an…

  4. Nonlinear Filtering with Fractional Brownian Motion

    SciTech Connect

    Amirdjanova, A.

    2002-12-19

    Our objective is to study a nonlinear filtering problem for the observation process perturbed by a Fractional Brownian Motion (FBM) with Hurst index 1/2 fractional' Zakai equation for the unnormalized optimal filter is derived.

  5. Fractional dynamics pharmacokinetics-pharmacodynamic models.

    PubMed

    Verotta, Davide

    2010-06-01

    While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics-pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics.

  6. Fractional dynamics pharmacokinetics–pharmacodynamic models

    PubMed Central

    2010-01-01

    While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics. PMID:20455076

  7. Fractional ablative laser skin resurfacing: a review.

    PubMed

    Tajirian, Ani L; Tarijian, Ani L; Goldberg, David J

    2011-12-01

    Ablative laser technology has been in use for many years now. The large side effect profile however has limited its use. Fractional ablative technology is a newer development which combines a lesser side effect profile along with similar efficacy. In this paper we review fractional ablative laser skin resurfacing.

  8. Assessing Students' Understanding of Fraction Multiplication

    ERIC Educational Resources Information Center

    Rumsey, Chepina; Guarino, Jody; Beltramini, Jennie; Cole, Shelbi; Farmer, Alicia; Gray, Kristin; Saxby, Morgan

    2016-01-01

    In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…

  9. Representations of the Magnitudes of Fractions

    ERIC Educational Resources Information Center

    Schneider, Michael; Siegler, Robert S.

    2010-01-01

    We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However,…

  10. Tin isotope fractionation in terrestrial cassiterites

    SciTech Connect

    McNaughton, N.J. ); Rosman, K.J.R. )

    1991-02-01

    The isotopic composition of tin has been measured in a range of cassiterites and pure reagents to assess the extent to which this element is isotopically fractionated in natural processes. Only two samples showed evidence of isotopic fractionation, and it is concluded that natural Sn isotope fractionation is small and uncommon. This feature reflects the world dominance of Sn-oxide ores Sn-sulfide ores, and the highly efficient processes of Sn dissolution and precipitation which negate equilibrium and kinetic fractionation of Sn isotopes, respectively. The two samples which show slight fractionation are a highly purified and cassiterite from the Archaean Greenbushes pegmatite, Western Australia. The latter Sn is 0.15{per thousand} per mass unit heavier than the authors laboratory standard, whereas the former is 0.12{per thousand} per mass unit lighter. Although the cassiterite fractionation is considered to result from natural geological processes, the fractionation of purified Sn may be either natural or relate to the purification process, the fractionation of this magnitude has a negligible effect on the current best estimate of the atomic weight of Sn, but it does place a lower limit on its associated accuracy.

  11. Unpacking Referent Units in Fraction Operations

    ERIC Educational Resources Information Center

    Philipp, Randolph A.; Hawthorne, Casey

    2015-01-01

    Although fraction operations are procedurally straightforward, they are complex, because they require learners to conceptualize different units and view quantities in multiple ways. Prospective secondary school teachers sometimes provide an algebraic explanation for inverting and multiplying when dividing fractions. That authors of this article…

  12. Fractions Instruction: Linking Concepts and Procedures

    ERIC Educational Resources Information Center

    Pitsolantis, Nicole; Osana, Helena P.

    2013-01-01

    It is not surprising, as research has shown, that fractions are one of the most difficult of the elementary school math topics to teach and learn in ways that are meaningful. The authors reference a work by James Hiebert, "Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions" (1992), that mathematical concepts should…

  13. In Search of the Prototypical Fraction

    ERIC Educational Resources Information Center

    Wright, Vince

    2013-01-01

    Vince Wright makes a convincing argument for presenting children with a different "prototype" of a fraction to the typical one-half. Consider how the prototype that Wright mentions may be applied to a variety of fraction concepts. We are sure that you will never look at a doughnut in quite the same way.

  14. Engaging Students with Multiple Models of Fractions

    ERIC Educational Resources Information Center

    Zhang, Xiaofen; Clements, M. A.; Ellerton, Nerida F.

    2015-01-01

    An understanding of unit fractions, and especially of one-half, one-third, and one-fourth, is crucially important for elementary school children's development of number sense (CCSSI 2010). We describe multimodal activities designed to assist elementary school students in gaining a rich understanding of unit fractions. Research has shown (Zhang,…

  15. Fractions: A New Slant on Slope

    ERIC Educational Resources Information Center

    Cheng, Ivan

    2010-01-01

    An understanding of fractions is foundational to proportional reasoning and algebra. For example, a direct-variation relationship may include a constant of proportionality that is rational, and linear equations may have solutions that are fractions. Beyond that, a grasp of the concept of proportionality and of rational numbers is necessary for…

  16. Using Technology Effectively to Teach about Fractions

    ERIC Educational Resources Information Center

    Hensberry, Karina K. R.; Moore, Emily B.; Perkins, Katherine

    2015-01-01

    In this article, the authors describe classroom use of technology that successfully engaged fourth grade students (typically aged 9-10) in the United States in learning about fractions. The activities involved the use of an interactive simulation designed to support student learning of fractions, and whole-class discussion where students were…

  17. Estimation's Role in Calculations with Fractions

    ERIC Educational Resources Information Center

    Johanning, Debra I.

    2011-01-01

    Estimation is more than a skill or an isolated topic. It is a thinking tool that needs to be emphasized during instruction so that students will learn to develop algorithmic procedures and meaning for fraction operations. For students to realize when fractions should be added, subtracted, multiplied, or divided, they need to develop a sense of…

  18. Levels of Students' "Conception" of Fractions

    ERIC Educational Resources Information Center

    Pantziara, Marilena; Philippou, George

    2012-01-01

    In this paper, we examine sixth grade students' degree of conceptualization of fractions. A specially developed test aimed to measure students' understanding of fractions along the three stages proposed by Sfard ("1991") was administered to 321 sixth grade students. The Rasch model was applied to specify the reliability of the test…

  19. Understanding Division of Fractions: An Alternative View

    ERIC Educational Resources Information Center

    Fredua-Kwarteng, E.; Ahia, Francis

    2006-01-01

    The purpose of this paper is to offer three alternatives to patterns or visualization used to justify division of fraction "algorithm" invert and multiply". The three main approaches are historical, similar denominators and algebraic, that teachers could use to justify the standard algorithm of division of fraction. The historical approach uses…

  20. Fractional populations in sex-linked inheritance

    NASA Astrophysics Data System (ADS)

    Pyo Lee, Seung; Chung, Myung-Hoon; Koo Kim, Chul; Nahm, Kyun

    2001-03-01

    We study the fractional populations in chromosome inherited diseases. The governing equations for the fractional populations are found and solved in the presence of mutation and selection. The physical fixed points obtained are used to discuss the cases of color blindness and hemophilia.

  1. Mathematical Analogs and the Teaching of Fractions.

    ERIC Educational Resources Information Center

    Charles, Kathy; Nason, Rod; Cooper, Tom

    The literature has noted that some mathematical analogs are more effective than others for the teaching of fractions. This study aimed to evaluate the efficacy of seven mathematical analogs commonly used in the teaching of the partitive quotient fraction construct. A sample of twelve purposively selected Year Three children were presented with…

  2. Egyptian Fractions: Ahmes to Fibonacci to Today.

    ERIC Educational Resources Information Center

    Hurd, Spencer P.

    1991-01-01

    Presented is the ancient Egyptian algorithm for the operations of multiplication and division of integers and fractions. Theorems involving unit fractions, proved by Fibonacci, justifying and extending the Egyptian or Ahmes' methods into the Hindu-Arabic numeric representational system are given. (MDH)

  3. Procedural and Conceptual Knowledge: Adults Reviewing Fractions

    ERIC Educational Resources Information Center

    Baker, William J.; Czarnocha, Bronislaw; Dias, Olen; Doyle, Kathleen; Kennis, James R.

    2012-01-01

    In the United States a majority of the students who enroll in community colleges require a review of secondary math before they are eligible for college level mathematics. In the pre-algebra course, that has a high drop-out rate, the most difficult topic for students is fractions. In order to better understand the fraction concept, Kieren…

  4. The Whole Story: Understanding Fraction Computation

    ERIC Educational Resources Information Center

    Dixon, Juli K.; Tobias, Jennifer M.

    2013-01-01

    What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

  5. Fractions Learning in Children with Mathematics Difficulties

    ERIC Educational Resources Information Center

    Tian, Jing; Siegler, Robert S.

    2016-01-01

    Learning of fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind TA peers in…

  6. [Carbon isotope fractionation inplants]. Final report

    SciTech Connect

    O`Leary, M.H.

    1990-12-31

    The objectives of this research are: To develop a theoretical and experimental framework for understanding isotope fractionations in plants; and to develop methods for using this isotope fractionation for understanding the dynamics of CO{sub 2} fixation in plants. Progress is described.

  7. Making Sense of Fractions and Percentages

    ERIC Educational Resources Information Center

    Whitin, David J.; Whitin, Phyllis

    2012-01-01

    Because fractions and percentages can be difficult for children to grasp, connecting them whenever possible is beneficial. Linking them can foster representational fluency as children simultaneously see the part-whole relationship expressed numerically (as a fraction and as a percentage) and visually (as a pie chart). NCTM advocates these…

  8. Reply to "Comment on 'Fractional quantum mechanics' and 'Fractional Schrödinger equation' ".

    PubMed

    Laskin, Nick

    2016-06-01

    The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum mechanics and fractional quantum mechanics has been presented to emphasize the features of fractional quantum mechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantum mechanics.

  9. Generalized space-time fractional diffusion equation with composite fractional time derivative

    NASA Astrophysics Data System (ADS)

    Tomovski, Živorad; Sandev, Trifce; Metzler, Ralf; Dubbeldam, Johan

    2012-04-01

    We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grünwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form δ(x)ṡ tΓ/(1-β) (β>0).

  10. Representations of the magnitudes of fractions.

    PubMed

    Schneider, Michael; Siegler, Robert S

    2010-10-01

    We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However, atypical characteristics of the presented fractions might have provoked the use of atypical comparison strategies in that study. In our 3 experiments, university and community college students compared more balanced sets of single-digit and multi-digit fractions and consistently exhibited a logarithmic distance effect. Thus, adults used integrated, analog representations, akin to a mental number line, to compare fraction magnitudes. We interpret differences between the past and present findings in terms of different stimuli eliciting different solution strategies.

  11. Fractional tunnelling resonance in plasmonic media

    PubMed Central

    Kang, Ji-Hun; -Han Park, Q.

    2013-01-01

    Metals can transmit light by tunnelling when they possess skin-depth thickness. Tunnelling can be resonantly enhanced if resonators are added to each side of a metal film, such as additional dielectric layers or periodic structures on a metal surface. Here we show that, even with no additional resonators, tunnelling resonance can arise if the metal film is confined and fractionally thin. In a slit waveguide filled with a negative permittivity metallic slab of thickness L, resonance is shown to arise at fractional thicknesses (L = Const./m; m = 1,2,3,…) by the excitation of ‘vortex plasmons'. We experimentally demonstrate fractional tunnelling resonance and vortex plasmons using microwave and negative permittivity metamaterials. The measured spectral peaks of the fractional tunnelling resonance and modes of the vortex plasmons agree with theoretical predictions. Fractional tunnelling resonance and vortex plasmons open new perspectives in resonance physics and promise potential applications in nanotechnology. PMID:23939460

  12. Neutron Imaging Calibration to Measure Void Fraction

    SciTech Connect

    Geoghegan, Patrick J; Bilheux, Hassina Z; Sharma, Vishaldeep; Fricke, Brian A

    2015-01-01

    Void fraction is an intuitive parameter that describes the fraction of vapor in a two-phase flow. It appears as a key variable in most heat transfer and pressure drop correlations used to design evaporating and condensing heat exchangers, as well as determining charge inventory in refrigeration systems. Void fraction measurement is not straightforward, however, and assumptions on the invasiveness of the measuring technique must be made. Neutron radiography or neutron imaging has the potential to be a truly non-invasive void fraction measuring technique but has until recently only offered qualitative descriptions of two-phase flow, in terms of flow maldistributions, for example. This paper describes the calibration approach necessary to employ neutron imaging to measure steady-state void fraction. Experiments were conducted at the High Flux Isotope Reactor (HFIR) Cold Guide 1D neutron imaging facility at Oak Ridge National Laboratory (ORNL), Oak Ridge, TN, USA.

  13. Variable-order fuzzy fractional PID controller.

    PubMed

    Liu, Lu; Pan, Feng; Xue, Dingyu

    2015-03-01

    In this paper, a new tuning method of variable-order fractional fuzzy PID controller (VOFFLC) is proposed for a class of fractional-order and integer-order control plants. Fuzzy logic control (FLC) could easily deal with parameter variations of control system, but the fractional-order parameters are unable to change through this way and it has confined the effectiveness of FLC. Therefore, an attempt is made in this paper to allow all the five parameters of fractional-order PID controller vary along with the transformation of system structure as the outputs of FLC, and the influence of fractional orders λ and μ on control systems has been investigated to make the fuzzy rules for VOFFLC. Four simulation results of different plants are shown to verify the availability of the proposed control strategy.

  14. Fractional kinetics in multi-compartmental systems.

    PubMed

    Dokoumetzidis, Aristides; Magin, Richard; Macheras, Panos

    2010-10-01

    Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems.

  15. A generalized fractional sub-equation method for fractional differential equations with variable coefficients

    NASA Astrophysics Data System (ADS)

    Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

    2012-08-01

    In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space-time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics.

  16. Fractional Modeling of Viscoelasticity in Brain Aneurysms

    NASA Astrophysics Data System (ADS)

    Yu, Yue; Karniadakis, George

    2014-11-01

    We develop fundamental new numerical methods for fractional order PDEs, and investigate corresponding models for arterial walls. Specifically, the arterial wall is a heterogeneous soft tissue with complex biomechanical properties, and its constitutive laws are typically derived using integer-order differential equations. However, recent simulations on 1D model have indicated that fractional order models may offer a more powerful alternative for describing arterial wall mechanics, because they are less sensitive to the parameter estimation compared with the integer-calculus-based models. We study the specific fractional PDEs that better model the properties of the 3D arterial walls, and for the first time employ them in simulating flow structure interactions for patient-specific brain aneurysms. A comparison study indicates that for the integer order models, the viscous behavior strongly depends on the relaxation parameters while the fractional order models are less sensitive. This finding is consistent with what is observed in the 1D models for arterial networks (Perdikaris & Karniadakis, 2014), except that when the fractional order is small, the 3D fractional-order models are more sensitive to the fractional order compared to the 1D models.

  17. Isotopic fractionation by diffusion in groundwater

    NASA Astrophysics Data System (ADS)

    Labolle, Eric M.; Fogg, Graham E.; Eweis, Juana B.; Gravner, Janko; Leaist, Derek G.

    2008-07-01

    During the last decade, isotopic fractionation has gained acceptance as an indicator of microbiological and chemical transformations of contaminants in groundwater. These transformation processes typically favor isotopically light, compared to isotopically heavy, contaminants, resulting in enrichment of the latter in the residual aqueous phase. In these isotope applications, it has been generally presumed that physical transport processes in groundwater have a negligible effect on isotopic enrichment. It is well known, however, that aqueous phase diffusion generally proceeds faster for isotopically light, compared to isotopically heavy, solute molecules, often resulting in isotopic fractionation in groundwater. This paper considers the potential for isotopic fractionation during transport in groundwater resulting from minute isotopic effects on aqueous diffusion coefficients. Analyses of transport in heterogeneous systems delimit the viable range of isotopic fractionation by diffusion in groundwater. Results show that diffusion can result in similar degrees of depletion and enrichment of isotopically heavy solutes during transport in heterogeneous systems with significant diffusion rate-limited mass transfer between fast- and slow-flow zones. Additional analyses and examples explore conditions that attenuate the development of significant fractionation. Examples are presented for 13C methyl tertiary butyl ether and deuterated and nondeuterated isopropanol and tertiary butyl alcohol using aqueous diffusion coefficients measured by the Taylor dispersion method with refractive index profiling as a part of this study. Examples elucidate the potential for diffusive fractionation as a confounder in isotope applications and emphasize the importance of hydrogeologic analysis for assessing the role of diffusive fractionation in isotope applications at contaminant field sites.

  18. Fractional calculus in bioengineering, part 3.

    PubMed

    Magin, Richard L

    2004-01-01

    Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

  19. Fractional Cable Models for Spiny Neuronal Dendrites

    NASA Astrophysics Data System (ADS)

    Henry, B. I.; Langlands, T. A. M.; Wearne, S. L.

    2008-03-01

    Cable equations with fractional order temporal operators are introduced to model electrotonic properties of spiny neuronal dendrites. These equations are derived from Nernst-Planck equations with fractional order operators to model the anomalous subdiffusion that arises from trapping properties of dendritic spines. The fractional cable models predict that postsynaptic potentials propagating along dendrites with larger spine densities can arrive at the soma faster and be sustained at higher levels over longer times. Calibration and validation of the models should provide new insight into the functional implications of altered neuronal spine densities, a hallmark of normal aging and many neurodegenerative disorders.

  20. Matrix approach to discrete fractional calculus II: Partial fractional differential equations

    NASA Astrophysics Data System (ADS)

    Podlubny, Igor; Chechkin, Aleksei; Skovranek, Tomas; Chen, YangQuan; Vinagre Jara, Blas M.

    2009-05-01

    A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny's matrix approach [I. Podlubny, Matrix approach to discrete fractional calculus, Fractional Calculus and Applied Analysis 3 (4) (2000) 359-386]. Four examples of numerical solution of fractional diffusion equation with various combinations of time-/space-fractional derivatives (integer/integer, fractional/integer, integer/fractional, and fractional/fractional) with respect to time and to the spatial variable are provided in order to illustrate how simple and general is the suggested approach. The fifth example illustrates that the method can be equally simply used for fractional differential equations with delays. A set of MATLAB routines for the implementation of the method as well as sample code used to solve the examples have been developed.

  1. Antioxidant activity of cod (Gadus morhua) protein hydrolysates: Fractionation and characterisation of peptide fractions.

    PubMed

    Sabeena Farvin, K H; Andersen, Lisa Lystbæk; Otte, Jeanette; Nielsen, Henrik Hauch; Jessen, Flemming; Jacobsen, Charlotte

    2016-08-01

    This study aimed to characterise peptide fractions (>5kDa, 3-5kDa and <3kDa) with antioxidative activity obtained from a cod protein hydrolysate. The free amino acids in all fractions were dominated by Ala, Gly, Glu and Ser. The total amino acid composition had high proportions of Lys, Ala and Glu. The 3-5kDa and <3kDa fractions were further fractionated by size exclusion chromatography. All sub-fractions showed high Fe(2+) chelating activity. The DPPH radical-scavenging activity of the 3-5kDa fraction was exerted mainly by one sub-fraction dominated by peptides with masses below 600Da. The DPPH radical-scavenging activity of the <3kDa fraction was exerted by sub-fractions with low molecular weight. The highest reducing power was found in a sub-fraction containing peptides rich in Arg, Tyr and Phe. Both free amino acids and low molecular weight peptides thus seemed to contribute to the antioxidative activity of the peptide fractions, and Tyr seemed to play a major role in the antioxidant activity.

  2. Synthesis, structure of [H{sub 3} dien].(MF{sub 6}).H{sub 2}O (M=Cr, Fe) and {sup 57}Fe Moessbauer study of [H{sub 3} dien].(FeF{sub 6}).H{sub 2}O

    SciTech Connect

    Ben Ali, Amor Trang Dang, Minh; Greneche, Jean-Marc; Hemon-Ribaud, Annie; Leblanc, Marc; Maisonneuve, Vincent

    2007-06-15

    Single crystals of [H{sub 3} dien].(FeF{sub 6}).H{sub 2}O (I) and [H{sub 3} dien].(CrF{sub 6}).H{sub 2}O (II) are obtained by solvothermal synthesis under microwave heating. I is orthorhombic (Pna2{sub 1}) with a=11.530(2) A, b=6.6446(8) A, c=13.787(3) A, V=1056.3(2) A{sup 3} and Z=4. II is monoclinic (P2{sub 1} /c) with a=13.706(1) A, b=6.7606(6) A, c=11.3181(9) A, {beta}=99.38(1){sup o}, V=1034.7(1) A{sup 3} and Z=4. The structure determinations, performed from single crystal X-ray diffraction data, lead to the R {sub 1}/wR {sub 2} reliability factors 0.028/0.066 for I and 0.035/0.102 for II. The structures of I and II are built up from isolated FeF{sub 6} or CrF{sub 6} octahedra, water molecules and triprotonated amines. In both structures, each octahedron is connected by hydrogen bonds to six organic cations and two water molecules. The iron-based compound is also characterized by {sup 57}Fe Moessbauer spectrometry: the hyperfine structure confirms the presence of Fe{sup 3+} in octahedral coordination and reveals the existence of paramagnetic spin fluctuations. - Graphical abstract: Moessbauer spectra of [H{sub 3} dien].(FeF{sub 6}).H{sub 2}O.

  3. A fractional-order infectivity SIR model

    NASA Astrophysics Data System (ADS)

    Angstmann, C. N.; Henry, B. I.; McGann, A. V.

    2016-06-01

    Fractional-order SIR models have become increasingly popular in the literature in recent years, however unlike the standard SIR model, they often lack a derivation from an underlying stochastic process. Here we derive a fractional-order infectivity SIR model from a stochastic process that incorporates a time-since-infection dependence on the infectivity of individuals. The fractional derivative appears in the generalised master equations of a continuous time random walk through SIR compartments, with a power-law function in the infectivity. We show that this model can also be formulated as an infection-age structured Kermack-McKendrick integro-differential SIR model. Under the appropriate limit the fractional infectivity model reduces to the standard ordinary differential equation SIR model.

  4. Tellurium Stable Isotope Fractionation in Chondritic Meteorites

    NASA Astrophysics Data System (ADS)

    Fehr, M. A.; Hammond, S. J.; Parkinson, I. J.

    2014-09-01

    New Te double spike procedures were set up to obtain high-precision accurate Te stable isotope data. Tellurium stable isotope data for 16 chondrite falls are presented, providing evidence for significant Te stable isotope fractionation.

  5. Developmental predictors of fraction concepts and procedures.

    PubMed

    Jordan, Nancy C; Hansen, Nicole; Fuchs, Lynn S; Siegler, Robert S; Gersten, Russell; Micklos, Deborah

    2013-09-01

    Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each contributed uniquely to later conceptual understanding of fractions. Number line estimation, attentive behavior, calculation fluency, and working memory made unique contributions to acquisition of fraction arithmetic procedures. Notably, number line estimation made the largest independent contribution in both models. The results suggest that although there is considerable shared variance among the predictors, both general and number-related competencies are uniquely important for explaining why some children struggle with fractions.

  6. Casimir Energy Associated With Fractional Derivative Field

    SciTech Connect

    Lim, S. C.

    2007-04-28

    Casimir energy associated with fractional derivative scalar massless field at zero and positive temperature can be obtained using the regularization based on generalized Riemann zeta function of Epstein-Hurwitz type.

  7. Ca isotope fractionation on the moon

    NASA Technical Reports Server (NTRS)

    Russell, W. A.; Papanastassiou, D. A.; Tombrello, T. A.; Epstein, S.

    1977-01-01

    Ca has been measured in a lunar soil in order to establish the presence of isotopically mass-fractionated components. Ca was extracted by a series of water leaches after the soils were 'activated' by brief exposures to fluorine gas. The O2 obtained by this fluorination is found to have delta (O-18) of +21 per mil and to be, therefore, significantly mass-fractionated. Ca obtained in the leaches was analyzed using the double-spike technique. Very small Ca isotope fractionation is found in the leaches of this soil of up to 1 per mil per mass unit difference. The small Ca effects are in marked contrast to the measured delta (O-18) for the same sample and to large effects observed in many soils for oxygen, silicon, sulfur, and potassium. The data on Ca provide stringent constraints on models which attempt to explain the isotope mass-fractionation effects in lunar soils.

  8. Early predictors of middle school fraction knowledge.

    PubMed

    Bailey, Drew H; Siegler, Robert S; Geary, David C

    2014-09-01

    Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic proficiency, domain general cognitive abilities, parental income and education, race, and gender. Similarly, knowledge of whole number arithmetic in first grade predicted knowledge of fraction arithmetic in middle school, controlling for whole number magnitude knowledge in first grade and the other control variables. In contrast, neither type of early whole number knowledge uniquely predicted middle school reading achievement. We discuss the implications of these findings for theories of numerical development and for improving mathematics learning.

  9. Bio-oil fractionation and condensation

    DOEpatents

    Brown, Robert C; Jones, Samuel T; Pollard, Anthony

    2013-07-02

    A method of fractionating bio-oil vapors which involves providing bio-oil vapors comprising bio-oil constituents is described. The bio-oil vapors are cooled in a first stage which comprises a condenser having passages for the bio-oil separated by a heat conducting wall from passages for a coolant. The coolant in the condenser of the first stage is maintained at a substantially constant temperature, set at a temperature in the range of 75 to 100.degree. C., to condense a first liquid fraction of liquefied bio-oil constituents in the condenser of the first stage. The first liquid fraction of liquified bio-oil constituents from the condenser in the first stage is collected. Also described are steps for subsequently recovering further liquid fractions of liquefied bio-oil constituents. Particular compositions of bio-oil condensation products are also described.

  10. [Plasma fractionation in the world: current status].

    PubMed

    Burnouf, T

    2007-05-01

    From 22 to 25 million liters of plasma are fractionated yearly in about 70 fractionation plants, either private or government-owned, mainly located in industrialized countries, and with a capacity ranging from 50000 to three million liters. In an increasingly global environment, the plasma industry has recently gone through a major consolidation phase that has seen mergers and acquisitions, and has led to the closure of a number of small plants in Europe. Currently, some fifteen countries are involved into contract plasma fractionation programs to ensure a supply of plasma-derived medicinal products. The majority of the plasma for fractionation is obtained by automated plasmapheresis, the remaining (recovered plasma) being prepared from whole blood as a by-product of red cell production. Plasma for fractionation should be produced, and controlled following well established procedures to meet the strict quality requirements set by regulatory authorities and fractionators. The plasma fractionation technology still relies heavily on the cold ethanol fractionation process, but has been improved by the introduction of modern chromatographic purification methods, and efficient viral inactivation and removal treatments, ensuring quality and safety to a large portfolio of fractionated plasma products. The safety of these products with regards to the risk of transmission of variant Creutzfeldt-Jakob disease seems to be provided, based on current scientific data, by extensive removal of the infectious agent during certain fractionation steps. The leading plasma product is now the intravenous immunoglobulin G, which has replaced factor VIII and albumin in this role. The supply of plasma products (most specifically coagulation products and immunoglobulin) at an affordable price and in sufficient quantity remains an issue; the problem is particularly acute in developing countries, as the switch to recombinant factor VIII in rich countries has not solved the supply issue and has

  11. Fractional calculus in bioengineering, part 2.

    PubMed

    Magin, Richard L

    2004-01-01

    Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

  12. Laser Resurfacing: Full Field and Fractional.

    PubMed

    Pozner, Jason N; DiBernardo, Barry E

    2016-07-01

    Laser resurfacing is a very popular procedure worldwide. Full field and fractional lasers are used in many aesthetic practices. There have been significant advances in laser resurfacing in the past few years, which make patient treatments more efficacious and with less downtime. Erbium and carbon dioxide and ablative, nonablative, and hybrid fractional lasers are all extremely effective and popular tools that have a place in plastic surgery and dermatology offices.

  13. Isotope fractionation of benzene during partitioning - Revisited.

    PubMed

    Kopinke, F-D; Georgi, A; Imfeld, G; Richnow, H-H

    2017-02-01

    Isotope fractionation between benzene-D0 and benzene-D6 caused by multi-step partitioning of the benzenes between water and two organic solvents, n-octane and 1-octanol, as well as between water and the gas phase, was measured. The obtained fractionation factors αH = KH/KD are αH = 1.080 ± 0.015 and αH = 1.074 ± 0.015 for extraction into n-octane and 1-octanol, respectively, and αH = 1.049 ± 0.010 for evaporation from aqueous solution. The comparison of solvent- and gas-phase partitioning reveals that about 2/3 of the driving force of fractionation is due to different interactions in the aqueous phase, whereas 1/3 is due to different interactions in the organic phase. The heavy benzene isotopologue behaves more 'hydrophilically' and the light one more 'hydrophobically'. This synergistic alignment gives rise to relatively large fractionation effects in partitioning between water and non-polar organic matter. In contrast to a previous study, there is no indication of strong fractionation by specific interactions between benzene and octanol. Partitioning under non-equilibrium conditions yields smaller apparent fractionation effects due to opposite trends of thermodynamic and kinetic fractionation parameters, i.e. partition and diffusion coefficients of the isotopologues. This may have consequences which should be taken into account when considering isotope fractionation due to sorption in environmental compartments.

  14. On the Cn/Zm fractional branes

    NASA Astrophysics Data System (ADS)

    Karp, Robert L.

    2009-02-01

    We construct several geometric representatives for the Cn/Zm fractional branes on either a partially or the completely resolved orbifold. In the process we use large radius and conifold-type monodromies and provide a strong consistency check. In particular, for C3/Z5 we give three different sets of geometric representatives. We also find the explicit Seiberg duality which connects our fractional branes to the ones given by the McKay correspondence.

  15. Locating Fraction on a Number Line

    ERIC Educational Resources Information Center

    Hannula, Markku S.

    2003-01-01

    Based on a survey of 3067 Finnish 5th and 7th graders and a task-based interview of 20 7th graders we examine student's understanding of fraction. Two tasks frame a specific fraction (3/4) in different contexts: as part of an eight-piece bar (area context) and as a location on a number line. The results suggest that students' understanding of…

  16. The Vertical Linear Fractional Initialization Problem

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    1999-01-01

    This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.

  17. Wave function methods for fractional electrons.

    PubMed

    Steinmann, Stephan N; Yang, Weitao

    2013-08-21

    Determining accurate chemical potentials is of considerable interest in various chemical and physical contexts: from small molecular charge-transfer complexes to bandgap in bulk materials such as semi-conductors. Chemical potentials are typically evaluated either by density functional theory, or, alternatively, by computationally more intensive Greens function based GW computations. To calculate chemical potentials, the ground state energy needs to be defined for fractional charges. We thus explore an extension of wave function theories to fractional charges, and investigate the ionization potential and electron affinity as the derivatives of the energy with respect to the electron number. The ultimate aim is to access the chemical potential of correlated wave function methods without the need of explicitly changing the numbers of electrons, making the approach readily applicable to bulk materials. We find that even though second order perturbation theory reduces the fractional charge error considerably compared to Hartree-Fock and standard density functionals, higher order perturbation theory is more accurate and coupled-cluster approaches are even more robust, provided the electrons are bound at the Hartree-Fock level. The success of post-HF approaches to improve over HF relies on two equally important aspects: the integer values are more accurate and the Coulomb correlation between the fractionally occupied orbital and all others improves the straight line behavior significantly as identified by a correction to Hartree-Fock. Our description of fractional electrons is also applicable to fractional spins, illustrating the ability of coupled-cluster singles and doubles to deal with two degenerate fractionally occupied orbitals, but its inadequacy for three and more fractional spins, which occur, for instance, for spherical atoms and when dissociating double bonds. Our approach explores the realm of typical wave function methods that are applied mostly in molecular

  18. Fokker Planck equation with fractional coordinate derivatives

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.; Zaslavsky, George M.

    2008-11-01

    Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations, with averaging with respect to a fast variable, is used. The main assumption is that the correlation function of probability densities of particles to make a step has a power-law dependence. As a result, we obtain a Fokker-Planck equation with fractional coordinate derivative of order 1<α<2.

  19. Void fraction prediction in subchannel geometry

    SciTech Connect

    Khan, H.J.; Kosaly, G.

    1986-01-01

    Two-phase flow void fraction calculation via drift flux formulation requires specific correlations for the distribution parameter, C/sub 0/, and the vapor drift velocity, V/sub gj/. The void fraction may then be calculated from Zuber-Findlay's void-quality model. The distribution parameter is defined using void and flow distributions. Different correlations for C/sub 0/ are available for bundle-averaged void fraction calculation. Yet no such correlations have been developed for subchannel void fraction calculation. The aim of this summary is to demonstrate the results of subchannel void fraction calculation obtained from the model developed here. The three-dimensional subchannel drift flux code CANAL has been used in the present analysis to perform the calculations. The code uses four conservation equations, which include liquid and vapor continuity equations in addition to mixture momentum and energy equations. The subchannel mass flux and quality prediction capability of CANAL has already been demonstrated for a wide range of experiments. Therefore, with the use of appropriate drift flux parameters, subchannel void fractions can be calculated by CANAL.

  20. Maximizing Tumor Immunity With Fractionated Radiation

    SciTech Connect

    Schaue, Doerthe; Ratikan, Josephine A.; Iwamoto, Keisuke S.; McBride, William H.

    2012-07-15

    Purpose: Technologic advances have led to increased clinical use of higher-sized fractions of radiation dose and higher total doses. How these modify the pathways involved in tumor cell death, normal tissue response, and signaling to the immune system has been inadequately explored. Here we ask how radiation dose and fraction size affect antitumor immunity, the suppression thereof, and how this might relate to tumor control. Methods and Materials: Mice bearing B16-OVA murine melanoma were treated with up to 15 Gy radiation given in various-size fractions, and tumor growth followed. The tumor-specific immune response in the spleen was assessed by interferon-{gamma} enzyme-linked immunospot (ELISPOT) assay with ovalbumin (OVA) as the surrogate tumor antigen and the contribution of regulatory T cells (Tregs) determined by the proportion of CD4{sup +}CD25{sup hi}Foxp3{sup +} T cells. Results: After single doses, tumor control increased with the size of radiation dose, as did the number of tumor-reactive T cells. This was offset at the highest dose by an increase in Treg representation. Fractionated treatment with medium-size radiation doses of 7.5 Gy/fraction gave the best tumor control and tumor immunity while maintaining low Treg numbers. Conclusions: Radiation can be an immune adjuvant, but the response varies with the size of dose per fraction. The ultimate challenge is to optimally integrate cancer immunotherapy into radiation therapy.

  1. Isotopic fractionation of tritium in biological systems.

    PubMed

    Le Goff, Pierre; Fromm, Michel; Vichot, Laurent; Badot, Pierre-Marie; Guétat, Philippe

    2014-04-01

    Isotopic fractionation of tritium is a highly relevant issue in radiation protection and requires certain radioecological considerations. Sound evaluation of this factor is indeed necessary to determine whether environmental compartments are enriched/depleted in tritium or if tritium is, on the contrary, isotopically well-distributed in a given system. The ubiquity of tritium and the standard analytical methods used to assay it may induce biases in both the measurement and the signification that is accorded to the so-called fractionation: based on an exhaustive review of the literature, we show how, sometimes large deviations may appear. It is shown that when comparing the non-exchangeable fraction of organically bound tritium (neOBT) to another fraction of tritium (e.g. tritiated water) the preparation of samples and the measurement of neOBT reported frequently led to underestimation of the ratio of tritium to hydrogen (T/H) in the non-exchangeable compartment by a factor of 5% to 50%. In the present study, corrections are proposed for most of the biological matrices studied so far. Nevertheless, the values of isotopic fractionation reported in the literature remain difficult to compare with each other, especially since the physical quantities and units often vary between authors. Some improvements are proposed to better define what should encompass the concepts of exchangeable and non-exchangeable fractions.

  2. Approximate solutions to fractional subdiffusion equations

    NASA Astrophysics Data System (ADS)

    Hristov, J.

    2011-03-01

    The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile. The solution was performed with Riemann-Liouville time-fractional derivative since the integral approach avoids the definition of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems): 1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed through the M-Wright function. The solutions demonstrate some basic issues of the suggested integral approach, among them: a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical results allowing comparisons to the known solutions expressed to the M-Wright function and error estimations.

  3. Sedimentary environments and preservation biases limit sulfur isotope fractionation observed in pyrite, despite large microbial fractionations

    NASA Astrophysics Data System (ADS)

    Halevy, I.; Wing, B. A.; Wenk, C.; Guimond, C.

    2015-12-01

    Microbial S isotope fractionations close to the thermodynamic fractionation between sulfate and sulfide (~70‰) are encountered only at the slowest rates of sulfate reduction in laboratory cultures. In turn, the slowest laboratory reduction rates overlap with only the highest values of cell-specific sulfate reduction rates measured in marine sediments. This chain-of-logic implies that sulfate-reducing microbes in the marine sedimentary biosphere fractionate S isotopes at magnitudes close to the thermodynamic limit. Recent observations from sulfate-poor environments indicate that fractionations are large even at micromolar sulfate concentrations, in agreement with model predictions of near-thermodynamic S isotope fractionation at these sulfate concentrations as long as cell-specific sulfate reduction rates are low. Despite the expectation of large microbial fractionations, pyrite in both modern marine sediments and Phanerozoic sedimentary rocks records apparent fractionations ranging from 0 to more than 70‰. We suggest that the observed range of modern marine and geologic apparent fractionations recorded in pyrite does not reflect variability in intrinsic microbial behavior, but an early diagenetic modulation of large microbial fractionations, which are pinned to the thermodynamic limit by the low natural rates of sulfate reduction. With a diagenetic model developed in this study, we show that the entire range of apparent fractionations is possible with microbial fractionations at the thermodynamic limit. Apparent fractionations depend on a variety of physical parameters of the sedimentary environment like sedimentation rate, porosity, and organic matter content, most of which correlate with water depth. These findings, in combination with knowledge about the preservation potential of sediments deposited at different depths, make predictions for the observed geologic range of apparent fractionations, and ways in which it differs from the range in modern marine

  4. The Two Faces of Fractionated Photodynamic Therapy: Increasing Efficacy With Light Fractionation or Adjuvant Use of Fractional Laser Technology.

    PubMed

    Juhasz, Margit L W; Levin, Melissa K; Marmur, Ellen S

    2016-11-01

    "Fractionated photodynamic therapy (PDT)" is a new term being used by dermatologists to describe advances in PDT technology including fractionated light or the adjuvant use of fractional lasers. Although dermatologists have used PDT since the early 1990s for the treatment of photodamage and precancerous lesions, newer developments in technology have allowed for the treatment of non-melanoma skin cancers (NMSCs), in ammatory disorders, and even uses in the eld of anti-aging. Recent developments in fractionated light therapy have allowed for PDT with dark intervals and two-fold illumination schemes to increase cellular damage and apoptosis. Combining PDT with fractional laser technology has allowed for enhanced dermal penetration of topical photosensitizers including 5-aminolevulinic acid (ALA) and methyl aminolevulinate (MAL), as well as increased ef cacy of treatment. These advances in PDT technology will allow for increased convenience, decreased treatment time, only one application of topical photosensitizer, and decreased cost to the patient and dermatologist. J Drugs Dermatol. 2016;15(11):1324-1328..

  5. Moessbauer spectroscopy of the SNC meteorite Zagami

    NASA Technical Reports Server (NTRS)

    Agerkvist, D. P.; Vistisen, L.

    1993-01-01

    We have performed Mossbauer spectroscopy on two different pieces of the meteorite Zagami belonging to the group of SNC meteorites. In one of the samples we found a substantial amount of olivine inter grown with one kind of pyroxene, and also another kind of pyroxene very similar to the pyroxene in the other sample we examined. Both samples showed less than 1 percent of Fe(3+) in the silicate phase. The group of SNC meteorites called shergottites, to which Zagami belongs, are achondrites whose texture, mineralogy and composition resembles those of terrestrial diabases. The results from the investigation are presented.

  6. Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

    NASA Astrophysics Data System (ADS)

    Xu, Kaixuan; Wang, Jun

    2017-02-01

    In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model.

  7. Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes.

    PubMed

    Matthews, Percival G; Chesney, Dana L

    2015-05-01

    This study presents evidence that humans have intuitive, perceptually based access to the abstract fraction magnitudes instantiated by nonsymbolic ratio stimuli. Moreover, it shows these perceptually accessed magnitudes can be easily compared with symbolically represented fractions. In cross-format comparisons, participants picked the larger of two ratios. Ratios were presented either symbolically as fractions or nonsymbolically as paired dot arrays or as paired circles. Response patterns were consistent with participants comparing specific analog fractional magnitudes independently of the particular formats in which they were presented. These results pose a challenge to accounts that argue human cognitive architecture is ill-suited for processing fractions. Instead, it seems that humans can process nonsymbolic ratio magnitudes via perceptual routes and without recourse to conscious symbolic algorithms, analogous to the processing of whole number magnitudes. These findings have important implications for theories regarding the nature of human number sense - they imply that fractions may in some sense be natural numbers, too.

  8. A high-speed algorithm for computation of fractional differentiation and fractional integration.

    PubMed

    Fukunaga, Masataka; Shimizu, Nobuyuki

    2013-05-13

    A high-speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm, the stored data are not the function to be differentiated or integrated but the weighted integrals of the function. The intervals of integration for the memory can be increased without loss of accuracy as the computing time-step n increases. The computing cost varies as n log n, as opposed to n(2) of standard algorithms.

  9. Jacobi wavelet operational matrix of fractional integration for solving fractional integro-differential equation

    NASA Astrophysics Data System (ADS)

    Rong, Loh Jian; Chang, Phang

    2016-02-01

    In this paper, we first define generalized shifted Jacobi polynomial on interval and then use it to define Jacobi wavelet. Then, the operational matrix of fractional integration for Jacobi wavelet is being derived to solve fractional differential equation and fractional integro-differential equation. This method can be seen as a generalization of other orthogonal wavelet operational methods, e.g. Legendre wavelets, Chebyshev wavelets of 1st kind, Chebyshev wavelets of 2nd kind, etc. which are special cases of the Jacobi wavelets. We apply our method to a special type of fractional integro-differential equation of Fredholm type.

  10. Fractional Adams-Bashforth/Moulton methods: An application to the fractional Keller-Segel chemotaxis system

    NASA Astrophysics Data System (ADS)

    Zayernouri, Mohsen; Matzavinos, Anastasios

    2016-07-01

    We first formulate a fractional class of explicit Adams-Bashforth (A-B) and implicit Adams-Moulton (A-M) methods of first- and second-order accuracy for the time-integration of τ 0 CDt u (x , t) = g (t ; u), τ ∈ (0 , 1 ], where τ 0 CDt denotes the fractional derivative in the Caputo sense. In this fractional setting and in contrast to the standard Adams methods, an extra history load term emerges and the associated weight coefficients are τ-dependent. However when τ = 1, the developed schemes reduce to the well-known A-B and A-M methods with standard coefficients. Hence, in terms of scientific computing, our approach constitutes a minimal modification of the existing Adams libraries. Next, we develop an implicit-explicit (IMEX) splitting scheme for linear and nonlinear fractional PDEs of a general advection-reaction-diffusion type, and we apply our scheme to the time-space fractional Keller-Segel chemotaxis system. In this context, we evaluate the nonlinear advection term explicitly, employing the fractional A-B method in the prediction step, and we treat the corresponding diffusion term implicitly in the correction step using the fractional A-M scheme. Moreover, we perform the corresponding spatial discretization by employing an efficient and spectrally-accurate fractional spectral collocation method. Our numerical experiments exhibit the efficiency of the proposed IMEX scheme in solving nonlinear fractional PDEs.

  11. On the origins of generalized fractional calculus

    NASA Astrophysics Data System (ADS)

    Kiryakova, Virginia

    2015-11-01

    In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer

  12. Attitude Estimation in Fractionated Spacecraft Cluster Systems

    NASA Technical Reports Server (NTRS)

    Hadaegh, Fred Y.; Blackmore, James C.

    2011-01-01

    An attitude estimation was examined in fractioned free-flying spacecraft. Instead of a single, monolithic spacecraft, a fractionated free-flying spacecraft uses multiple spacecraft modules. These modules are connected only through wireless communication links and, potentially, wireless power links. The key advantage of this concept is the ability to respond to uncertainty. For example, if a single spacecraft module in the cluster fails, a new one can be launched at a lower cost and risk than would be incurred with onorbit servicing or replacement of the monolithic spacecraft. In order to create such a system, however, it is essential to know what the navigation capabilities of the fractionated system are as a function of the capabilities of the individual modules, and to have an algorithm that can perform estimation of the attitudes and relative positions of the modules with fractionated sensing capabilities. Looking specifically at fractionated attitude estimation with startrackers and optical relative attitude sensors, a set of mathematical tools has been developed that specify the set of sensors necessary to ensure that the attitude of the entire cluster ( cluster attitude ) can be observed. Also developed was a navigation filter that can estimate the cluster attitude if these conditions are satisfied. Each module in the cluster may have either a startracker, a relative attitude sensor, or both. An extended Kalman filter can be used to estimate the attitude of all modules. A range of estimation performances can be achieved depending on the sensors used and the topology of the sensing network.

  13. Current Status of Fractional Laser Resurfacing.

    PubMed

    Carniol, Paul J; Hamilton, Mark M; Carniol, Eric T

    2015-01-01

    Fractional lasers were first developed based on observations of lasers designed for hair transplantation. In 2007, ablative fractional laser resurfacing was introduced. The fractionation allowed deeper tissue penetration, leading to greater tissue contraction, collagen production and tissue remodeling. Since then, fractional erbium:YAG resurfacing lasers have also been introduced. These lasers have yielded excellent results in treating photoaging, acne scarring, and dyschromia. With the adjustment of microspot density, pulse duration, number of passes, and fluence, the surgeon can adjust the treatment effects. These lasers have allowed surgeons to treat patients with higher Fitzpatrick skin types (types IV to VI) and greater individualize treatments to various facial subunits. Immunohistochemical analysis has demonstrated remodeling effects of the tissues for several months, producing longer lasting results. Adjuvant treatments are also under investigation, including concomitant face-lift, product deposition, and platelet-rich plasma. Finally, there is a short recovery time from treatment with these lasers, allowing patients to resume regular activities more quickly. Although there is a relatively high safety profile for ablative fractionated lasers, surgeons should be aware of the limitations of specific treatments and the associated risks and complications.

  14. On sampling fractions and electron shower shapes

    SciTech Connect

    Peryshkin, Alexander; Raja, Rajendran; /Fermilab

    2011-12-01

    We study the usage of various definitions of sampling fractions in understanding electron shower shapes in a sampling multilayer electromagnetic calorimeter. We show that the sampling fractions obtained by the conventional definition (I) of (average observed energy in layer)/(average deposited energy in layer) will not give the best energy resolution for the calorimeter. The reason for this is shown to be the presence of layer by layer correlations in an electromagnetic shower. The best resolution is obtained by minimizing the deviation from the total input energy using a least squares algorithm. The 'sampling fractions' obtained by this method (II) are shown to give the best resolution for overall energy. We further show that the method (II) sampling fractions are obtained by summing the columns of a non-local {lambda} tensor that incorporates the correlations. We establish that the sampling fractions (II) cannot be used to predict the layer by layer energies and that one needs to employ the full {lambda} tensor for this purpose. This effect is again a result of the correlations.

  15. Minimizing metastatic risk in radiotherapy fractionation schedules

    NASA Astrophysics Data System (ADS)

    Badri, Hamidreza; Ramakrishnan, Jagdish; Leder, Kevin

    2015-11-01

    Metastasis is the process by which cells from a primary tumor disperse and form new tumors at distant anatomical locations. The treatment and prevention of metastatic cancer remains an extremely challenging problem. This work introduces a novel biologically motivated objective function to the radiation optimization community that takes into account metastatic risk instead of the status of the primary tumor. In this work, we consider the problem of developing fractionated irradiation schedules that minimize production of metastatic cancer cells while keeping normal tissue damage below an acceptable level. A dynamic programming framework is utilized to determine the optimal fractionation scheme. We evaluated our approach on a breast cancer case using the heart and the lung as organs-at-risk (OAR). For small tumor α /β values, hypo-fractionated schedules were optimal, which is consistent with standard models. However, for relatively larger α /β values, we found the type of schedule depended on various parameters such as the time when metastatic risk was evaluated, the α /β values of the OARs, and the normal tissue sparing factors. Interestingly, in contrast to standard models, hypo-fractionated and semi-hypo-fractionated schedules (large initial doses with doses tapering off with time) were suggested even with large tumor α/β values. Numerical results indicate the potential for significant reduction in metastatic risk.

  16. Variable Order and Distributed Order Fractional Operators

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    2002-01-01

    Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

  17. From Students' Problem-Solving Strategies to Connections in Fractions

    ERIC Educational Resources Information Center

    Flores, Alfinio; Klein, Erika

    2005-01-01

    Strategies that children used to solve a fraction problem are presented, and an insight into how students think about divisions and fractions is described. Teachers can use these strategies to help students establish connections related to fractions.

  18. Extension of many-body theory and approximate density functionals to fractional charges and fractional spins.

    PubMed

    Yang, Weitao; Mori-Sánchez, Paula; Cohen, Aron J

    2013-09-14

    The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G(0), the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G(0). We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the

  19. Deuterium Fractionation just after the Star Formation

    NASA Astrophysics Data System (ADS)

    Shibata, D.; Sakai, N.; Yamamoto, S.

    2013-10-01

    We have recently conducted a five-point strip observation of the DCO+, H13CO+, DNC, HN13C, and N2H+ lines toward low mass Class I protostar L1551 IRS5, and have evaluated the deuterium fractionation ratios DCO+/HCO+ and DNC/HNC. The DCO+/HCO+ ratio is found to be lower toward the protostar position than those toward the adjacent positions. On the other hand, the DNC/HNC ratio does not show such a decrease toward the protostar position. This suggests that the deuterium fractionation ratio of the neutral species is conserved after the star formation. If so, the deuterium fractionation of the neutral species can be used as a novel tracer to investigate the initial condition of the star formation process.

  20. Fractional Fourier processing of quantum light.

    PubMed

    Sun, Yifan; Tao, Ran; Zhang, Xiangdong

    2014-01-13

    We have extended Fourier transform of quantum light to a fractional Fourier processing, and demonstrated that a classical optical fractional Fourier processor can be used for the shaping of quantum correlations between two or more photons. Comparing the present method with that of Fourier processing, we find that fractional Fourier processing for quantum light possesses many advantages. Based on such a method, not only quantum correlations can be shaped more rich, but also the initial states can be easily identified. Moreover, the twisted phase information can be recovered and quantum states are easily controlled in performing quantum information experiments. Our findings open up new avenues for the manipulation of correlations between photons in optical quantum information processing.

  1. Fractionalized Z_{2} Classical Heisenberg Spin Liquids.

    PubMed

    Rehn, J; Sen, Arnab; Moessner, R

    2017-01-27

    Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalized spin liquid phase, the so-called Coulomb or U(1) spin liquid, has until recently been identified: This exhibits algebraic spin correlations and impurity moments, "orphan spins," whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalization in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z_{2} spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavor.

  2. Surfactant recovery from water using foam fractionation

    SciTech Connect

    Tharapiwattananon, N.; Osuwan, S.; Scamehorn, J.F.

    1996-05-01

    The purpose of this study was to investigate the use of foam fractionation to recover surfactant from water. A simple continuous mode foam fractionation was used and three surfactants were studied (two anionic and one cationic). The effects of air flow rate, foam height, liquid height, liquid feed surfactant concentration, and sparger porosity were studied. This technique was shown to be effective in either surfactant recovery or the reduction of surfactant concentration in water to acceptable levels. As an example of the effectiveness of this technique, the cetylpyridinium chloride concentration in water can be reduced by 90% in one stage with a liquid residence time of 375 minutes. The surfactant concentration in the collapsed foam is 21.5 times the feed concentration. This cationic surfactant was easier to remove from water by foam fractionation than the anionic surfactants studied.

  3. Isotope Fractionation in the Interstellar Medium

    NASA Technical Reports Server (NTRS)

    Charnley, Steven

    2011-01-01

    Anomalously fractionated isotopic material is found in many primitive Solar System objects, such as meteorites and comets. It is thought, in some cases, to trace interstellar matter that was incorporated into the Solar Nebula without undergoing significant processing. We will present the results of models of the nitrogen, oxygen, and carbon fractionation chemistry in dense molecular clouds, particularly in cores where substantial freeze-out of molecules on to dust has occurred. The range of fractionation ratios expected in different interstellar molecules will be discussed and compared to the ratios measured in molecular clouds, comets and meteoritic material. These models make several predictions that can be tested in the near future by molecular line observations, particularly with ALMA.

  4. Models of Isotopic Fractionation in Prestellar Cores

    NASA Technical Reports Server (NTRS)

    Charnley, Steven B.

    2012-01-01

    Anomalously fractionated isotopic material is found in many primitive Solar System objects, such as meteorites and comets. It is thought, in some cases, to trace interstellar matter that was incorporated into the Solar Nebula without undergoing significant processing. We will present the results of models of the nitrogen, oxygen, and carbon fractionation chemistry in dense molecular clouds, particularly in cores where substantial freeze-out of molecules on to dust has occurred. The range of fractionation ratios expected in different interstellar molecules will be discussed and compared to the ratios measured in molecular clouds, comets and meteoritic material. These studies make several predictions that can be tested in the near future by high-resolution molecular line observations with ALMA.

  5. Oxygen isotope fractionation in divalent metal carbonates

    USGS Publications Warehouse

    O'Neil, J.R.; Clayton, R.N.; Mayeda, T.K.

    1969-01-01

    Equilibrium fractionation factors for the distribution of 18O between alkaline-earth carbonates and water have been measured over the temperature range 0-500??C. The fractionation factors ?? can be represented by the equations CaCO3-H2O, 1000 ln??=2.78(106 T-2)-3.39, SrCO3-H 2O, 1000 ln??=2.69(106 T-2)-3.74, BaCO3-H2O, 1000 ln??=2.57(106 T -2)-4.73. Measurements on MnCO3, CdCO3, and PbCO3 were made at isolated temperatures. A statistical-mechanical calculation of the isotopic partition function ratios gives reasonably good agreement with experiment. Both cationic size and mass are important in isotopic fractionation, the former predominantly in its effect on the internal vibrations of the anion, the latter in its effect on the lattice vibrations.

  6. Iron Isotope Fractionation in the Lower Mantle

    NASA Astrophysics Data System (ADS)

    Yang, H.; Lin, J. F.; Dauphas, N.

    2015-12-01

    Knowledge of iron isotopes in the deep Earth is of great importance, for it provides clues for determining the history of planetary differentiation and core formation, as well as the origin of the Earth. However, iron isotope composition of the Earth's interior is rarely known due to lack of samples. Previous theoretical and experimental results are insufficient because they presume the spin state of iron or they are based on relatively low quality experimental data. Here we will use a newly developed technique --NRIXS(Nuclear Resonant Inelastic X-ray Scattering)-- to measure the force constant of lower mantle mineral candidates ferropericlase and pervoskite at relevant pressure. A reliable iron isotope fractionation factor will then be derived using SciPhon, which is a software designed specifically for the isotope fractionation factor derivation from NRIXS data. We report new high pressure 57Fe NRIXS spectra collected at beamline 3 ID-B of the Advanced Photon Source, with the aim to understand the pressure effect on iron isotope fractionation. The experiments were conducted using a 3-fold Diamond Anvil Cell and a >95% 57Fe enriched sample fp25((Fe0.25Mg0.75)O). NRIXS spectra were collected by tuning the x-ray energy range within ± 200meV around the 57Fe resonant energy of 14.4125keV. We will present the force constants and derived iron isotope fractionation factors of ferropericlase. It is expected that pressure will have an effect on the iron isotope fractionation factor and should be taken into account when modeling isotope fractionation of planetary scale and when using iron isotope systems to constrain the planetary differentiation. We will also use first-principle studies and geochemical observations to study the Fe,O,Si isotope system in the deep Earth. Our ultimate goal is to build a self-consistent geophysical and geochemical model that can be used in deciphering the mystery of Earth's history.

  7. Adsorption and isotopic fractionation of Xe

    NASA Technical Reports Server (NTRS)

    Bernatowicz, T. J.; Podosek, F. A.

    1986-01-01

    A theoretical description of the mechanisms of isotopic fractionation arising during adsorption of noble gases in a Henry's Law pressure regime is given. Experimental data on the isotopic composition of Xe adsorbed on activated charcoal in the temperature range 220 K to 350 K are presented. Both theoretical considerations and the experimental data indicate that equilibrium adsorption does not significantly alter the isotopic structure of adsorbed structure of adsorbed noble gases. Therefore, if adsorption is responsible for the elemental noble gas pattern in meteorites and the earth, the heavy noble gas isotopic fractionation between them must have been produced prior to and by a different process than equilibrium adsorption.

  8. Isotope Fractionation During Microbial Metal Assimilation

    NASA Astrophysics Data System (ADS)

    Anbar, A.; Wasylenki, L.; Liermann, L.; Mathur, R.; Brantley, S.

    2006-12-01

    The possibility that metal stable isotopes record the influence of microbes on metal geochemical cycling has motivated much recent research on "non-traditional" stable isotopes, particularly Fe. The initial wave of research on biogenic metal isotope effects focused on Fe isotope fractionation during microbially-mediated dissimilatory reduction or oxidation of Fe. Although isotope variations arising from biogenic effects have been reported in laboratory systems it is difficult to ascribe comparable variations in nature to biology because of pervasive and significant abiotic fractionation. As an alternative approach, we are investigating isotope fractionation during microbial assimilation of transition metals. Assimilation occurs because a large number of metals are essential intracellular constituents. Although assimilatory isotope fractionation is not likely to be unique in direction or magnitude compared to other processes, the large number of elements potentially involved greatly broadens the number of elements that can be examined for biogenic isotope effects in materials of interest. This raises the possibility of multi- element isotope "fingerprints" of biological metal processing. In experiments with Azotobacter vinelandii, a nitrogen-fixing soil bacterium that does not use Fe or other metals in dissimilatory respiration, fractionation of both Fe and Mo isotopes are observed. The two systems exhibit opposite sense fractionation: preferential assimilation of heavy isotopes is observed for Fe, while Mo assimilation favors uptake of light isotopes. Rayleigh-type behavior is seen in both cases; α = 1.0011 and 0.9997, respectively. The Fe isotope results are most readily interpreted in terms of an equilibrium fractionation between inorganic Fe complexes and strongly bound Fe-siderophore complexes that are taken into the cell. In contrast, the Mo isotope results may reflect a kinetic isotope effect. However, it is alternatively possible that Mo isotope

  9. Fractional laser photothermolysis using Bessel beams

    PubMed Central

    Mignon, Charles; Rodriguez, Aura Higuera; Palero, Jonathan A.; Varghese, Babu; Jurna, Martin

    2016-01-01

    Fractional photothermolysis uses lasers to generate a pattern of microscopic columnar thermal lesions within the skin stimulating collagen remodeling. In this paper we investigate the use of Bessel beams as an alternative to conventional Gaussian beams in creating laser photothermal lesions of different aspect ratios in skin. We show for the first time the improved photothermal lesion depth-to-diameter aspect ratio using Bessel beams in ex vivo human skin as well as in numerical simulations using electric field Monte Carlo photon transport, finite difference methods and Arrhenius model. Bessel beams allow the creation of deep and narrow thermal lesions necessary for improved efficacy in fractional photothermolysis. PMID:28018718

  10. Chaos in a Fractional Order Chua System

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.; Qammar, Helen Killory

    1996-01-01

    This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.

  11. Learning to Use Fractions: Examining Middle School Students Emerging Fraction Literacy

    ERIC Educational Resources Information Center

    Johanning, Debra I.

    2008-01-01

    This article describes one prevalent practice that a group of 6th- and 7th-grade students engaged in when they used fractions in the context of area and perimeter, decimal operations, similarity, and ratios and proportions. The study's results revealed that students did not simply take the concepts and skills learned in formal fractions units and…

  12. Limited Intervention at Sub Concept of Fractions in the Object Conversion into Fractions

    ERIC Educational Resources Information Center

    Kurniawan, Henry; Nusantara, Toto; Subanji; Susiswo; Setiawan, Iwan; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muksar, Makbul

    2016-01-01

    This research is an exploratory study with a qualitative approach, which is based on interviews with a task-based the purpose of this study is to describe the understanding of elementary school students in interpreting sub concept fractions in changing of the object is given to fractions with limit intervention. While intervention on problems…

  13. Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditions

    SciTech Connect

    Eab, C. H.; Lim, S. C.; Teo, L. P.

    2007-08-15

    This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed.

  14. Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative

    NASA Astrophysics Data System (ADS)

    He, Shaobo; Sun, Kehui; Mei, Xiaoyong; Yan, Bo; Xu, Siwei

    2017-01-01

    In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM). We found that CADM is an effective method for numerical solution of conformable fractional-order differential equations. Taking the conformable fractional-order simplified Lorenz system as an example, the numerical solution and chaotic behaviors of the conformable fractional-order simplified Lorenz system are investigated. It is found that rich dynamics exist in the conformable fractional-order simplified Lorenz system, and the minimum order for chaos is even less than 2. The results are validated by means of bifurcation diagram, Lyapunov characteristic exponents and phase portraits.

  15. Shot-Noise Evidence of Fractional Quasiparticle Creation in a Local Fractional Quantum Hall State

    NASA Astrophysics Data System (ADS)

    Hashisaka, Masayuki; Ota, Tomoaki; Muraki, Koji; Fujisawa, Toshimasa

    2015-02-01

    We experimentally identify fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T1(1 -T1) over a wide range of T1 , where T1 is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process enables us to elucidate the dynamics of Laughlin quasiparticles in FQH systems.

  16. Students' Distributive Reasoning with Fractions and Unknowns

    ERIC Educational Resources Information Center

    Hackenberg, Amy J.; Lee, Mi Yeon

    2016-01-01

    To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite…

  17. FRACTIONAL PENETRATION OF PAINT OVERSPRAY ARRESTORS

    EPA Science Inventory

    The report describes the development of fractional penetration curves for liquid droplet penetration of overspray arrestors for discrete droplet diameters from 0.3 to 10 micrometers. (NOTE: Fine particulates are particles with diameters of 10 micrometers or less.) These data poin...

  18. Generalized Functions for the Fractional Calculus

    NASA Technical Reports Server (NTRS)

    Lorenzo, Carl F.; Hartley, Tom T.

    1999-01-01

    Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

  19. Fractionated radiotherapy and radiosurgery of intracranial meningiomas.

    PubMed

    Biau, J; Khalil, T; Verrelle, P; Lemaire, J-J

    2015-06-19

    This review focuses on the role of radiosurgery and fractionated radiotherapy in the management of intracranial meningiomas, which are the most common benign intracranial tumors. Whenever feasible, surgery remains a cornerstone of treatment in effective health care treatment where modern radiotherapy plays an important role. Irradiation can be proposed as first-line treatment, as adjuvant treatment, or as a second-line treatment after recurrence. Stereotactic radiosurgery consists of delivering, a high-dose of radiation with high precision, to the tumor in a single-fraction with a minimal exposure of surrounding healthy tissue. Stereotactic radiosurgery, especially with the gamma knife technique, has reached a high level of success for the treatment of intracranial meningiomas with excellent local control and low morbidity. However, stereotactic radiosurgery is limited by tumor size,<3-4cm, and location, i.e. reasonable distance from the organs at risk. Fractionated radiation therapy is an interesting alternative (5 to 6weeks treatment time) for large inoperable tumors. The results of fractionated radiation therapy seem encouraging as regards both local control and morbidity although long-term prospective studies are still needed.

  20. 9 CFR 113.7 - Multiple fractions.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... production make provisions and set forth conditions for use of the same animals for testing different... 9 Animals and Animal Products 1 2013-01-01 2013-01-01 false Multiple fractions. 113.7 Section 113.7 Animals and Animal Products ANIMAL AND PLANT HEALTH INSPECTION SERVICE, DEPARTMENT OF...

  1. 9 CFR 113.7 - Multiple fractions.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... production make provisions and set forth conditions for use of the same animals for testing different... 9 Animals and Animal Products 1 2012-01-01 2012-01-01 false Multiple fractions. 113.7 Section 113.7 Animals and Animal Products ANIMAL AND PLANT HEALTH INSPECTION SERVICE, DEPARTMENT OF...

  2. 9 CFR 113.7 - Multiple fractions.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... production make provisions and set forth conditions for use of the same animals for testing different... 9 Animals and Animal Products 1 2014-01-01 2014-01-01 false Multiple fractions. 113.7 Section 113.7 Animals and Animal Products ANIMAL AND PLANT HEALTH INSPECTION SERVICE, DEPARTMENT OF...

  3. Developmental Predictors of Fraction Concepts and Procedures

    ERIC Educational Resources Information Center

    Jordan, Nancy C.; Hansen, Nicole; Fuchs, Lynn S.; Siegler, Robert S.; Gersten, Russell; Micklos, Deborah

    2013-01-01

    Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…

  4. Isolation and Suborganellar Fractionation of Arabidopsis Chloroplasts.

    PubMed

    Flores-Pérez, Úrsula; Jarvis, Paul

    2017-01-01

    Chloroplasts are structurally complex organelles containing ~2000-3000 proteins. They are delimited by a double membrane system or envelope, have an inner aqueous compartment called the stroma, and possess a second internal membrane system called the thylakoids. Thus, determining the suborganellar location of a chloroplast protein is vital to understanding or verifying its function. One way in which protein localization can be addressed is through fractionation. Here we present two rapid and simple methods that may be applied sequentially on the same day: (a) The isolation of intact chloroplasts from Arabidopsis thaliana plants that may be used directly (e.g., for functional studies such as protein import analysis), or for further processing as follows; (b) separation of isolated chloroplasts into three suborganellar fractions (envelope membranes, a soluble fraction containing stromal proteins, and the thylakoids). These methods are routinely used in our laboratory, and they provide a good yield of isolated chloroplasts and suborganellar fractions that can be used for various downstream applications.

  5. Arterial viscoelasticity: a fractional derivative model.

    PubMed

    Craiem, Damien O; Armentano, Ricardo L

    2006-01-01

    Arteries are viscoelastic materials. Viscoelastic laws are fully characterized by measuring a complex modulus. Arterial mechanics can be described using stress-strain dynamic measurements applied to the particular cylindrical geometry. Most materials show an energy loss per cycle that increases steadily with frequency. By contrast, the frequency modulus response in arteries presents a frequency independence describing a plateau above a corner frequency near 4Hz. Traditional methods to fit this response include several spring and dashpot elements to model integer order differential equations in time domain. Recently, fractional derivative models proved to be efficient to describe rheological tissues, reducing the number of parameters and showing a natural power-law response. In this work a fractional derivative model with 4-parameter was selected to describe the arterial wall mechanics in-vivo. Strain and stress were measured simultaneously in an anaesthetized sheep. A fractional model was applied. The order resulted alpha=0.12, confirming the manifest elastic response of the aorta. The fractional derivative model proved to naturally mimic the elastic modulus spectrum with only 4 parameters and a reasonable small computational effort.

  6. Composite fermions for fractionally filled Chern bands

    NASA Astrophysics Data System (ADS)

    Shankar, R.

    2012-02-01

    We consider fractionally filled bands with a non-zero Chern index that exhibit the Fractional Quantum Hall Effect in zero external fieldootnotetextR. Roy and S. Sondhi, Physics 4, 46 (2011) and papers reviewed therein. a possibility supported by numerical work.ootnotetextIbid. Analytic treatments are complicated by a non-constant Berry flux and the absence of Composite Fermions (CF), which would not only single out preferred fractions, but also allow us compute numerous response functions at nonzero frequencies, wavelengths and temperature using either Chern-Simons field theory or our Hamiltonian formalism.ootnotetextG. Murthy and R. Shankar, Rev. Mod. Phys., 75, 1101, (2003) We describe a way to introduce CF's by embedding the Chern band in an auxiliary problem involving Landau levels. The embedded band can be designed to approximate a prescribed Chern density in k space which determines the commutation relations of the charge densities and hence preserve all dynamical and algebraic aspects of the original problem. We find some states for which the filling fraction and dimensionless Hall conductance are not equal. The approach extends to two-dimensional time-reversal invariant topological insulators and to composite bosons.

  7. Resonant tunneling in fractional Hall effect

    NASA Astrophysics Data System (ADS)

    Shi, Chuntai; Jain, Jainendra

    2006-03-01

    We study theoretically the possible transitions of a fractional quantum Hall island surrounded by another fractional quantum Hall state, induced by either the variation of the magnetic field or a backgate voltage, and find a rich set of possibilities in addition to the one considered previously[1],The elementary transitions correspond to the addition or removal of a composite fermion from the edge or the interior of the island; combinations of elementary transitions may occur simultaneously due to electrostatic constraints. Relevance to a recent experiment[2] is considered, which measures the resonant tunneling of composite fermions through their quasi-bound states around such a 2/5 island surrounded by the 1/3 sea. It is shown that the results are consistent with the notion of fractional braiding statistics, but can be explained on the basis of fractional charge alone. We also perform calculations based on microscopic composite fermion wavefunctions of finite systems to test the theoretical considerations. [1]J.K.Jain, S.A.Kivelson, and D.J.Thouless, Phys.Rev.Lett.71, 3003(1993). [2]F.E.Camino, W.Zhou, and V.J.Goldman, Phys.Rev.B 72, 075342(2005).

  8. (Carbon isotope fractionation in plants: Progress report)

    SciTech Connect

    Not Available

    1987-01-01

    The purpose of this work is to use carbon isotope fractionation as a means of studying photosynthetic efficiency in plants. During the past year we have developed a new short-term method for measuring the isotope fractionation over a period of about an hour. This method is being used to study a variety of environmental and developmental effects in both C/sub 3/ and C/sub 4/ plants, and these results are being compared with results of the traditional combustion method. We have made extensive studies of aspartic acid, malic acid, and citric acid as possible indicators of the functioning of phosphoenolpyruvate carboxylase in C/sub 3/ plants. We find that most of the aspartic acid in proteins in C/sub 3/ plants is synthesized by action of phosphoenolpyruvate carboxylase on atmospheric CO/sub 2/ and phosphoenolpyruvate produced by glycolysis. The metabolically active pool of malate, aspartate, and citrate, on the other hand, appear not to be principally synthesized by this route. Studies of C/sub 4/ plants are in progress. During deacidification, CAM plants lose CO/sub 2/ to the atmosphere, and this material is highly enriched in carbon-13. Field-grown and growth-chamber grown CAM plants show similar isotope fractionations. Ploidy effects on isotope fractionation in alfalfa are extremely small.

  9. Modeling Students' Mathematics Using Steffe's Fraction Schemes

    ERIC Educational Resources Information Center

    Norton, Anderson H.; McCloskey, Andrea V.

    2008-01-01

    Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…

  10. Fraction Photo Frenzy: A New Exploration

    ERIC Educational Resources Information Center

    Canada, Daniel L.

    2009-01-01

    This article relates how a class of elementary preservice teachers used technology to share their thinking about a topic that is traditionally difficult to model and discuss--dividing fractions. One type of technology they used, a digital camera, was familiar to most students, but the other type, a SMART Board[TM], was relatively unfamiliar.…

  11. Dean's Great Discovery: Multiplication, Division and Fractions

    ERIC Educational Resources Information Center

    Vale, Colleen; Davies, Anne

    2007-01-01

    Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem…

  12. Void fraction instrument acceptance test procedure

    SciTech Connect

    Pearce, K.L.

    1994-09-15

    This acceptance test procedure (ATP) was written to test the void fraction instrument (VFI) and verify that the unit is ready for field service. The procedure verifies that the mechanical and electrical features (not specifically addressed in the software ATP) and software alarms are operating as designed.

  13. Relativistic equations with fractional and pseudodifferential operators

    SciTech Connect

    Babusci, D.; Dattoli, G.; Quattromini, M.

    2011-06-15

    In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with noninteger exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schroedinger and Dirac equations.

  14. A Statistical Treatment of Bioassay Pour Fractions

    NASA Technical Reports Server (NTRS)

    Barengoltz, Jack; Hughes, David W.

    2014-01-01

    The binomial probability distribution is used to treat the statistics of a microbiological sample that is split into two parts, with only one part evaluated for spore count. One wishes to estimate the total number of spores in the sample based on the counts obtained from the part that is evaluated (pour fraction). Formally, the binomial distribution is recharacterized as a function of the observed counts (successes), with the total number (trials) an unknown. The pour fraction is the probability of success per spore (trial). This distribution must be renormalized in terms of the total number. Finally, the new renormalized distribution is integrated and mathematically inverted to yield the maximum estimate of the total number as a function of a desired level of confidence ( P(fraction. The extension to recovery efficiency corrections is also presented. Now the product of recovery efficiency and pour fraction may be small enough that the likely value may be much larger than the usual calculation: the number of spores divided by that product. The use of this analysis would not be limited to microbiological data.

  15. Fractional Quantization of the Hall Effect

    DOE R&D Accomplishments Database

    Laughlin, R. B.

    1984-02-27

    The Fractional Quantum Hall Effect is caused by the condensation of a two-dimensional electron gas in a strong magnetic field into a new type of macroscopic ground state, the elementary excitations of which are fermions of charge 1/m, where m is an odd integer. A mathematical description is presented.

  16. Introducing the fractional order robotic Darwinian PSO

    NASA Astrophysics Data System (ADS)

    Couceiro, Micael S.; Martins, Fernando M. L.; Rocha, Rui P.; Ferreira, Nuno M. F.

    2012-11-01

    The Darwinian Particle Swarm Optimization (DPSO) is an evolutionary algorithm that extends the Particle Swarm Optimization using natural selection to enhance the ability to escape from sub-optimal solutions. An extension of the DPSO to multi-robot applications has been recently proposed and denoted as Robotic Darwinian PSO (RDPSO), benefiting from the dynamical partitioning of the whole population of robots, hence decreasing the amount of required information exchange among robots. This paper further extends the previously proposed algorithm using fractional calculus concepts to control the convergence rate, while considering the robot dynamical characteristics. Moreover, to improve the convergence analysis of the RDPSO, an adjustment of the fractional coefficient based on mobile robot constraints is presented and experimentally assessed with 2 real platforms. Afterwards, this novel fractional-order RDPSO is evaluated in 12 physical robots being further explored using a larger population of 100 simulated mobile robots within a larger scenario. Experimental results show that changing the fractional coefficient does not significantly improve the final solution but presents a significant influence in the convergence time because of its inherent memory property.

  17. Goldstone bosons as fractional cosmic neutrinos.

    PubMed

    Weinberg, Steven

    2013-06-14

    It is suggested that Goldstone bosons may be masquerading as fractional cosmic neutrinos, contributing about 0.39 to what is reported as the effective number of neutrino types in the era before recombination. The broken symmetry associated with these Goldstone bosons is further speculated to be the conservation of the particles of dark matter.

  18. PNEUMATIC FRACTIONATOR FOR CLEANING GINNED LINT

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The pneumatic fractionator has long been used to determine foreign matter content of seed cotton at the USDA Cotton Ginning Laboratories. Spawned from discussions at a Cotton Incorporated Lint Cleaning Summit and building on 1970s research at the Southwestern Cotton Ginning Research Laboratory, an e...

  19. Direct observation of a fractional charge

    NASA Astrophysics Data System (ADS)

    de-Picciotto, R.; Reznikov, M.; Heiblum, M.; Umansky, V.; Bunin, G.; Mahalu, D.

    1997-09-01

    Since Millikan's famous oil-drop experiments, it has been well known that electrical charge is quantized in units of the charge of an electron, e. For this reason, the theoretical prediction, by Laughlin of the existence of fractionally charged `quasiparticles'-proposed as an explanation for the fractional quantum Hall (FQH) effect-is very counterintuitive. The FQH effect is a phenomenon observed in the conduction properties of a two-dimensional electron gas subjected to a strong perpendicular magnetic field. This effect results from the strong interaction between electrons, brought about by the magnetic field, giving rise to the aforementioned fractionally charged quasiparticles which carry the current. Here we report the direct observation of these counterintuitive entities by using measurements of quantum shot noise. Quantum shot noise results from the discreteness of the current-carrying charges and so is proportional to both the charge of the quasiparticles and the average current. Our measurements of quantum shot noise show unambiguously that current in a two-dimensional electron gas in the FQH regime is carried by fractional charges-e/3 in the present case-in agreement with Laughlin's prediction.

  20. 9 CFR 113.7 - Multiple fractions.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 9 Animals and Animal Products 1 2011-01-01 2011-01-01 false Multiple fractions. 113.7 Section 113.7 Animals and Animal Products ANIMAL AND PLANT HEALTH INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE VIRUSES, SERUMS, TOXINS, AND ANALOGOUS PRODUCTS; ORGANISMS AND VECTORS STANDARD REQUIREMENTS...

  1. 9 CFR 113.7 - Multiple fractions.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 9 Animals and Animal Products 1 2010-01-01 2010-01-01 false Multiple fractions. 113.7 Section 113.7 Animals and Animal Products ANIMAL AND PLANT HEALTH INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE VIRUSES, SERUMS, TOXINS, AND ANALOGOUS PRODUCTS; ORGANISMS AND VECTORS STANDARD REQUIREMENTS...

  2. A Fractional Calculus Model of Aeroelasticity

    DTIC Science & Technology

    1989-12-01

    Coefficient Data I This appendix compares fractional approximations of unsteady aerodynamic pressures to data on an airfoil ( NACA 64A010 ) oscillating in...oscillating airfoils in subsonic flow. The data in this 3 section represent a 64A010 airfoil oscillating in pitch in a high Reynolds number subsonic

  3. Folate in oats and its milling fractions.

    PubMed

    Edelmann, Minnamari; Kariluoto, Susanna; Nyström, Laura; Piironen, Vieno

    2012-12-01

    Total folate content in oat varieties from three harvesting years (2006-2008), and in oats milling fractions, was determined using microbiological assay. Furthermore, folate vitamer distribution in milling fractions were examined with the UPLC method, which was taken in use and validated. The total folate content of the cultivars varied moderately within each year. The average content in the 2008 samples was 685ng/gdm. The UPLC method proved fast and sensitive for determining seven folate monoglutamates in cereal samples. Folate content in fractions, which are normally discarded, such as flour from oat cutting and flaking, were 1.5- to 2.5-fold higher than in native grain. The main folate vitamers found in the oat fractions were 5-CH(3)-H(4)folate, 5-HCO-H(4)folate, and 5,10-CH(+)-H(4)folate. The UPLC results more closely matched the microbiological results compared to those that are usually achieved with HPLC methods. This study illustrates that oats and, especially, by-products of milling are good sources of folate.

  4. Adaptive processing of fractions--evidence from eye-tracking.

    PubMed

    Huber, S; Moeller, K; Nuerk, H-C

    2014-05-01

    Recent evidence indicated that fraction pair type determined whether a particular fraction is processed holistically, componentially or in a hybrid manner. Going beyond previous studies, we investigated how participants adapt their processing of fractions not only to fraction type, but also to experimental context. To examine adaptation in fraction processing, we recorded participants' eye-fixation behaviour in a fraction magnitude comparison task. Participants' eye fixation behaviour indicated componential processing of fraction pairs with common components for which the decision-relevant components are easy to identify. Importantly, we observed that fraction processing was adapted to experimental context: Evidence for componential processing was stronger, when experimental context allowed valid expectations about which components are decision-relevant. Taken together, we conclude that fraction processing is adaptive beyond the comparison of different fraction types, because participants continuously adjust to the experimental context in which fractions are processed.

  5. Fermentation and dry fractionation increase bioactivity of cloudberry (Rubus chamaemorus).

    PubMed

    Puupponen-Pimiä, Riitta; Nohynek, Liisa; Juvonen, Riikka; Kössö, Tuija; Truchado, Pilar; Westerlund-Wikström, Benita; Leppänen, Tiina; Moilanen, Eeva; Oksman-Caldentey, Kirsi-Marja

    2016-04-15

    Phenolic composition and bioactivity of cloudberry was modified by bioprocessing, and highly bioactive fractions were produced by dry fractionation of the press cake. During fermentation polymeric ellagitannins were partly degraded into ellagic acid derivatives. Phenolic compounds were differentially distributed in seed coarse and fine fractions after dry fractionation process. Tannins concentrated in fine fraction, and flavonol derivatives were mainly found in coarse fraction. Ellagic acid derivatives were equally distributed between the dry fractions. Fermentation and dry fractionation increased statistically significantly anti-adhesion and anti-inflammatory activity of cloudberry. The seed fine fraction showed significant inhibition of P fimbria-mediated haemagglutination assay of uropathogenic Escherichia coli. The seed coarse fraction significantly reduced NO and IL-6 production and iNOS expression in activated macrophages. Fermentation did not affect antimicrobial activity, but slight increase in activity was detected in dry fractions. The results indicate the potential of cloudberry in pharma or health food applications.

  6. [Mutagenicity of 3 organic fractions of atmospheric dust and gas chromatographic analysis of the basic fraction].

    PubMed

    Gottlieb, A; Schleibinger, H; Ketseridis, G; Wullenweber, M; Rüden, H

    1983-01-01

    Suspended particulate matter (PM) with a Dae less than 0.4 micron was collected from July 1981 till January 1982. The ether/benzene soluble extract (EEOM) and the acidic, basic and neutral fractions were determined and investigated for their mutagenic activities in the Ames bioassay. In addition particles (Dae) less than 10.2 micron derived in January were investigated. Five compounds of the basic fraction were determined by gaschromatography. The following results were obtained: Suspended particulate matter (Dae less than 0.4 micron) and the ether/benzene extract increase from July to January. The lowest rates occur in July (PM: 16.9 micron/m3) and August (EEOM: 3.0 micrograms/m3), the highest in January (PM: 48.9 micrograms/m3, EEOM: 10.5 micrograms/m3). The ether/benzene soluble portion of the suspended particulate matter increases from the average rate of 16.3% (July-September) to 22.7% (November-January). The neutral fraction amounts to 44.9%, the acidic fraction to 27.3% and the basic fraction to 3.5% of the organic matter (on an average). In experiments with metabolic activation 99% of the total mutagenicity during the period of July till September can be demonstrated by summing up the mutagenicity of the three fractions on the other hand only 59.7% from November till January. The EEOMs derived from winter exhibit without metabolic activation (250 micrograms/plate) distinctively higher numbers of revertants than the single fractions. Dose-response curves of extracts derived from back-up filters (Dae less than 0.4 micron) in January show that the acidic fraction has a slightly higher mutagenic activity than the neutral fraction (mean values of tests with and without S9-mix). The basic fraction shows no mutagenicity without S9-mix, with activation the mutagenic activity is lower than that of the other fractions. Mutagenicity expressed as rev./m3 air shows, that the neutral fraction is most efficient. The number of revertants per plate reveals-in relation to

  7. PREFACE: Fractional Differentiation and its Applications (FDA08) Fractional Differentiation and its Applications (FDA08)

    NASA Astrophysics Data System (ADS)

    Baleanu, Dumitru; Tenreiro Machado, J. A.

    2009-10-01

    The international workshop, Fractional Differentiation and its Applications (FDA08), held at Cankaya University, Ankara, Turkey on 5-7 November 2008, was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance. Fractional calculus, which deals with derivatives and integrals of any order, is now recognized as playing an important role in modeling multi-scale problems that span a wide range of time or length scales. Fractional calculus provides a natural link to the intermediate-order dynamics that often reflects the complexity of micro- and nanostructures through fractional-order differential equations. Unlike the more established techniques of mathematical physics, the methods of fractional differentiation are still under development; while it is true that the ideas of fractional calculus are as old as the classical integer-order differential operators, modern work is proceeding by both expanding the capabilities of this mathematical tool and by widening its range of applications. Hence, the interested reader will find papers here that focus on the underlying mathematics of fractional calculus, that extend fractional-order operators into new domains, and that apply well established methods to experimental and theoretical problems. The organizing committee invited presentations from experts representing the international community of scholars in fractional calculus and welcomed contributions from the growing number of researchers who are applying fractional differentiation to complex technical problems. The selection of papers in this topical issue of Physica Scripta reflects the success of the FDA08 workshop, with the emergence of a variety of novel areas of application. With these ideas in mind, the guest editors would like to honor the many distinguished scientists that have promoted the development of fractional calculus and, in particular, Professor George M

  8. Absorbed fractions for electrons in ellipsoidal volumes

    NASA Astrophysics Data System (ADS)

    Amato, E.; Lizio, D.; Baldari, S.

    2011-01-01

    We applied a Monte Carlo simulation in Geant4 in order to calculate the absorbed fractions for monoenergetic electrons in the energy interval between 10 keV and 2 MeV, uniformly distributed in ellipsoids made from soft tissue. For each volume, we simulated a spherical shape, four oblate and four prolate ellipsoids, and one scalene shape. For each energy and for every geometrical configuration, an analytical relationship between the absorbed fraction and a 'generalized radius' was found, and the dependence of the fit parameters from electron energy is discussed and fitted by proper parametric functions. With the proposed formulation, the absorbed fraction for electrons in the 10-2000 keV energy range can be calculated for all volumes and for every ellipsoidal shape of practical interest. This method can be directly applied to evaluation of the absorbed fraction from the radionuclide emission of monoenergetic electrons, such as Auger or conversion electrons. The average deposited energy per disintegration in the case of extended beta spectra can be evaluated through integration. Two examples of application to a pure beta emitter such as 90Y and to 131I, whose emission include monoenergetic and beta electrons plus gamma photons, are presented. This approach represent a generalization of our previous studies, allowing a comprehensive treatment of absorbed fractions from electron and photon sources uniformly distributed in ellipsoidal volumes of any ellipticity and volume, in the whole range of practical interest for internal dosimetry in nuclear medicine applications, as well as in radiological protection estimations of doses from an internal contamination.

  9. Absorbed fractions for electrons in ellipsoidal volumes.

    PubMed

    Amato, E; Lizio, D; Baldari, S

    2011-01-21

    We applied a Monte Carlo simulation in Geant4 in order to calculate the absorbed fractions for monoenergetic electrons in the energy interval between 10 keV and 2 MeV, uniformly distributed in ellipsoids made from soft tissue. For each volume, we simulated a spherical shape, four oblate and four prolate ellipsoids, and one scalene shape. For each energy and for every geometrical configuration, an analytical relationship between the absorbed fraction and a 'generalized radius' was found, and the dependence of the fit parameters from electron energy is discussed and fitted by proper parametric functions. With the proposed formulation, the absorbed fraction for electrons in the 10-2000 keV energy range can be calculated for all volumes and for every ellipsoidal shape of practical interest. This method can be directly applied to evaluation of the absorbed fraction from the radionuclide emission of monoenergetic electrons, such as Auger or conversion electrons. The average deposited energy per disintegration in the case of extended beta spectra can be evaluated through integration. Two examples of application to a pure beta emitter such as (90)Y and to (131)I, whose emission include monoenergetic and beta electrons plus gamma photons, are presented. This approach represent a generalization of our previous studies, allowing a comprehensive treatment of absorbed fractions from electron and photon sources uniformly distributed in ellipsoidal volumes of any ellipticity and volume, in the whole range of practical interest for internal dosimetry in nuclear medicine applications, as well as in radiological protection estimations of doses from an internal contamination.

  10. Polarity based fractionation of fulvic acids.

    PubMed

    Li, Aimin; Hu, Jundong; Li, Wenhui; Zhang, Wei; Wang, Xuejun

    2009-11-01

    Fulvic acids from the soil of Peking University (PF) and a Nordic river (NF) were separated into well defined sub-fractions using sequential elution techniques based on eluent polarity. The chemical properties of the fractions including: PF1 and NF1 (eluted by 0.01 M HCl), PF2 and NF2 (eluted by 0.01 M HCl+20% methanol), PF3 and NF3 (eluted by 0.01 M HCl+40% methanol), and PF4 and NF4 (eluted by 100% methanol), were characterized using UV-Visible spectroscopy, elemental analysis and (13)C NMR. The results showed that the UV absorptions of the elution peaks at 280 nm (A280) increased from PF2 to PF4 and NF2 to NF4. No elution peaks were observed for PF1 and NF1. The carbon contents increased from 43.34% to 51.90% and 43.06% to 53.26% while the oxygen contents decreased from 46.39% to 36.76% and 49.76% to 40.03% for PF1-PF4 and NF1-NF4, respectively. As a polarity indicator, the (O+N)/C ratio for PF1-PF4 and NF1-NF4 decreased from 0.88 to 0.62 and 0.89 to 0.58, respectively. The aromatic carbon content increased from PF1 to PF4 and NF1 to NF4, suggesting an increase of the hydrophobicity of these fractions. The polarity was positively related to the ratio of UV absorption at 250 nm and 365 nm (E2/E3), and negatively related to the aromaticity. A high positive relationship between the aromaticity and E2/E3 of fulvic acid fractions was also obtained. The use of an eluent with a decreasing polarity allowed to providing simpler fractions of soil and aquatic fulvic acids.

  11. Assessing regional intake fractions in North America.

    PubMed

    Humbert, Sebastien; Manneh, Rima; Shaked, Shanna; Wannaz, Cédric; Horvath, Arpad; Deschênes, Louise; Jolliet, Olivier; Margni, Manuele

    2009-08-15

    This paper develops the IMPACT North America model, a spatially resolved multimedia, multi-pathway, fate, exposure and effect model that includes indoor and urban compartments. IMPACT North America allows geographic differentiation of population exposure of toxic emissions for comparative risk assessment and life cycle impact assessment within U.S. and Canada. It looks at air, water, soil, sediment and vegetation media, and divides North America into several hundred zones. It is nested within a single world box to account for emissions leaving North America. It is a multi-scale model, covering three different spatial scales--indoor, urban and regional--in all zones in North America. Model results are evaluated against monitored emissions and concentrations of benzo(a)pyrene, 2,3,7,8-TCDD and mercury. Most of the chemical concentrations predicted by the model fall within two orders of magnitude of the monitored data. The model shows that urban intake fractions are one order of magnitude higher than rural intake fractions. The model application and importance is demonstrated by a case study on spatially-distributed emissions over the life cycle of diesel fuel. Depending on population densities and agricultural intensities, intake fractions can vary by eight orders of magnitudes, and even limited indoor emissions can lead to intakes comparable to those from outdoor emissions. To accurately assess these variations in intake fraction, we require the essential three original features described in the present paper: i) inclusion of the continental model within a world box for persistent pollutants, ii) addition of an urban box for short- and medium-lived substances (for grid size larger than 100 km), and iii) assess indoor emissions. This model can therefore be used to screen chemicals and assess regionalized intake fractions within North America for population-based human exposure assessment, life cycle impact assessment, and comparative risk assessment. The model can be

  12. Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods

    SciTech Connect

    Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang

    2014-11-15

    In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same.

  13. Deuterium fractionation in the Ophiuchus molecular cloud

    NASA Astrophysics Data System (ADS)

    Punanova, A.; Caselli, P.; Pon, A.; Belloche, A.; André, Ph.

    2016-03-01

    Context. In cold (T< 25 K) and dense (nH> 104 cm-3) interstellar clouds, molecules such as CO are significantly frozen onto dust grain surfaces. Deuterium fractionation is known to be very efficient in these conditions as CO limits the abundance of H3+, which is the starting point of deuterium chemistry. In particular, N2D+ is an excellent tracer of dense and cold gas in star-forming regions. Aims: We measure the deuterium fraction, RD, and the CO depletion factor, fd, towards a number of starless and protostellar cores in the L1688 region of the Ophiuchus molecular cloud complex and search for variations based upon environmental differences across L1688. The kinematic properties of the dense gas traced by the N2H+ and N2D+ (1-0) lines are also discussed. Methods: Deuterium fraction has been measured via observations of the J = 1-0 transition of N2H+ and N2D+ towards 33 dense cores in different regions of L1688. We estimated the CO depletion factor using C17O(1-0) and 850 μm dust continuum emission from the SCUBA survey. We carried out all line observations with the IRAM 30 m antenna. Results: The dense cores show large (≃2-40%) deuterium fractions with significant variations between the sub-regions of L1688. The CO depletion factor also varies from one region to another (between ≃1 and 7). Two different correlations are found between deuterium fraction and CO depletion factor: cores in regions A, B2, and I show increasing RD with increasing fd, similar to previous studies of deuterium fraction in pre-stellar cores; cores in regions B1, B1B2, C, E, F, and H show a steeper RD - fd correlation with large deuterium fractions occurring in fairly quiescent gas with relatively low CO freeze-out factors. These are probably recently formed, centrally concentrated starless cores, which have not yet started the contraction phase towards protostellar formation. We also find that the deuterium fraction is affected by the amount of turbulence, dust temperature, and

  14. Fractional Solutions of Bessel Equation with N-Method

    PubMed Central

    Bas, Erdal; Yilmazer, Resat; Panakhov, Etibar

    2013-01-01

    This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator Nν method, we derive the fractional solutions of the equation. PMID:24023534

  15. 21 CFR 862.1630 - Protein (fractionation) test system.

    Code of Federal Regulations, 2013 CFR

    2013-04-01

    ... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Protein (fractionation) test system. 862.1630... Systems § 862.1630 Protein (fractionation) test system. (a) Identification. A protein (fractionation) test system is a device intended to measure protein fractions in blood, urine, cerebrospinal fluid, and...

  16. 5 CFR 551.521 - Fractional hours of work.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ...) A quarter of an hour shall be the largest fraction of an hour used for crediting irregular or... ADMINISTRATION UNDER THE FAIR LABOR STANDARDS ACT Overtime Pay Provisions Fractional Hours of Work § 551.521... than the full fraction, odd minutes shall be rounded up or rounded down to the nearest full fraction...

  17. 5 CFR 551.521 - Fractional hours of work.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ...) A quarter of an hour shall be the largest fraction of an hour used for crediting irregular or... ADMINISTRATION UNDER THE FAIR LABOR STANDARDS ACT Overtime Pay Provisions Fractional Hours of Work § 551.521... than the full fraction, odd minutes shall be rounded up or rounded down to the nearest full fraction...

  18. Argon isotope fractionation induced by stepwise heating

    NASA Astrophysics Data System (ADS)

    Trieloff, Mario; Falter, Martina; Buikin, Alexei I.; Korochantseva, Ekaterina V.; Jessberger, Elmar K.; Altherr, Rainer

    2005-03-01

    Noble gas isotopes are widely used to elucidate the history of the rocks in which they have been trapped, either from distinct reservoirs or by accumulation following radioactive decay. To extract noble gases from their host rocks, stepwise heating is the most commonly used technique to deconvolve isotopically different components, e.g., atmospheric, in situ radiogenic, or excess radiogenic from mantle or crustal reservoirs. The accurate determination of the isotopic composition of these different components is of crucial importance, e.g., for ages obtained by 40Ar- 39Ar stepheating plateaus. However, diffusion theory-based model calculations predict that the stepwise thermal extraction process from mineral phases induces isotope fractionation and, hence, adulterates the original composition. Such effects are largely unconsidered, as they are small and a compelling experimental observation is lacking. We report the first unequivocal evidence for significant mass fractionation of argon isotopes during thermal extraction, observed on shungite, a carbon-rich Precambrian sedimentary rock. The degree of fractionation, as monitored by 38Ar/ 36Ar and 40Ar/ 36Ar ratios, very well agrees with theoretical predictions assuming an inverse square root dependence of diffusion coefficient and atomic mass, resulting in easier extraction of lighter isotopes. Hence, subatmospheric 40Ar/ 36Ar ratios obtained for argon extracted at low temperatures may not represent paleoatmospheric argon. Shungite argon resembles modern atmospheric composition, but constraints on the timing of trapping appear difficult to obtain, as shungites are multicomponent systems. In 40Ar- 39Ar stepwise heating, the isotope fractionation effect could cause systematic underestimations of plateau ages, between 0.15 and 0.4% depending on age, or considerably higher if samples contain appreciable atmospheric Ar. The magnitude of this effect is similar to the presently achieved uncertainties of this increasingly

  19. The Fraction of KBO Contact Binaries

    NASA Astrophysics Data System (ADS)

    Lacerda, Pedro

    2007-05-01

    We use Roche binary models to improve previous estimates of the contact binariy fraction within the Kuiper Belt object (KBO) population (Sheppard & Jewitt 2004). Our simulations can be used to determine the lightcurve range of Roche binaries at arbitrary observing geometries, and for different surface types. This allows us to better correct the apparent fraction for observing geometry effects. We find that at least 9% of KBOs are contact binaries. Such high incidence of KBOs contact binaries has important implications to binary formation and collisional evolution scenarios. PL is grateful to the Portuguese Fundacao para a Ciencia e a Tecnologia (BPD/SPFH/18828/2004) for financial support. This work was supported, in part, by a grant from the NSF to David C. Jewitt.

  20. Fractionated total body irradiation for metastatic neuroblastoma

    SciTech Connect

    Kun, L.E.; Casper, J.T.; Kline, R.W.; Piaskowski, V.D.

    1981-11-01

    Twelve patients over one year old with neuroblastoma (NBL) metastatic to bone and bone marrow entered a study of adjuvant low-dose, fractionated total body irradiation (TBI). Six children who achieved a ''complete clinical response'' following chemotherapy (cyclophosphamide and adriamycin) and surgical resection of the abdominal primary received TBI (10 rad/fraction to totals of 100-120 rad/10-12 fx/12-25 days). Two children received concurrent local irradiation for residual abdominal tumor. The intervals from cessation of chemotherapy to documented progression ranged from 2-16 months, not substatially different from patients receiving similar chemotherapy and surgery without TBI. Three additional children with progressive NBL received similar TBI (80-120 rad/8-12 fx) without objective response.

  1. Carbon isotopic fractionation in heterotrophic microbial metabolism.

    PubMed Central

    Blair, N; Leu, A; Muñoz, E; Olsen, J; Kwong, E; Des Marais, D

    1985-01-01

    Differences in the natural-abundance carbon stable isotopic compositions between products from aerobic cultures of Escherichia coli K-12 were measured. Respired CO2 was 3.4% depleted in 13C relative to the glucose used as the carbon source, whereas the acetate was 12.3% enriched in 13C. The acetate 13C enrichment was solely in the carboxyl group. Even though the total cellular carbon was only 0.6% depleted in 13C, intracellular components exhibited a significant isotopic heterogeneity. The protein and lipid fractions were -1.1 and -2.7%, respectively. Aspartic and glutamic acids were -1.6 and +2.7%, respectively, yet citrate was isotopically identical to the glucose. Probable sites of carbon isotopic fractionation include the enzyme, phosphotransacetylase, and the Krebs cycle. PMID:2867741

  2. Carbon isotopic fractionation in heterotrophic microbial metabolism

    NASA Technical Reports Server (NTRS)

    Blair, N.; Leu, A.; Munoz, E.; Olsen, J.; Kwong, E.; Des Marais, D.

    1985-01-01

    Differences in the natural-abundance carbon stable isotopic compositions between products from aerobic cultures of Escherichia coli K-12 were measured. Respired CO2 was 3.4 percent depleted in C-13 relative to the glucose used as the carbon source, whereas the acetate was 12.3 percent enriched in C-13. The acetate C-13 enrichment was solely in the carboxyl group. Even though the total cellular carbon was only 0.6 percent depleted in C-13, intracellular components exhibited a significant isotopic heterogeneity. The protein and lipid fractions were -1.1 and -2.7 percent, respectively. Aspartic and glutamic acids were -1.6 and +2.7 percent, respectively, yet citrate was isotopically identical to the glucose. Probable sites of carbon isotopic fractionation include the enzyme, phosphotransacetylase, and the Krebs cycle.

  3. Carbon isotopic fractionation in heterotrophic microbial metabolism

    SciTech Connect

    Blair, N.; Leu, A.; Munoz, E.; Olsen, J.; Kwong, E.; Des Marais, D.

    1985-10-01

    Differences in the natural-abundance carbon stable isotopic compositions between products from aerobic cultures of Escherichia coli K-12 were measured. Respired CO2 was 3.4 percent depleted in C-13 relative to the glucose used as the carbon source, whereas the acetate was 12.3 percent enriched in C-13. The acetate C-13 enrichment was solely in the carboxyl group. Even though the total cellular carbon was only 0.6 percent depleted in C-13, intracellular components exhibited a significant isotopic heterogeneity. The protein and lipid fractions were -1.1 and -2.7 percent, respectively. Aspartic and glutamic acids were -1.6 and +2.7 percent, respectively, yet citrate was isotopically identical to the glucose. Probable sites of carbon isotopic fractionation include the enzyme, phosphotransacetylase, and the Krebs cycle. 38 references.

  4. Silica fractionation and reactivity in soils

    NASA Astrophysics Data System (ADS)

    Unzué Belmonte, Dácil; Barão, Lúcia; Vandevenne, Floor; Schoelynck, Jonas; Struyf, Eric; Meire, Patrick

    2014-05-01

    The Si cycle is a globally important biogeochemical cycle, with strong connections to other biogeochemical cycles, including C. Silica is taken up by plants to form protective structures called phytoliths, which become a part of the soil and contribute strongly to soil Si cycling upon litter burial. Different silica fractions are found in soils, with phytoliths among the most easily soluble, especially compared to silicate minerals. A whole set of secondary non-biogenic fractions exist, that also have a high reactivity (adsorbed Si, reactive secondary minerals…). A good characterization of the different fractions of reactive silica is crucial to move forward knowledge on ecosystem Si cycling, which has been recognized in the last decade as crucial for terrestrial Si fluxes. A new method to analyze the different fractions of silica in soils has been described by Koning et al. (2002) and adapted by our research team (Barão et al. 2013). Using a continuous extraction of Si and aluminum in 0.5M NaOH, biogenic and non-biogenic reactive fractions are separated based on their Si/Al ratios and their reactivity in NaOH. Applying this new method I will investigate three emerging ideas on how humans can affect directly terrestrial Si fluxes. -Land use. I expect strong silica fractionation and reactivity differences in different land uses. These effects due to agricultural and forestry management have already been shown earlier in temperate soils (Vandevenne et al. 2012). Now we will test this hypothesis in recently deforested soils, in the south of Brazil. 'Pristine' forest, managed forest and tobacco field soils (with and without rotation crops) will be studied. This research belongs to an interdisciplinary project on soils and global change. -Fire. According to the IPCC report, extreme events such as fires (number and intensity) would increase due to climate change. We analyzed litter from spruce forest, beech forest and peat soils at two burning levels, after 350°C and

  5. Complex network approach to fractional time series

    SciTech Connect

    Manshour, Pouya

    2015-10-15

    In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacency matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.

  6. Extraction of TNT from aggregate soil fractions.

    PubMed

    Williford, C W; Mark Bricka, R

    1999-04-23

    Past explosives manufacture, disposal, and training activities have contaminated soil at many military facilities, posing health and environmental risks through contact, potential detonation, and leaching into ground water. While methods have been confirmed for extraction and measuring explosives concentration in soil, no work has addressed aggregate size material (the >2 mm gravel and cobbles) that often occurs with the smaller soil fractions. This paper describes methods and results for extraction and measurement of TNT (2,4,6-trinitrotoluene) in aggregate material from 1/2 to 2-1/1 from a WWII era ammunition plant. TNT was extracted into acetonitrile by both Soxhlet and ultrasonic extraction methods. High pressure liquid chromatography analyses of extracts showed expected variation among samples. Also effective extraction and determination of TNT concentration for each aggregate size fraction was achieved.

  7. Methods And Apparatus For Acoustic Fiber Fractionation

    DOEpatents

    Brodeur, Pierre

    1999-11-09

    Methods and apparatus for acoustic fiber fractionation using a plane ultrasonic wave field interacting with water suspended fibers circulating in a channel flow using acoustic radiation forces to separate fibers into two or more fractions based on fiber radius, with applications of the separation concept in the pulp and paper industry. The continuous process relies on the use of a wall-mounted, rectangular cross-section piezoelectric ceramic transducer to selectively deflect flowing fibers as they penetrate the ultrasonic field. The described embodiment uses a transducer frequency of approximately 150 kHz. Depending upon the amount of dissolved gas in water, separation is obtained using a standing or a traveling wave field.

  8. Flip-flopping fractional flux quanta.

    PubMed

    Ortlepp, T; Ariando; Mielke, O; Verwijs, C J M; Foo, K F K; Rogalla, H; Uhlmann, F H; Hilgenkamp, H

    2006-06-09

    The d-wave pairing symmetry in high-critical temperature superconductors makes it possible to realize superconducting rings with built-in pi phase shifts. Such rings have a twofold degenerate ground state that is characterized by the spontaneous generation of fractional magnetic flux quanta with either up or down polarity. We have incorporated pi phase-biased superconducting rings in a logic circuit, a flip-flop, in which the fractional flux polarity is controllably toggled by applying single flux quantum pulses at the input channel. The integration of p rings into conventional rapid single flux quantum logic as natural two-state devices should alleviate the need for bias current lines, improve device symmetry, and enhance the operation margins.

  9. Precision of the fractionator from Cavalieri designs.

    PubMed

    Cruz-Orive, L M

    2004-02-01

    A popular procedure to predict the variance of the fractionator consists in splitting the initial collection of fragments into two subsets, in order to use the corresponding particle counts (or any other pertinent measure), in the calculation. The current formula does not account for local or 'nugget' errors inherent in the estimation of fragment contents, however. Moreover, it does not account for the fact that the contribution of the variability between fragments or slices should rapidly decrease as the sampling fraction increases. For these reasons, an update to the formula is overdue. It should be stressed, however, that the formula applies to Cavalieri slices designs - its application for arbitrary partition designs is therefore not warranted.

  10. Dynamical models of happiness with fractional order

    NASA Astrophysics Data System (ADS)

    Song, Lei; Xu, Shiyun; Yang, Jianying

    2010-03-01

    This present study focuses on a dynamical model of happiness described through fractional-order differential equations. By categorizing people of different personality and different impact factor of memory (IFM) with different set of model parameters, it is demonstrated via numerical simulations that such fractional-order models could exhibit various behaviors with and without external circumstance. Moreover, control and synchronization problems of this model are discussed, which correspond to the control of emotion as well as emotion synchronization in real life. This study is an endeavor to combine the psychological knowledge with control problems and system theories, and some implications for psychotherapy as well as hints of a personal approach to life are both proposed.

  11. RNA isolation and fractionation with compaction agents

    NASA Technical Reports Server (NTRS)

    Murphy, J. C.; Fox, G. E.; Willson, R. C.

    2001-01-01

    A new approach to the isolation of RNA from bacterial lysates employs selective precipitation by compaction agents, such as hexammine cobalt and spermidine. Using 3.5 mM hexammine cobalt, total RNA can be selectively precipitated from a cell lysate. At a concentration of 2 mM hexammine cobalt, rRNA can be fractionated from low molecular weight RNA. The resulting RNA mixture is readily resolved to pure 5S and mixed 16S/23S rRNA by nondenaturing anion-exchange chromatography. Using a second stage of precipitation at 8 mM hexammine cobalt, the low molecular weight RNA fraction can be isolated by precipitation. Compaction precipitation was also applied to the purification of an artificial stable RNA derived from Escherichia coli 5S rRNA and to the isolation of an Escherichia coli-expressed ribozyme. Copyright 2001 Academic Press.

  12. Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

    NASA Astrophysics Data System (ADS)

    Dabiri, Arman; Butcher, Eric A.; Nazari, Morad

    2017-02-01

    Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

  13. Hamiltonian theory of the fractional quantum Hall effect: Conserving approximation for incompressible fractions

    NASA Astrophysics Data System (ADS)

    Murthy, Ganpathy

    2001-11-01

    A microscopic Hamiltonian theory of the fractional quantum Hall effect developed by Shankar and the present author based on the fermionic Chern-Simons approach has recently been quite successful in calculating gaps and finite-tempertature properties in fractional quantum Hall states. Initially proposed as a small-q theory, it was subsequently extended by Shankar to form an algebraically consistent theory for all q in the lowest Landau level. Such a theory is amenable to a conserving approximation in which the constraints have vanishing correlators and decouple from physical response functions. Properties of the incompressible fractions are explored in this conserving approximation, including the magnetoexciton dispersions and the evolution of the small-q structure factor as ν-->12. Finally, a formalism capable of dealing with a nonuniform ground-state charge density is developed and used to show how the correct fractional value of the quasiparticle charge emerges from the theory.

  14. Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

    PubMed

    Jeon, Jae-Hyung; Metzler, Ralf

    2010-02-01

    Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

  15. On tests of equal effect per fraction in microcolony assays of survival after fractionated irradiations.

    PubMed

    Taylor, J M

    1985-01-01

    H. D. Thames, Jr. and H. R. Withers [Br. J. Radiol. 53, 1071-1077 (1980)] propose a test of an equal effect per fraction in microcolony assays after fractionated radiation, in which the total effect is measured by counting microcolonies derived from surviving cells in a tissue. The factors considered to influence the cytocidal effect per fraction are incomplete repair, repopulation, and synchrony. The statistics used in the method are criticized and conditions are given under which the test should not be used. An alternative method of testing for an equal effect per fraction is proposed. The pros and cons of each test are discussed and compared using some mouse jejunal crypt cell survival data.

  16. Aging and Rejuvenation with Fractional Derivatives

    DTIC Science & Technology

    2007-11-02

    Science, University of North Texas, P. O. Box 311427, Denton, Texas 76203-1427, USA 2Dipartimento di Fisica dell’Università di Pisa and INFM, via...interval 2,m,3, yield a generalized master equation equivalent to the sum of an ordinary Markov contribution and a fractional derivative term. We show...though these processes are associated with quite different physical phenomena [14]. His general argu- ments rested on three assumptions: (1) microscopic

  17. The Value Proposition for Fractionated Space Architectures

    DTIC Science & Technology

    2006-09-01

    typical of the aircraft and mass market high-tech industries. Analogously to a Beowulf cluster26 delivering the capability of a massive...architecture for effecting massive parallel processing capability with cluster of personal computers. See, e.g., http://en.wikipedia.org/wiki...Flexibility Provided by Fractionated Spacecraft,” AIAA-2005-6700, AIAA Space 2005, Long Beach, CA (2005). AIAA-2006-7506 - 19 - Cluster Flying

  18. Silicon isotope fractionation during magmatic differentiation

    NASA Astrophysics Data System (ADS)

    Savage, Paul S.; Georg, R. Bastian; Williams, Helen M.; Burton, Kevin W.; Halliday, Alex N.

    2011-10-01

    The Si isotopic composition of Earth's mantle is thought to be homogeneous (δ 30Si = -0.29 ± 0.08‰, 2 s.d.) and not greatly affected by partial melting and recycling. Previous analyses of evolved igneous material indicate that such rocks are isotopically heavy relative to the mantle. To understand this variation, it is necessary to investigate the degree of Si isotopic fractionation that takes place during magmatic differentiation. Here we report Si isotopic compositions of lavas from Hekla volcano, Iceland, which has formed in a region devoid of old, geochemically diverse crust. We show that Si isotopic composition varies linearly as a function of silica content, with more differentiated rocks possessing heavier isotopic compositions. Data for samples from the Afar Rift Zone, as well as various igneous USGS standards are collinear with the Hekla trend, providing evidence of a fundamental relationship between magmatic differentiation and Si isotopes. The effect of fractionation has been tested by studying cumulates from the Skaergaard Complex, which show that olivine and pyroxene are isotopically light, and plagioclase heavy, relative to the Si isotopic composition of the Earth's mantle. Therefore, Si isotopes can be utilised to model the competing effects of mafic and felsic mineral fractionation in evolving silicate liquids and cumulates. At an average SiO 2 content of ˜60 wt.%, the predicted δ 30Si value of the continental crust that should result from magmatic fractionation alone is -0.23 ± 0.05‰ (2 s.e.), barely heavier than the mantle. This is, at most, a maximum estimate, as this does not take into account weathered material whose formation drives the products toward lighter δ 30Si values. Mass balance calculations suggest that removal of continental crust of this composition from the upper mantle will not affect the Si isotopic composition of the mantle.

  19. Magnesium isotope fractionation during continental weathering

    NASA Astrophysics Data System (ADS)

    Teng, F. Z.; Huang, K. J.; Li, W.; Liu, X. M.; Ma, L.

    2014-12-01

    Continental weathering links the atmosphere, hydrosphere and continents as it regulates the CO2 content of the atmosphere, shifts the composition of the continental crust from basaltic to andesitic, and ultimately controls the chemical composition of river waters and seawater. Magnesium is a water-soluble major element in the hydrosphere, continental crust and the mantle, and has three stable isotopes (24Mg, 25Mg and 26Mg). Studies of Mg isotopes during continental weathering may help to document the interactions between hydrosphere, crust and mantle. Previous studies have shown that the continental crust has a heterogeneous but on average heavier Mg isotopic composition than the mantle, whereas the hydrosphere is isotopically light. The complementary characteristics of Mg isotopic compositions between continental and hydrosphere have been attributed to continental weathering, with light Mg isotopes partitioned into water, leaving heavy Mg isotopes behind in the crustal residue. Here we summarize our studies of Mg isotope fractionation in four weathering profiles under various climate conditions. We show that large Mg isotope fractionation can occur during continental weathering. Although the weathered residue is usually enriched in heavier Mg isotopes than unaltered parent rocks, some heavily weathered products can be quite light in Mg isotopic composition. The complicated behaviors of Mg isotopes reflect different control factors during weathering such as parent rock lithology, primary mineral dissolution, secondary mineral formation, ion exchange, vegetation uptake etc. Though studies of natural samples can provide direct evidence on isotope fractionation, more well-controlled laboratory experiments on Mg isotope fractionation between fluids and minerals are needed in order to fully understand the behaviors of Mg isotopes during weathering, which ultimately lays the foundation for making Mg isotope geochemistry an important tool for studying different geological

  20. Chiral anomaly, bosonization, and fractional charge

    SciTech Connect

    Mignaco, J.A.; Monteiro, M.A.R.

    1985-06-15

    We present a method to evaluate the Jacobian of chiral rotations, regulating determinants through the proper-time method and using Seeley's asymptotic expansion. With this method we compute easily the chiral anomaly for ..nu.. = 4,6 dimensions, discuss bosonization of some massless two-dimensional models, and handle the problem of charge fractionization. In addition, we comment on the general validity of Fujikawa's approach to regulate the Jacobian of chiral rotations with non-Hermitian operators.

  1. Microbial isotopic fractionation of perchlorate chlorine.

    PubMed

    Coleman, Max L; Ader, Magali; Chaudhuri, Swades; Coates, John D

    2003-08-01

    Perchlorate contamination can be microbially respired to innocuous chloride and thus can be treated effectively. However, monitoring a bioremediative strategy is often difficult due to the complexities of environmental samples. Here we demonstrate that microbial respiration of perchlorate results in a significant fractionation ( approximately -15 per thousand ) of the chlorine stable isotope composition of perchlorate. This can be used to quantify the extent of biotic degradation and to separate biotic from abiotic attenuation of this contaminant.

  2. Solubilization and fractionation of paired helical filaments.

    PubMed

    González, P J; Correas, I; Avila, J

    1992-09-01

    Paired helical filaments isolated from brains of two different patients with Alzheimer's disease were extensively treated with the ionic detergent, sodium dodecyl sulphate. Filaments were solubilized at different extents, depending on the brain examined, thus suggesting the existence of two types of paired helical filaments: sodium dodecyl sulphate-soluble and insoluble filaments. In the first case, the number of structures resembling paired helical filaments greatly decreased after the detergent treatment, as observed by electron microscopy. Simultaneously, a decrease in the amount of sedimentable protein was also observed upon centrifugation of the sodium dodecyl sulfate-treated paired helical filaments. A sodium dodecyl sulphate-soluble fraction was isolated as a supernatant after low-speed centrifugation of the sodium dodecyl sulphate-treated paired helical filaments. The addition of the non-ionic detergent Nonidet-P40 to this fraction resulted in the formation of paired helical filament-like structures. When the sodium dodecyl sulphate-soluble fraction was further fractionated by high-speed centrifugation, three subfractions were observed: a supernatant, a pellet and a thin layer between these two subfractions. No paired helical filaments were observed in any of these subfractions, even after addition of Nonidet P-40. However, when they were mixed back together, the treatment with Nonidet P-40 resulted in the visualization of paired helical filament-like structures. These results suggest that at least two different components are needed for the reconstitution of paired helical filaments as determined by electron microscopy. The method described here may allow the study of the components involved in the formation of paired helical filaments and the identification of possible factors capable of blocking this process.

  3. Approximate Solution of Time-Fractional Advection-Dispersion Equation via Fractional Variational Iteration Method

    PubMed Central

    İbiş, Birol

    2014-01-01

    This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie's modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs. PMID:24578662

  4. Mineral equilibrium in fractionated nebular systems

    NASA Technical Reports Server (NTRS)

    Wood, John A.; Hashimoto, Akihiko

    1993-01-01

    We investigated the equilibrium mineral assemblages in chemically fractionated nebular systems, using a computer routine that finds the set of minerals and gases which minimizes the Gibbs free energy of a system with stipulated elemental abundances. Diagrams are presented showing the equilibrium mineralogy, as a function of temperature (400-2300 K), for unfractionated solar material and five fractionated systems. The fractionated systems were defined by mixing, in various proportions, the following four volatility components that solar material can be divided into: refractory dust, carbonaceous matter, ices, and H2 gas. Dust enrichment is seen to increase temperatures of condensation/evaporation and the Fe(2+) content of mafic minerals and to permit existence of stable melt phases. Enrichment of dust and organic matter produces mineral assemblages that are similar in many ways to those of enstatite chondrites, but with mafic minerals that are far more reduced than those in primitive enstatite chondrites. Enrichment of dust, organics, and ices leads to highly ferrous mineralogies even at the highest temperatures but does not predict the stability of hydrous phases above about 450 K.

  5. Fractional statistics and the butterfly effect

    NASA Astrophysics Data System (ADS)

    Gu, Yingfei; Qi, Xiao-Liang

    2016-08-01

    Fractional statistics and quantum chaos are both phenomena associated with the non-local storage of quantum information. In this article, we point out a connection between the butterfly effect in (1+1)-dimensional rational conformal field theories and fractional statistics in (2+1)-dimensional topologically ordered states. This connection comes from the characterization of the butterfly effect by the out-of-time-order-correlator proposed recently. We show that the late-time behavior of such correlators is determined by universal properties of the rational conformal field theory such as the modular S-matrix and conformal spins. Using the bulk-boundary correspondence between rational conformal field theories and (2+1)-dimensional topologically ordered states, we show that the late time behavior of out-of-time-order-correlators is intrinsically connected with fractional statistics in the topological order. We also propose a quantitative measure of chaos in a rational conformal field theory, which turns out to be determined by the topological entanglement entropy of the corresponding topological order.

  6. Anticancer activity of selected Colocasia gigantia fractions.

    PubMed

    Pornprasertpol, Apichai; Sereemaspun, Amornpun; Sooklert, Kanidta; Satirapipatkul, Chutimon; Sukrong, Suchada

    2015-01-01

    The objective of this study is to investigate the anticancer potential of the extract of Colocasia gigantea C. gigantea), a plant member of the Araceae family. In the present study, we investigated the cytotoxic activity of C. gigantea extract on cervical cancer (Hela) and human white blood cells (WBC) in vitro. The authors then identified the bioactive ingredients that demonstrated cytotoxicity on tested cells and evaluated those bioactive ingredients using the bioassay-guided fractionation method. The results showed that not all parts of C. gigantea promote cytotoxic activity. The dichloromethane leaf fraction showed significant cell proliferation effect on Hela cells, but not on WBCs. Only the n-hexane tuber fraction (Fr. 1T) exhibited significant cytotoxicity on Hela cells (IC50 = 585 μg/ml) and encouraged WBC cell proliferation. From GC-Mass spectrometry, 4,22-Stigmastadiene-3-one, Diazoprogesterone, 9-Octadecenoic acid (Z)-, hexyl ester and Oleic Acid were the components of Fr 1T that demonstrated cytotoxic potential. In conclusion, C. gigantea's Fr 1T shows potential for cervical cancer treatment.

  7. Edge reconstructions in fractional quantum Hall systems.

    NASA Astrophysics Data System (ADS)

    Joglekar, Yogesh; Nguyen, Hoang; Murthy, Ganpathy

    2003-03-01

    Two dimensional electron systems exhibiting fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations are possible [1]. We present a microscopic calculation of these egde-states at filling factors ν=1/3 and ν=2/5 using the Hamiltonian theory of the fractional quantum Hall effect [2]. We find that the quantum Hall egde undergoes a reconstruction as the confining potential, produced by the background charge density, softens [3,4]. Our results have implications to the tunneling experiments into the edge of a fractional quantum Hall system [5]. 1: X. G.Wen, Phys. Rev. Lett. 64, 2206 (1990). 2: R. Shankar and G. Murthy, Phys. Rev. Lett. 79, 4437 (1997). 3: C. de C. Chamon and X. G. Wen, Phys. Rev. B 49, 8227 (1994). 4: X. Wan, K. Yang, and E. H. Razayi, Phys. Rev. Lett. 88, 056802 (2002). 5: A.M.Chang et al., Phys. Rev. Lett. 86, 143 (2000).

  8. Measurement of tau lepton branching fractions

    SciTech Connect

    Nicol, Neil Allen

    1993-09-30

    We present τ- lepton branching fraction measurements based on data from the TPC/Two-Gamma detector at PEP. Using a sample of τ- → vτK-π+π- events, we examine the resonance structure of the K-π+π- system and obtain the first measurements of branching fractions for τ- → vτK$-\\atop{1}$(1270) and τ- → vτK$-\\atop{1}$(1400). We also describe a complete set of branching fraction measurements in which all the decays of the τ- lepton are separated into classes defined by the identities of the charged particles and an estimate of the number of neutrals. This is the first such global measurement with decay classes defined by the four possible charged particle species, e, μ, π, and K.

  9. Iron isotopic fractionation during continental weathering

    SciTech Connect

    Fantle, Matthew S.; DePaolo, Donald J.

    2003-10-01

    The biological activity on continents and the oxygen content of the atmosphere determine the chemical pathways through which Fe is processed at the Earth's surface. Experiments have shown that the relevant chemical pathways fractionate Fe isotopes. Measurements of soils, streams, and deep-sea clay indicate that the {sup 56}Fe/{sup 54}Fe ratio ({delta}{sup 56}Fe relative to igneous rocks) varies from +1{per_thousand} for weathering residues like soils and clays, to -3{per_thousand} for dissolved Fe in streams. These measurements confirm that weathering processes produce substantial fractionation of Fe isotopes in the modern oxidizing Earth surface environment. The results imply that biologically-mediated processes, which preferentially mobilize light Fe isotopes, are critical to Fe chemistry in weathering environments, and that the {delta}{sup 56}Fe of marine dissolved Fe should be variable and negative. Diagenetic reduction of Fe in marine sediments may also be a significant component of the global Fe isotope cycle. Iron isotopes provide a tracer for the influence of biological activity and oxygen in weathering processes through Earth history. Iron isotopic fractionation during weathering may have been smaller or absent in an oxygen-poor environment such as that of the early Precambrian Earth.

  10. Xenon Fractionation and Archean Hydrogen Escape

    NASA Technical Reports Server (NTRS)

    Zahnle, K. J.

    2015-01-01

    Xenon is the heaviest gas found in significant quantities in natural planetary atmospheres. It would seem the least likely to escape. Yet there is more evidence for xenon escape from Earth than for any element other than helium and perhaps neon. The most straightforward evidence is that most of the radiogenic Xe from the decay of (129)I (half-life 15.7 Myr) and (244)Pu (half-life 81 Myr) that is Earth's birthright is missing. The missing xenon is often attributed to the impact erosion of early atmospheres of Earth and its ancestors. It is obvious that if most of the radiogenic xenon were driven off by impacts, most of the rest of the atmophiles fared the same fate. The other line of evidence is in the nonradiogenic isotopes of xenon and its silent partner, krypton. Atmospheric xenon is strongly mass fractionated (at about 4% per amu) compared to any known solar system source (Figure 1). This is in stark contrast to krypton, which may not be fractionated at all: atmospheric Kr is slightly heavier than solar Kr (at about 0.5% per amu), but it is the same as in carbonaceous chondrites. Nonradiogenic xenon is also under abundant relative to krypton (the so-called "missing xenon" problem). Together these observations imply that xenon has been subject to fractionating escape and krypton not.

  11. Confounding and bias in the attributable fraction.

    PubMed

    Darrow, Lyndsey A; Steenland, N Kyle

    2011-01-01

    Inappropriate methods are frequently used to calculate the population attributable fraction (AF) for a given exposure of interest. This commonly occurs when authors use adjusted relative risks (RRs) reported in the literature (the "source" data), without access to the original data. In this analysis, we examine the relationship between the direction and magnitude of confounding in the source data and resulting bias in the attributable fraction when incorrect methods are used. We assess confounding by the confounding risk ratio, which is the ratio of the crude RR to the adjusted RR. We assess bias in the AF by the ratio of the incorrectly calculated AF to the correctly calculated AF. Using generated data, we examine the relationship between confounding and AF bias under various scenarios of population prevalence of exposure and strength of the exposure-disease association. For confounding risk ratios greater than 1.0 (ie, crude RR >adjusted RR), the AF is underestimated; for confounding risk ratios less than 1.0 (ie, crude RR fraction estimates commonly reported in the epidemiologic literature.

  12. Zn Isotope Fractionation during Sorption onto Kaolinite.

    PubMed

    Guinoiseau, Damien; Gélabert, Alexandre; Moureau, Julien; Louvat, Pascale; Benedetti, Marc F

    2016-02-16

    In this study, we quantify zinc isotope fractionation during its sorption onto kaolinite, by performing experiments under various pH, ionic strength, and total Zn concentrations. A systematic enrichment in heavy Zn isotopes on the surface of kaolinite was measured, with Δ(66)Znadsorbed-solution ranging from 0.11‰ at low pH and low ionic strength to 0.49‰ at high pH and high ionic strength. Both the measured Zn concentration and its isotopic ratio are correctly described using a thermodynamic sorption model that considers two binding sites: external basal surfaces and edge sites. Based on this modeling approach, two distinct Zn isotopic fractionation factors were calculated: Δ(66)Znadsorbed-solution = 0.18 ± 0.06‰ for ion exchange onto basal sites, and Δ(66)Znadsorbed-solution = 0.49 ± 0.06‰ for specific complexation onto edge sites. These two distinct factors indicate that Zn isotope fractionation is dominantly controlled by the chemical composition of the solution (pH, ionic strength).

  13. Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus

    NASA Astrophysics Data System (ADS)

    Atangana, Abdon

    2016-10-01

    In order to describe more complex problems using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with the generalized Mittag-Leffler function. The first order is included in the power law function and the second one is in the generalized Mittag-Leffler function. Each order therefore plays an important role while modeling, for instance, problems with two layers with different properties. This is the case, for instance, in thermal science for a reaction diffusion within a media with two different layers with different properties. Another case is that of groundwater flowing within an aquifer where geological formation is formed with two layers with different properties. The paper presents new fractional operators that will open new doors for research and investigations in modeling real world problems. Some useful properties of the new operators are presented, in particular their relationship with existing integral transforms, namely the Laplace, Sumudu, Mellin and Fourier transforms. The numerical approximation of the new fractional operators are presented. We apply the new fractional operators on the model of groundwater plume with degradation and limited sorption and solve the new model numerically with some numerical simulations. The numerical simulation leaves no doubt in believing that the new fractional operators are powerfull mathematical tools able to portray complexes real world problems.

  14. Paper-based flow fractionation system for preconcentration and field-flow fractionation.

    NASA Astrophysics Data System (ADS)

    Hong, Seokbin; Kwak, Rhokyun; Kim, Wonjung

    2015-11-01

    We present a novel paper-based flow fractionation system for preconcentration and field-flow fractionation. The paper fluidic system consisting of a straight channel connected with expansion regions can generate a fluid flow with a constant flow rate for 10 min without any external pumping devices. The flow bifurcates with a fraction ratio of up to 30 depending on the control parameters of the channel geometry. Utilizing this simple paper-based bifurcation system, we developed a continuous-flow preconcentrator and a field-flow fractionator on a paper platform. Our experimental results show that the continuous-flow preconcentrator can produce a 33-fold enrichment of the ion concentration and that the flow fractionation system successfully separates the charged dyes. Our study suggests simple, cheap ways to construct preconcentration and field-flow fractionation systems for paper-based microfluidic diagnostic devices. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (NRF-2015R1A2A2A04006181).

  15. Computational solutions of unified fractional reaction-diffusion equations with composite fractional time derivative

    NASA Astrophysics Data System (ADS)

    Saxena, R. K.; Mathai, A. M.; Haubold, H. J.

    2015-10-01

    This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized fractional time-derivative defined by Hilfer (2000), the space derivative of second order by the Riesz-Feller fractional derivative and adding the function ϕ (x, t) which is a nonlinear function governing reaction. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The main result obtained in this paper provides an elegant extension of the fundamental solution for the space-time fractional diffusion equation obtained earlier by Mainardi et al. (2001, 2005) and a result very recently given by Tomovski et al. (2011). Computational representation of the fundamental solution is also obtained explicitly. Fractional order moments of the distribution are deduced. At the end, mild extensions of the derived results associated with a finite number of Riesz-Feller space fractional derivatives are also discussed.

  16. Copper isotope fractionation in acid mine drainage

    USGS Publications Warehouse

    Kimball, B.E.; Mathur, R.; Dohnalkova, A.C.; Wall, A.J.; Runkel, R.L.; Brantley, S.L.

    2009-01-01

    We measured the Cu isotopic composition of primary minerals and stream water affected by acid mine drainage in a mineralized watershed (Colorado, USA). The ??65Cu values (based on 65Cu/63Cu) of enargite (??65Cu = -0.01 ?? 0.10???; 2??) and chalcopyrite (??65Cu = 0.16 ?? 0.10???) are within the range of reported values for terrestrial primary Cu sulfides (-1??? < ??65Cu < 1???). These mineral samples show lower ??65Cu values than stream waters (1.38??? ??? ??65Cu ??? 1.69???). The average isotopic fractionation (??aq-min = ??65Cuaq - ??65Cumin, where the latter is measured on mineral samples from the field system), equals 1.43 ?? 0.14??? and 1.60 ?? 0.14??? for chalcopyrite and enargite, respectively. To interpret this field survey, we leached chalcopyrite and enargite in batch experiments and found that, as in the field, the leachate is enriched in 65Cu relative to chalcopyrite (1.37 ?? 0.14???) and enargite (0.98 ?? 0.14???) when microorganisms are absent. Leaching of minerals in the presence of Acidithiobacillus ferrooxidans results in smaller average fractionation in the opposite direction for chalcopyrite (??aq-mino = - 0.57 ?? 0.14 ???, where mino refers to the starting mineral) and no apparent fractionation for enargite (??aq-mino = 0.14 ?? 0.14 ???). Abiotic fractionation is attributed to preferential oxidation of 65Cu+ at the interface of the isotopically homogeneous mineral and the surface oxidized layer, followed by solubilization. When microorganisms are present, the abiotic fractionation is most likely not seen due to preferential association of 65Cuaq with A. ferrooxidans cells and related precipitates. In the biotic experiments, Cu was observed under TEM to occur in precipitates around bacteria and in intracellular polyphosphate granules. Thus, the values of ??65Cu in the field and laboratory systems are presumably determined by the balance of Cu released abiotically and Cu that interacts with cells and related precipitates. Such isotopic signatures

  17. Environmental Controls on Stratocumulus Cloud Fraction

    NASA Astrophysics Data System (ADS)

    Burleyson, Casey Dale

    Marine stratocumulus clouds are widespread, low, optically thick, and persist for long periods of time. Their high albedo allows stratocumulus clouds to reflect large amounts of incoming shortwave radiation. Understanding the processes that lead to changes in stratocumulus cloud fraction is critically important in capturing the effects of stratocumulus in global climate models (GCMs). This research presents two analyses which seek to better understand the governing processes that drive variability in the stratocumulus-topped boundary layer system. The diurnal cycle of marine stratocumulus in cloud-topped boundary layers is examined using ship-based meteorological data obtained during the 2008 VAMOS Ocean-Cloud-Atmosphere-Land Study Regional Experiment (VOCALS-REx). The high temporal and spatial continuity of the ship data, as well as the 31-day sample size, allows us to resolve the diurnal transition in degree of coupling of the stratocumulus-topped boundary layer. The amplitude of diurnal variation was comparable to the magnitude of longitudinal differences between regions east and west of 80°W for most of the cloud, surface, and precipitation variables examined. The diurnal cycle of precipitation is examined in terms of areal coverage, number of drizzle cells, and estimated rain rate. East of 80°W, the drizzle cell frequency and drizzle area peaks just prior to sunrise. West of 80°W, total drizzle area peaks at 3:00 am, 2-3 hours before sunrise. Peak drizzle cell frequency is three times higher west of 80°W compared to east of 80°W. The waning of drizzle several hours prior to the ramp up of shortwave fluxes may be related to the higher peak drizzle frequencies in the west. The ensemble effect of localized subcloud evaporation of precipitation may make drizzle a self-limiting process where the areal density of drizzle cells is sufficiently high. The daytime reduction in vertical velocity variance in a less coupled boundary layer is accompanied by enhanced

  18. Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis

    NASA Astrophysics Data System (ADS)

    Jiao, Yujian; Wang, Li-Lian; Huang, Can

    2016-01-01

    The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.

  19. Noble gas fractionation during subsurface gas migration

    NASA Astrophysics Data System (ADS)

    Sathaye, Kiran J.; Larson, Toti E.; Hesse, Marc A.

    2016-09-01

    Environmental monitoring of shale gas production and geological carbon dioxide (CO2) storage requires identification of subsurface gas sources. Noble gases provide a powerful tool to distinguish different sources if the modifications of the gas composition during transport can be accounted for. Despite the recognition of compositional changes due to gas migration in the subsurface, the interpretation of geochemical data relies largely on zero-dimensional mixing and fractionation models. Here we present two-phase flow column experiments that demonstrate these changes. Water containing a dissolved noble gas is displaced by gas comprised of CO2 and argon. We observe a characteristic pattern of initial co-enrichment of noble gases from both phases in banks at the gas front, followed by a depletion of the dissolved noble gas. The enrichment of the co-injected noble gas is due to the dissolution of the more soluble major gas component, while the enrichment of the dissolved noble gas is due to stripping from the groundwater. These processes amount to chromatographic separations that occur during two-phase flow and can be predicted by the theory of gas injection. This theory provides a mechanistic basis for noble gas fractionation during gas migration and improves our ability to identify subsurface gas sources after post-genetic modification. Finally, we show that compositional changes due to two-phase flow can qualitatively explain the spatial compositional trends observed within the Bravo Dome natural CO2 reservoir and some regional compositional trends observed in drinking water wells overlying the Marcellus and Barnett shale regions. In both cases, only the migration of a gas with constant source composition is required, rather than multi-stage mixing and fractionation models previously proposed.

  20. Gravitational fractionation of solutes and isotopes

    NASA Astrophysics Data System (ADS)

    Bons, Paul D.; Gomez-Rivas, Enrique

    2014-05-01

    In a stagnant pore fluid, dissolved heavy components tend to gravitate downwards, while light components concentrate towards the top of the reservoir. This gravitational gravitation (Bons & Gomez-Rivas, 2013) is counteracted by Fickian diffusion, which strives to equalize concentrations of all components. Numerical simulations show that gravitational fractionation can be significant in crustal fluid reservoirs, provided the fluid is stagnant for prolonged periods of times (tens of millions of years) and that the vertical connectivity of the pores extends over at least a few kilometres. In that case, up to double digit shifts in hydrogen and oxygen isotopic signatures can develop and, for example, Cl/Br ratios can be modified by more than a factor of two. Stagnant fluid reservoirs can be expected in basement rocks under unconformities, such as the Variscan basement in Western Europe during the Mesozoic. Published fluid ages based on halogen isotopes confirm that basement fluids can be tens of millions of years old (e.g. Fehn & Snyder, 2005). Considering that fluid compositions (isotopic signatures, halogen ratios, etc.) are commonly used to determine origin of fluids and the processes that may have modified them, recognizing the potential modification of fluid signatures by gravitational fractionation is of importance in models for crustal fluid flow and ore formation. Bons, P.D., Gomez-Rivas, E. 2013. Gravitational fractionation of isotopes and dissolved components as a first-order process in hydrothermal crustal fluids. Economic Geology 108, 1195-120. Fehn, U., and Snyder, G.T. 2005. Residence times and source ages of deep crustal fluids: interpretation of 129I and 36Cl results from the KTB-VB drill site, Germany. Geofluids 5, 42-51.

  1. Outcomes of ablative fractional laser scar treatment.

    PubMed

    Kim, Deok-Woo; Hwang, Na-Hyun; Yoon, Eul-Sik; Dhong, Eun-Sang; Park, Seung-Ha

    2015-04-01

    Ablative fractional laser (AFL) systems are commonly used to treat various scars, and recent reports have indicated that early scar treatment with fractional lasers has good aesthetic results. Some scars respond dramatically to AFL treatment, incurring high levels of patient satisfaction; however, other scars respond poorly or became worse after treatment. This study was designed to clarify prognostic factors that predict AFL scar treatment outcomes. A total of 108 patients were included in this study. The fractional laser treatments were repeated every 4 weeks until the scar site was acceptable and no additional improvement was expected or the patient discontinued the treatment. The scar improvements were defined as changes in the Manchester scar scale (MSS) from before to after laser treatment. A digital camera was used to acquire digital photographs of the scars under the same light source, the same background, exposure, and white balance. This study developed a modification of the MSS for image analysis in which colour assessment was based on L*a*b* colour co-ordinates of the digital images. The mean MSS values prior to and after laser treatments were 11.6 ± 3.6 and 9.5 ± 2.9, respectively (p < 0.01). AFL treatment improved the qualities of each scar, and the improvements were evident in colour and contour. Scar elevation, pigmentation, high vascularity, early onset of treatment, and the number of treatment sessions were directly related to scar improvement after AFL therapy (p < 0.05). AFL treatments were effective methods for scar treatment. Clinicians can use these prognostic factors to determine treatment plans and to estimate scar improvement after AFL treatment.

  2. Estimating the Kinematic Viscosity of Petroleum Fractions

    NASA Astrophysics Data System (ADS)

    AlMulla, Hessa A.; Albahri, Tareq A.

    2017-04-01

    Kinematic viscosity correlation has been developed for liquid petroleum fractions at 37.78°C and 98.89°C (100 and 210°F) standard temperatures using a large variety of experimental data. The only required inputs are the specific gravity and the average boiling point temperature. The accuracy of the correlation was compared with several other correlations available in the literature. The proposed correlations proved to be more accurate in predicting the viscosity at 37.78°C and 98.89°C with average absolute deviations of 0.39 and 0.72 mm2/s, respectively. Another objective was to develop a relation for the variation of viscosity with temperature to predict the viscosity of petroleum fraction at a certain temperature from the knowledge of the viscosity for the same liquid at two other temperatures. The newly developed correlation represents a wide array of temperatures from 20°C to 150°C and viscosities from 0.14 mm2/s to 343.64 mm2/s. The results have been validated with experimental data consisting of 9558 data points, yielding an overall deviation of 0.248 mm2/s and R2 of 0.998. In addition, new formulas were developed to interconvert the viscosity of petroleum fractions from one unit of measure to another based on finding the best fit for a set of experimental data from the literature with R2 as high as 1.0 for many cases. Detailed analysis showed good agreement between the predicted values and the experimental data.

  3. D/H Fractionation in Circumstellar Disks

    NASA Astrophysics Data System (ADS)

    Kessler, J. E.; Qi, C.; Blake, G. A.

    2000-12-01

    In recent years millimeter-wave interferometers have imaged the gas and dust surrounding over a dozen T Tauri and Herbig Ae stars (see Sargent 1996 in Disks and Outflows from Young Stars, pp. 1-23, for review). These studies demonstrate the potential to improve dramatically our understanding of disk physical and chemical structure, providing unique insights that will ultimately enable a more comprehensive understanding of star and planet formation. In particular, through the comparison of disk properties such as (D/H) fractionation with those of comets and Kuiper belt objects the origin of primitive solar system bodies can be investigated. In this study, 1.3 mm transitions of the deuterated species DCN and HDO were detected toward the T Tauri star LkCa 15 using the Owens Valley Radio Observatory Millimeter Array (for previous observations of various molecules toward LkCa 15 see Qi, PhD thesis, 2000). The resulting DCN abundance was compared to that found for HCN and H13CN. The measured intensity ratios of the (DCN/HCN) transitions lead to (D/H) ratios of <0.5, but are clearly influenced by opacity in the HCN 1-0 transition. Observations of the optically thin isotope H13CN, yield an estimated DCN/HCN ratio of ~ 0.01. This value is much larger than the estimated protosolar D/H of ~ 1.6e-5 (Gautier & Morel 1997 A&A 323, L9) and quite close to that observed in dark molecular clouds, 0.01-0.05 (Wooten 1987 Astrochem 120, 311), indicating that the assignment of cometary origin using D/H fractionation is a complicated endeavor. Through the combination of the observations presented here and chemical models of circumstellar material, the temperature dependence of fractionation and enrichment of deuterium through gas-grain surface reactions can be explored. Further, although H2O cannot be observed and thus HDO/H2O was not measured, differences in the morphology of maps of the observed emission from DCN and HDO may shed light on differences in fractionation seen in the

  4. Polyfunctional catalyst for processiing benzene fractions

    SciTech Connect

    G. Byakov; B.D. Zubitskii; B.G. Tryasunov; I.Ya. Petrov

    2009-05-15

    A by-product of the coke industry is a raw benzene fraction benzene- 1 which may serve as for catalytic processes. The paper reports a study on the influence of the composition and temperatures on the activity and selectivity of NiO-V{sub 2}O{sub 6}-MoO{sub 3}/{gamma}-Al{sub 2}O{sub 3} catalysts and the corresponding binary and tertiary subsystems are studied by a pulse method in model reactions; the hydrodealkylating of toluene and the hydrodesulfurizing of thioprhene. The optimal catalyst composition is established. The new catalyst is compared with industrial catalysts.

  5. Fast permutation preconditioning for fractional diffusion equations.

    PubMed

    Wang, Sheng-Feng; Huang, Ting-Zhu; Gu, Xian-Ming; Luo, Wei-Hua

    2016-01-01

    In this paper, an implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is used to discretize the fractional diffusion equations with constant diffusion coefficients. The coefficient matrix possesses the Toeplitz structure and the fast Toeplitz matrix-vector product can be utilized to reduce the computational complexity from [Formula: see text] to [Formula: see text], where N is the number of grid points. Two preconditioned iterative methods, named bi-conjugate gradient method for Toeplitz matrix and bi-conjugate residual method for Toeplitz matrix, are proposed to solve the relevant discretized systems. Finally, numerical experiments are reported to show the effectiveness of our preconditioners.

  6. Fractional statistical theory of finite multilayer adsorption

    NASA Astrophysics Data System (ADS)

    Takara, E. A.; Quiroga, E.; Matoz-Fernandez, D. A.; Ochoa, N. A.; Ramirez-Pastor, A. J.

    2016-01-01

    In the present paper, finite multilayer adsorption is described as a fractional statistics problem, based on Haldane's statistics. In this scheme, the Helmholtz free energy and its derivatives are written in terms of a parameter g, which relates to the configuration of the molecules in the adsorbed state. For values of g ranging between 0 and 1 the formalism is used to model experimental data of bovine serum albumin (BSA) adsorbed onto an ion exchange resin for different values of pH and temperature. Excellent agreement between theory and experiments was found.

  7. Anomalous hydrodynamics of fractional quantum Hall states

    SciTech Connect

    Wiegmann, P.

    2013-09-15

    We propose a comprehensive framework for quantum hydrodynamics of the fractional quantum Hall (FQH) states. We suggest that the electronic fluid in the FQH regime can be phenomenologically described by the quantized hydrodynamics of vortices in an incompressible rotating liquid. We demonstrate that such hydrodynamics captures all major features of FQH states, including the subtle effect of the Lorentz shear stress. We present a consistent quantization of the hydrodynamics of an incompressible fluid, providing a powerful framework to study the FQH effect and superfluids. We obtain the quantum hydrodynamics of the vortex flow by quantizing the Kirchhoff equations for vortex dynamics.

  8. Applications of fractional calculus to epidemiological models

    NASA Astrophysics Data System (ADS)

    Skwara, Urszula; Martins, José; Ghaffari, Peyman; Aguiar, Maíra; Boto, João; Stollenwerk, Nico

    2012-09-01

    Epidemiological spreading does not only happen from person to neighbouring person but often over wide distances, when infected but asymptomatic persons travel and carry infection to others over wide distances. Superdiffusion has been suggested to model such spreading in spatially restriced contact networks, i.e. there is still a notion of geographical distance, but spreading happens with high probability proportional to large distances. From fractional calculus several ways of describing superdiffusion are know. Here we investigate the representation in Fourier space and which is easily generalizable to higher dimensional space in order to compare with stochastic models of epidemiological spreading.

  9. Isotopic Fractionation of Selenium Oxyanions in Wetlands

    NASA Astrophysics Data System (ADS)

    Clark, S. K.; Johnson, T. M.

    2004-05-01

    As oxic surface waters pass through aquatic macrophytes and over anoxic sediments in wetlands and lakes, the dissolved Se load often decreases; and, Se isotope ratio measurements can provide information about the mechanisms involved. Previous work on microbially induced isotopic fractionation of Se oxyanions under nearly natural conditions using wetland sediments shows consistent Se isotopic shifts during reduction of Se(VI) and Se(IV) to insoluble Se(0). However, previous isotopic studies of total dissolved selenium in wetlands found little to no isotopic shift as dissolved selenium concentrations decreased. This suggests that plant/algal uptake, followed by deposition and degradation, is the primary route of Se transfer into sediments. However, it is possible that the effective isotopic fractionation between Se in the surface water and Se deposited into sediments is somehow much less than the fractionation induced by the reduction reaction, or that cycling of organically bound Se is involved. In this study, we report Se isotope data for Se(VI), Se(IV) and total dissolved Se, Se(T), in surface waters from three wetland/lake sites: Sweitzer Lake, CO; 33-Mile Reservoir, WY; and, a small pond adjacent to Benton Lake, MT. We isolated Se(IV) via hydride generation, and Se(VI) via ion exchange. Se(T), including any organic components, was also analyzed. Isotope analysis was performed on an Isoprobe MC-ICPMS, using a method modified from that of Rouxel et al. (2002). We used the 82Se + 74Se double spike approach, and spiked samples before species separation. Our results for all three locations indicate similar trends in concentration changes and isotopic shifts between the inflow and outflow waters. Se(T) concentrations decrease by 45-70%, and Se(VI) concentrations decrease by 60-90%, whereas Se(IV) concentrations increase by 60-150%. Concomitant 80Se/76Se shifts are +0.5-0.8‰ for Se(T); -0.1-0.5‰ for Se(VI); and +0.4-6.5‰ for Se(IV). These data provide greater

  10. The fractionation of working memory

    PubMed Central

    Baddeley, Alan

    1996-01-01

    In performing many complex tasks, it is necessary to hold information in temporary storage to complete the task. The system used for this is referred to as working memory. Evidence for the need to postulate separable memory systems is summarized, and one particular model of working memory is described, together with its fractionation into three principal subsystems. The model has proved durable and useful and, with the development of electrophysiological and positive emission tomography scanning measures, is proving to map readily onto recent neuroanatomical developments. PMID:8942958

  11. Is Fractional Electric Charge Problematic for QCD?

    NASA Astrophysics Data System (ADS)

    Slansky, R.

    1982-11-01

    A model of broken QCD is described here; SU3c is broken to SO3g (``g'' for ``glow'') such that color triplets become glow triplets. With this breaking pattern, there should exist low-mass, fractionally-charged diquark states that are not strongly bound to nuclei, but are rarely produced at present accelerator facilities. The breaking of QCD can be done with a 27c, in which case, this strong interaction theory is easily embedded in unified models such as those based on SU5, SO10, or E6. This work was done in collaboration with Terry Goldman of Los Alamos and Gordon Shaw of U.C., Irvine.

  12. Excitons in the Fractional Quantum Hall Effect

    DOE R&D Accomplishments Database

    Laughlin, R. B.

    1984-09-01

    Quasiparticles of charge 1/m in the Fractional Quantum Hall Effect form excitons, which are collective excitations physically similar to the transverse magnetoplasma oscillations of a Wigner crystal. A variational exciton wavefunction which shows explicitly that the magnetic length is effectively longer for quasiparticles than for electrons is proposed. This wavefunction is used to estimate the dispersion relation of these excitons and the matrix elements to generate them optically out of the ground state. These quantities are then used to describe a type of nonlinear conductivity which may occur in these systems when they are relatively clean.

  13. Altered Fractional Anisotropy in Early Huntington's Disease

    PubMed Central

    Singh, Silky; Mehta, Hasit; Fekete, Robert

    2013-01-01

    Huntington's disease (HD) is a dominantly inherited neurodegenerative disease best known for chorea. The disorder includes numerous other clinical features including mood disorder, eye movement abnormalities, cognitive disturbance, pendular knee reflexes, motor impersistence, and postural instability. We describe a mild case of HD early in the disease course with depression and subtle neurological manifestations. In addition, we review MRI and diffusion tensor imaging features in this patient. The bicaudate ratio, a measure of caudate atrophy, was increased. Fractional anisotropy values of the bilateral caudate and putamen were increased, signifying neurodegeneration of these structures in HD. PMID:23525910

  14. Chlorine isotope fractionation in the stratosphere.

    PubMed

    Laube, J C; Kaiser, J; Sturges, W T; Bönisch, H; Engel, A

    2010-09-03

    Chlorinated organic compounds are important contributors to the anthropogenic enhancement of stratospheric ozone depletion. We report measurements of stratospheric isotope fractionation in such a compound. Stratospheric and tropospheric difluorodichloromethane (CF2Cl2) were found to have the largest relative 37Cl/35Cl isotope ratio difference ever measured for a natural compound. The increase of the relative isotope ratio difference with altitude was tightly correlated to the corresponding decrease in the CF2Cl2 mixing ratio. The observed relationship has a high potential to provide new insights into atmospheric chemistry and transport processes.

  15. Fractional field equations for highly improbable events

    NASA Astrophysics Data System (ADS)

    Kleinert, H.

    2013-06-01

    Free and weakly interacting particles perform approximately Gaussian random walks with collisions. They follow a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. By contrast, the fields of strongly interacting particles extremize more involved effective actions obeying fractional wave equations with anomalous dimensions. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies.

  16. Hydrolysis and fractionation of lignocellulosic biomass

    DOEpatents

    Torget, Robert W.; Padukone, Nandan; Hatzis, Christos; Wyman, Charles E.

    2000-01-01

    A multi-function process is described for the hydrolysis and fractionation of lignocellulosic biomass to separate hemicellulosic sugars from other biomass components such as extractives and proteins; a portion of the solubilized lignin; cellulose; glucose derived from cellulose; and insoluble lignin from said biomass comprising one or more of the following: optionally, as function 1, introducing a dilute acid of pH 1.0-5.0 into a continual shrinking bed reactor containing a lignocellulosic biomass material at a temperature of about 94 to about 160.degree. C. for a period of about 10 to about 120 minutes at a volumetric flow rate of about 1 to about 5 reactor volumes to effect solubilization of extractives, lignin, and protein by keeping the solid to liquid ratio constant throughout the solubilization process; as function 2, introducing a dilute acid of pH 1.0-5.0, either as virgin acid or an acidic stream from another function, into a continual shrinking bed reactor containing either fresh biomass or the partially fractionated lignocellulosic biomass material from function 1 at a temperature of about 94-220.degree. C. for a period of about 10 to about 60 minutes at a volumetric flow rate of about 1 to about 5 reactor volumes to effect solubilization of hemicellulosic sugars, semisoluble sugars and other compounds, and amorphous glucans by keeping the solid to liquid ratio constant throughout the solubilization process; as function 3, optionally, introducing a dilute acid of pH 1.0-5.0 either as virgin acid or an acidic stream from another function, into a continual shrinking bed reactor containing the partially fractionated lignocellulosic biomass material from function 2 at a temperature of about 180-280.degree. C. for a period of about 10 to about 60 minutes at a volumetric flow rate of 1 to about 5 reactor volumes to effect solubilization of cellulosic sugars by keeping the solid to liquid ratio constant throughout the solubilization process; and as function 4

  17. Fast finite difference methods for space-fractional diffusion equations with fractional derivative boundary conditions

    NASA Astrophysics Data System (ADS)

    Jia, Jinhong; Wang, Hong

    2015-07-01

    Numerical methods for space-fractional diffusion equations often generate dense or even full stiffness matrices. Traditionally, these methods were solved via Gaussian type direct solvers, which requires O (N3) of computational work per time step and O (N2) of memory to store where N is the number of spatial grid points in the discretization. In this paper we develop a preconditioned fast Krylov subspace iterative method for the efficient and faithful solution of finite difference methods (both steady-state and time-dependent) space-fractional diffusion equations with fractional derivative boundary conditions in one space dimension. The method requires O (N) of memory and O (Nlog ⁡ N) of operations per iteration. Due to the application of effective preconditioners, significantly reduced numbers of iterations were achieved that further reduces the computational cost of the fast method. Numerical results are presented to show the utility of the method.

  18. Heart failure with preserved ejection fraction

    PubMed Central

    ElGuindy, Ahmed; Yacoub, Magdi H

    2012-01-01

    Abstract Heart failure with preserved ejection fraction (HFpEF) has recently emerged as a major cause of cardiovascular morbidity and mortality. Contrary to initial beliefs, HFpEF is now known to be as common as heart failure with reduced ejection fraction (HFrEF) and carries an unacceptably high mortality rate. With a prevalence that has been steadily rising over the past two decades, it is very likely that HFpEF will represent the dominant heart failure phenotype over the coming few years. The scarcity of trials in this semi-discrete form of heart failure and lack of unified enrolment criteria in the studies conducted to date might have contributed to the current absence of specific therapies. Understanding the epidemiological, pathophysiological and molecular differences (and similarities) between these two forms of heart failure is cornerstone to the development of targeted therapies. Carefully designed studies that adhere to unified diagnostic criteria with the recruitment of appropriate controls and adoption of practical end-points are urgently needed to help identify effective treatment strategies. PMID:25610841

  19. Radio observations of D I and fractionation

    NASA Technical Reports Server (NTRS)

    Heiles, Carl; Mccullough, Peter R.; Glassgold, Alfred E.

    1993-01-01

    We report observations to detect the 327 MHz line of atomic deuterium in the primarily molecular clouds towards Cas A and Sgr A, making appropriate choices of spectral and spatial resolution. Our best results for Cas A, based on 1253 hr of observing with the 85 foot (26 m) Hat Creek telescope and 45 hr with the very large array (VLA), yield an upper limit for the fraction of deuterium in atomic form, D I, of 0.14. We present an approximate analytical analysis of deuterium fractionation in translucent clouds, which shows that gas-phase ion-molecule reactions, assisted by dust and HD line self-shielding, are efficient in converting deuterium to HD. We conclude that little atomic deuterium is present in the molecular clumps in the Cas A clouds and that much higher sensitivity observations would be required to detect 327 MHz line in molecular clouds. We have also attempted to detect the 72 GHz line of DCO(+) toward Cas A. The observed upper limit to the DCO(+)/HCO(+) ratio of approximately 0.03 is not much larger than our theoretical estimate, and the DCO(+) line should be detectable with existing instrumentation, unless the temperature of these clouds is much larger than usually assumed.

  20. Universality in the Fractional Quantum Hall effect

    NASA Astrophysics Data System (ADS)

    Fradkin, Eduardo; Lopez, Ana

    1993-11-01

    In this lectures we review the fermion field theoretic approach to the Fractional Quantum Hall Effect and use it to discuss the origin of its remarkable universality. We discuss the semiclassical expansion around the average field approximation (AFA). We reexamine the AFA and the role of fluctuations. We argue that, order-by-order in the semiclassical expansion, the response functions obey the correct symmetry properties required by Galilean and Gauge Invariance and by the incompressibility of the fluid. In particular, we find that the low-momentum limit of the semiclassical approximation to the response functions is exact and that it saturates the f-sum rule. We discuss the nature of the spectrum of collective excitations of FQHE systems in the low-momentum limit. We applied these results to the problem of the screening of external charges and fluxes by the electron fluid, and obtained asymptotic expressions of the charge and current density profiles, for different types of interactions. The universality of the FQHE is demonstrated by deriving the form of the wave function of the ground state at long distances. We show that the wave functions of the fluid ground states of Fractional Quantum Hall systems, in the thermodynamic limit, are universal at long distances and that they have a generalized Laughlin form. This universality is a consequence of the analytic properties of the equal-time density correlation functions at long distances.

  1. Universality in the Fractional Quantum Hall

    NASA Astrophysics Data System (ADS)

    Fradkin, Eduardo; Lopez, Ana

    In this set of lectures we review the fermion field theoretic approach to the Fractional Quantum Hall Effect and use it to discuss the origin of its remarkable universality. We discuss the semiclassical expansion around the average field approximation (AFA). We reexamine the AFA and the role of fluctuations. We argue that, order-by-order in the semiclassical expansion, the response functions obey the correct symmetry properties required by Galilean and Gauge Invariance and by the incompressibility of the fluid. In particular, we find that the low-momentum limit of the semiclassical approximation to the response functions is exact and that it saturates the f-sum rule. We discuss the nature of the spectrum of collective excitations of FQHE systems in the low-momentum limit. We applied these results to the problem of the screening of external charges and fluxes by the electron fluid, and obtained asymptotic expressions of the charge and current density profiles, for different types of interactions. The universality of the FQHE is demonstrated by deriving the form of the wave function of the ground state at long distances. We show that the wave functions of the fluid ground states of Fractional Quantum Hall systems, in the thermodynamic limit, are universal at long distances and that they have a generalized Laughlin form. This universality is a consequence of the analytic properties of the equaltime density correlation functions at long distances.

  2. TURBULENT DYNAMOS WITH SHEAR AND FRACTIONAL HELICITY

    SciTech Connect

    Kaepylae, Petri J.; Brandenburg, Axel

    2009-07-10

    Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modeled in terms of an {alpha}{omega} dynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the {alpha}-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional helicities of the small and large-scale fields, as predicted by a simple nonlinear mean-field model. As the magnetic Reynolds number (Re{sub M}) based on the wavenumber of the energy-carrying eddies is increased from 1 to 180, the cycle frequency of the large-scale field is found to decrease by a factor of about 6 in cases where the turbulence is fully helical. This is interpreted in terms of the turbulent magnetic diffusivity, which is found to be only weakly dependent on the Re{sub M}.

  3. Monopoles and fractional vortices in chiral superconductors

    PubMed Central

    Volovik, G. E.

    2000-01-01

    I discuss two exotic objects that must be experimentally identified in chiral superfluids and superconductors. These are (i) the vortex with a fractional quantum number (N = 1/2 in chiral superfluids, and N = 1/2 and N = 1/4 in chiral superconductors), which plays the part of the Alice string in relativistic theories and (ii) the hedgehog in the ^l field, which is the counterpart of the Dirac magnetic monopole. These objects of different dimensions are topologically connected. They form the combined object that is called a nexus in relativistic theories. In chiral superconductors, the nexus has magnetic charge emanating radially from the hedgehog, whereas the half-quantum vortices play the part of the Dirac string. Each half-quantum vortex supplies the fractional magnetic flux to the hedgehog, representing 1/4 of the “conventional” Dirac string. I discuss the topological interaction of the superconductor's nexus with the ‘t Hooft–Polyakov magnetic monopole, which can exist in Grand Unified Theories. The monopole and the hedgehog with the same magnetic charge are topologically confined by a piece of the Abrikosov vortex. Such confinement makes the nexus a natural trap for the magnetic monopole. Other properties of half-quantum vortices and monopoles are discussed as well, including fermion zero modes. PMID:10716980

  4. Fractional stereo matching using expectation-maximization.

    PubMed

    Xiong, Wei; Chung, Hin Shun; Jia, Jiaya

    2009-03-01

    In our fractional stereo matching problem, a foreground object with a fractional boundary is blended with a background scene using unknown transparencies. Due to the spatially varying disparities in different layers, one foreground pixel may be blended with different background pixels in stereo images, making the color constancy commonly assumed in traditional stereo matching not hold any more. To tackle this problem, in this paper, we introduce a probabilistic framework constraining the matching of pixel colors, disparities, and alpha values in different layers, and propose an automatic optimization method to solve a Maximizing a Posterior (MAP) problem using Expectation-Maximization (EM), given only a short-baseline stereo input image pair. Our method encodes the effect of background occlusion by layer blending without requiring a special detection process. The alpha computation process in our unified framework can be regarded as a new approach by natural image matting, which handles appropriately the situation when the background color is similar to that of the foreground object. We demonstrate the efficacy of our method by experimenting with challenging stereo images and making comparisons with state-of-the-art methods.

  5. Fractionated Stereotactic Radiotherapy for Facial Nerve Schwannomas

    PubMed Central

    Shi, Wenyin; Jain, Varsha; Kim, Hyun; Champ, Colin; Jain, Gaurav; Farrell, Christopher; Andrews, David W.; Judy, Kevin; Liu, Haisong; Artz, Gregory; Werner-Wasik, Maria; Evans, James J.

    2015-01-01

    Purpose Data on the clinical course of irradiated facial nerve schwannomas (FNS) are lacking. We evaluated fractionated stereotactic radiotherapy (FSRT) for FNS. Methods Eight consecutive patients with FNS treated at our institution between 1998 and 2011 were included. Patients were treated with FSRT to a median dose of 50.4 Gy (range: 46.8–54 Gy) in 1.8 or 2.0 Gy fractions. We report the radiographic response, symptom control, and toxicity associated with FSRT for FNS. Results The median follow-up time was 43 months (range: 10–75 months). All patients presented with symptoms including pain, tinnitus, facial asymmetry, diplopia, and hearing loss. The median tumor volume was 1.57 cc. On the most recent follow-up imaging, five patients were noted to have stable tumor size; three patients had a net reduction in tumor volume. Additionally, six patients had improvement in clinical symptoms, one patient had stable clinical findings, and one patient had worsened House-Brackmann grade due to cystic degeneration. Conclusion FSRT treatment of FNS results in excellent control of growth and symptoms with a small rate of radiation toxicity. Given the importance of maintaining facial nerve function, FSRT could be considered as a primary management modality for enlarging or symptomatic FNS. PMID:26949592

  6. The AGN Luminosity Fraction in Galaxy Mergers

    NASA Astrophysics Data System (ADS)

    Dietrich, Jeremy; Weiner, Aaron; Ashby, Matthew; Martinez-Galarza, Juan Rafael; Smith, Howard Alan

    2017-01-01

    Galaxy mergers are key events in galaxy evolution, generally triggering massive starbursts and AGNs. However, in these chaotic systems, it is not yet known what fraction each of these two mechanisms contributes to the total luminosity. Here we measure and model spectral energy distributions (SEDs) using the Code for Investigating Galaxy Emission (CIGALE) in up to 33 broad bands from the UV to the far-IR for 23 IR-luminous galaxies to estimate the fraction of the bolometric IR luminosity that can be attributed to the AGN. The galaxies are split nearly evenly into two subsamples: late-stage mergers, found in the IRAS Revised Bright Galaxy Sample or Faint Source Catalog, and early-stage mergers found in the Spitzer Interacting Galaxy Sample. We find that the AGN contribution to the total IR luminosity varies greatly from system to system, from 0% up to ~90%, but is substantially greater in the later-stage and brighter mergers. This is consistent with what is known about galaxy evolution and the triggering of AGNs.The SAO REU program is funded in part by the National Science Foundation REU and Department of Defense ASSURE programs under NSF Grant no. 1262851, and by the Smithsonian Institution.

  7. Fractionation of mineral species by electrophoresis

    NASA Technical Reports Server (NTRS)

    Dunning, J. D.; Herren, B. J.; Tipps, R. W.; Snyder, R. S.

    1982-01-01

    The fractionation of fine-grained aggregates into their major components is a problem in many scientific areas including earth and planetary science. Electrophoresis, the transport of electrically charged particles, immersed in a suspension medium, by a direct current field (Bier, 1959), was employed in this study as a means of separating simulated lunar soil into its constituent minerals. In these tests, conducted in a static analytical cylindrical microelectrophoresis apparatus, samples of simulated lunar soil and samples of pure mineral constituents were placed in the chamber; the electrophoretic mobilities of the lunar soil and the individual mineral constituents were measured. In most of the suspension buffers employed separability was indicated, on the basis of differences in mobility, for all the constituent mineral species except ilmenite and pyroxene, which were not efficiently separable in any of the buffers. Although only a few suspension media were employed, the success of this initial study suggests that electrophoresis may be an important mineral fractionation option in fine-grained aggregate processing.

  8. Tunneling current through fractional quantum Hall interferometers

    NASA Astrophysics Data System (ADS)

    Smits, O.; Slingerland, J. K.; Simon, S. H.

    2014-01-01

    We calculate the tunneling current through a Fabry-Pérot interferometer in the fractional quantum Hall regime. Within linear response theory (weak tunneling but arbitrary source-drain voltage), we find a general expression for the current due to tunneling of quasiparticles in terms of Carlson's R function. Our result is valid for fractional quantum Hall states with an edge theory consisting of a charged channel and any number of neutral channels, with possibly different edge velocities and different chiralities. We analyze the case with a single neutral channel in detail, which applies for instance to the edge of the Moore-Read state. In addition, we consider an asymmetric interferometer with different edge lengths between the point contacts on opposite edges, and we study the behavior of the current as a function of varying edge length. Recent experiments attempted to measure the Aharanov-Bohm effect by changing the area inside the interferometer using a plunger gate. Theoretical analyses of these experiments have so far not taken into account the accompanying change in the edge lengths. We show that the tunneling current exhibits multiple oscillations as a function of this edge length, with frequencies proportional to the injected edge current and inversely proportional to the edge velocities. In particular, the edge velocities can be measured by looking at the Fourier spectrum of the edge current. We provide a numerical scheme to calculate and plot the R function, and include sample plots for a variety of edge states with parameter values, which are experimentally relevant.

  9. Chemodestructive fractionation of soil organic matter

    NASA Astrophysics Data System (ADS)

    Popov, A. I.; Rusakov, A. V.

    2016-06-01

    The method of chemodestructive fractionation is suggested to assess the composition of soil organic matter. This method is based on determination of the resilience of soil organic matter components and/or different parts of organic compounds to the impact of oxidizing agents. For this purpose, a series of solutions with similar concentration of the oxidant (K2Cr2O7), but with linearly increasing oxidative capacity was prepared. Chemodestructive fractionation showed that the portion of easily oxidizable (labile) organic matter in humus horizons of different soil types depends on the conditions of soil formation. It was maximal in hydromorphic soils of the taiga zone and minimal in automorphic soils of the dry steppe zone. The portion of easily oxidizable organic matter in arable soils increased with an increase in the rate of organic fertilizers application. The long-lasting agricultural use of soils and burying of the humus horizons within the upper one-meter layer resulted in the decreasing content of easily oxidizable organic matter. It was found that the portion of easily oxidizable organic matter decreases by the mid-summer or fall in comparison with the spring or early summer period.

  10. Process for stabilization of coal liquid fractions

    DOEpatents

    Davies, Geoffrey; El-Toukhy, Ahmed

    1987-01-01

    Coal liquid fractions to be used as fuels are stabilized against gum formation and viscosity increases during storage, permitting the fuel to be burned as is, without further expensive treatments to remove gums or gum-forming materials. Stabilization is accomplished by addition of cyclohexanol or other simple inexpensive secondary and tertiary alcohols, secondary and tertiary amines, and ketones to such coal liquids at levels of 5-25% by weight with respect to the coal liquid being treated. Cyclohexanol is a particularly effective and cost-efficient stabilizer. Other stabilizers are isopropanol, diphenylmethanol, tertiary butanol, dipropylamine, triethylamine, diphenylamine, ethylmethylketone, cyclohexanone, methylphenylketone, and benzophenone. Experimental data indicate that stabilization is achieved by breaking hydrogen bonds between phenols in the coal liquid, thereby preventing or retarding oxidative coupling. In addition, it has been found that coal liquid fractions stabilized according to the invention can be mixed with petroleum-derived liquid fuels to produce mixtures in which gum deposition is prevented or reduced relative to similar mixtures not containing stabilizer.

  11. Roller milling process for fractionation of fenugreek seeds (Trigonella foenumgraecum) and characterization of milled fractions.

    PubMed

    Sakhare, Suresh D; Inamdar, Aashitosh A; Prabhasankar, Pichan

    2015-04-01

    The fenugreek seed is the richest source of soluble and insoluble fiber and also known for its medicinal and functional properties. The major objective of this present study is fractionation of the fenugreek by roller milling method and characterization of roller milled fractions. The effects of moisture conditioning on fenugreek roller milling were studied using standard methods. The results observed were increase in coarse husk from 33.75-42.46 % and decrease in flour yield from 49.52-41.62 % with increase in addition of moisture from 12-20 %. At 16 % conditioning moisture, the yield of coarse husk was 40.87 % with dietary fiber and protein content of 73.4 % and 6.96 % respectively. The yellowness value (b) for the coarse husk (29.68) found to be lowest at 16 % conditioning moisture compared to the other coarse husk samples, showing maximum clean separation. The fiber fractions showed the viscosity of 6,392 cps at 2 % w/v concentration. The flour fraction was higher in protein (41.83 %) and fat (13.22 %) content. Roller milling process of fenugreek was able to produce > 40 % of coarse husk with 73.4 % dietary fiber (25.56 % soluble & 47.84 % insoluble) and > 48 % flour with 41.83 % protein content, where as the whole fenugreek contained 22.5 % protein & 51.25 % dietary fiber. Thus roller milling has proved to be a valuable method for the fractionation of fenugreek to obtain fiber and protein rich fractions.

  12. Fractional angular momentum in cold-atom systems.

    PubMed

    Zhang, Yuhe; Sreejith, G J; Gemelke, N D; Jain, J K

    2014-10-17

    The quantum statistics of bosons or fermions are manifest through the even or odd relative angular momentum of a pair. We show theoretically that, under certain conditions, a pair of certain test particles immersed in a fractional quantum Hall state possesses, effectively, a fractional relative angular momentum, which can be interpreted in terms of fractional braid statistics. We propose that the fractionalization of the angular momentum can be detected directly through the measurement of the pair correlation function in rotating ultracold atomic systems in the fractional quantum Hall regime. Such a measurement will also provide direct evidence for the effective magnetic field resulting from Berry phases arising from attached vortices, and of excitations with a fractional particle number, analogous to the fractional charge of the electron fractional quantum Hall effect.

  13. Fractional Angular Momentum in Cold-Atom Systems

    NASA Astrophysics Data System (ADS)

    Zhang, Yuhe; Sreejith, G. J.; Gemelke, N. D.; Jain, J. K.

    2014-10-01

    The quantum statistics of bosons or fermions are manifest through the even or odd relative angular momentum of a pair. We show theoretically that, under certain conditions, a pair of certain test particles immersed in a fractional quantum Hall state possesses, effectively, a fractional relative angular momentum, which can be interpreted in terms of fractional braid statistics. We propose that the fractionalization of the angular momentum can be detected directly through the measurement of the pair correlation function in rotating ultracold atomic systems in the fractional quantum Hall regime. Such a measurement will also provide direct evidence for the effective magnetic field resulting from Berry phases arising from attached vortices, and of excitations with a fractional particle number, analogous to the fractional charge of the electron fractional quantum Hall effect.

  14. A Convenient Method for Comparison of Efficiency of Fractionating Columns.

    ERIC Educational Resources Information Center

    Higgins, Robert H.

    1990-01-01

    Presented is a method for demonstrating the use of various fractionating columns to resolve mixtures into individual components and to correlate the resolving powers of column packings to their "hold-up" volumes. Fractions were analyzed using refractive indices. (KR)

  15. A Canadian Effort to Address Fractions Teaching and Learning Challenges

    ERIC Educational Resources Information Center

    Yearley, Shelley; Bruce, Catherine D.

    2014-01-01

    Teaching and learning fraction concepts provides challenges in primary schools all over the world. In this article, Shelley Yearley and Catherine Bruce describe a fractions-based research project conducted in Ontario, Canada.

  16. A continued fraction representation for Theodorsen's circulation function

    NASA Technical Reports Server (NTRS)

    Desmarais, R. N.

    1980-01-01

    Theodorsen's circulation function relates lift to downwash in unsteady two dimensional incompressible flow. A continued fraction representation for the circulation function is described. The continued fraction converges and has a particularly simple coefficient pattern.

  17. Fractions We Cannot Ignore: The Nonsymbolic Ratio Congruity Effect.

    PubMed

    Matthews, Percival G; Lewis, Mark R

    2016-10-20

    Although many researchers theorize that primitive numerosity processing abilities may lay the foundation for whole number concepts, other classes of numbers, like fractions, are sometimes assumed to be inaccessible to primitive architectures. This research presents evidence that the automatic processing of nonsymbolic magnitudes affects processing of symbolic fractions. Participants completed modified Stroop tasks in which they selected the larger of two symbolic fractions while the ratios of the fonts in which the fractions were printed and the overall sizes of the compared fractions were manipulated as irrelevant dimensions. Participants were slower and less accurate when nonsymbolic dimensions of printed fractions were incongruent with the symbolic comparison decision. Results indicated a robust basic sensitivity to nonsymbolic ratios that exceeds prior conceptions about the accessibility of fraction values. Results also indicated a congruity effect for overall fraction size, contrary to findings of prior research. These findings have implications for extending theory about the nature of human number sense and mathematical cognition more generally.

  18. Tank SY-101 void fraction instrument functional design criteria

    SciTech Connect

    McWethy, L.M.

    1994-10-18

    This document presents the functional design criteria for design, analysis, fabrication, testing, and installation of a void fraction instrument for Tank SY-101. This instrument will measure the void fraction in the waste in Tank SY-101 at various elevations.

  19. Fractional-step Tow-Thomas biquad filters

    NASA Astrophysics Data System (ADS)

    Freeborn, Todd J.; Maundy, Brent; Elwakil, Ahmed

    In this paper we propose the use of fractional capacitors in the Tow-Thomas biquad to realize both fractional lowpass and asymmetric bandpass filters of order 0<α1+α2≤2, where α1 and α2 are the orders of the fractional capacitors and 0<α1,2≤1. We show how these filters can be designed using an integer-order transfer function approximation of the fractional capacitors. MATLAB and PSPICE simulations of first order fractional-step low and bandpass filters of order 1.1, 1.5, and 1.9 are given as examples. Experimental results of fractional low pass filters of order 1.5 implemented with silicon-fabricated fractional capacitors verify the operation of the fractional Tow-Thomas biquad.

  20. The dynamics of Soil Organic Carbon fractions defined by alternative fractionation schemes

    NASA Astrophysics Data System (ADS)

    Sohi, Saran; Stack, Philip; Dondini, Marta; McNamara, Niall; Rowe, Rebecca

    2014-05-01

    A change in (1) soil carbon input or (2) rate of stabilisation of new inputs, results in a trajectory for soil organic carbon (SOC) towards a new equilibrium level. The ultimate change in SOC may become statistically significant over decades, but is not easily detected within 1-10 years. Pool-based soil carbon models suggest that larger changes should occur in the distribution of carbon between fractions that differ in turnover rate. These effects may be measurable, indicative of change and potentially diagnostic. Alternative schemes exist for isolating sets of contrasting SOC fractions. In the Ecosystem Land Use Modelling & Soil Carbon GHG Flux Trial (ELUM) project, two schemes have been applied to soils from 20 sites in transitions from pasture and/or arable to different types of short rotation forestry (biomass energy crops). Both schemes target carbon fractions of intermediate stability that should show proportional changes. These fractions should decline with higher decomposition and increase with greater soil inputs. In this work we show the relationship between fractions obtained using "sand plus aggregate protected SOC" (Zimmerman et al., 2007) and "intra-aggregate SOC" (Sohi et al., 2001). The correlation is first made for soils continuing in historical land use at each site, as well as adjacent soils changed to one or more types of forestry. The variable of interest here is the quantitative comparability of the fractions, as well as the effect of site specific factors (notably soil texture and land-use). This is shown as a proportion of SOC as well as amount of SOC. Secondly, we compare the status of the alternate fractions in transition. A different relationship relative to soils at equilibrium could suggest they are characterised by a different reactivity in the soil (turnover rate, mapping to modelled SOC pools), or that they are affected differently by soil texture, initial total SOC, etc. This reveals information on the fractions' likely use as

  1. Modeling some real phenomena by fractional differential equations

    NASA Astrophysics Data System (ADS)

    Almeida, Ricardo; Bastos, Nuno R. O.; Monteiro, M. Teresa T.

    2016-11-01

    This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.

  2. Exp-function method for solving fractional partial differential equations.

    PubMed

    Zheng, Bin

    2013-01-01

    We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

  3. Lord Brouncker's forgotten sequence of continued fractions for pi

    NASA Astrophysics Data System (ADS)

    Osler, Thomas J.

    2010-01-01

    'Lord Brouncker's continued fraction for π' is a well-known result. In this article, we show that Brouncker found not only this one continued fraction, but an entire infinite sequence of related continued fractions for π. These were recorded in the Arithmetica Infinitorum by John Wallis, but appear to have been ignored and forgotten by modern mathematicians. We identify these continued fractions and give a modern derivation.

  4. Random walks models with intermediate fractional diffusion asymptotics

    NASA Astrophysics Data System (ADS)

    Saichev, Alexander I.; Utkin, Sergei G.

    2004-05-01

    Random walk process was investigated with PDF of random time intervals similar to fractional exponential law on small times and to regular exponential law on long times. Generalized fractional Kolmogorov-Feller equation was derived for such kind of process. Asymptotics of its PDF in the long time limit and for intermediate times were found. They obey standard diffusion law or fractional diffusion law respectively. Exact solutions of mentioned equations were numerically calculated, demonstrating crossover of fractional diffusion law into the linear one.

  5. Thermal cracking of heavy fraction of hydrocarbon hydrogenate

    SciTech Connect

    Kreuter, W.; Schliebener, C.; Wernicke, H.J.

    1981-04-07

    To obtain olefins by the thermal cracking of hydrocarbons, E.G., vacuum gas oil, by hydrogenation and subsequent steam cracking, an intermediate fractionation of the hydrogenate is provided so that the light fraction enriched in branched isomers can be used as fuel and the heavy fraction only is subjected to the steam cracking.

  6. 21 CFR 640.90 - Plasma Protein Fraction (Human).

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... 21 Food and Drugs 7 2010-04-01 2010-04-01 false Plasma Protein Fraction (Human). 640.90 Section...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall...

  7. 21 CFR 640.90 - Plasma Protein Fraction (Human).

    Code of Federal Regulations, 2011 CFR

    2011-04-01

    ... 21 Food and Drugs 7 2011-04-01 2010-04-01 true Plasma Protein Fraction (Human). 640.90 Section 640...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall...

  8. 21 CFR 640.90 - Plasma Protein Fraction (Human).

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ... 21 Food and Drugs 7 2012-04-01 2012-04-01 false Plasma Protein Fraction (Human). 640.90 Section...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall...

  9. 21 CFR 640.90 - Plasma Protein Fraction (Human).

    Code of Federal Regulations, 2013 CFR

    2013-04-01

    ... 21 Food and Drugs 7 2013-04-01 2013-04-01 false Plasma Protein Fraction (Human). 640.90 Section...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall...

  10. 21 CFR 640.90 - Plasma Protein Fraction (Human).

    Code of Federal Regulations, 2014 CFR

    2014-04-01

    ... 21 Food and Drugs 7 2014-04-01 2014-04-01 false Plasma Protein Fraction (Human). 640.90 Section...) BIOLOGICS ADDITIONAL STANDARDS FOR HUMAN BLOOD AND BLOOD PRODUCTS Plasma Protein Fraction (Human) § 640.90 Plasma Protein Fraction (Human). (a) Proper name and definition. The proper name of the product shall...

  11. Conceptualization of Fractions and Categorization of Problems for Adolescents

    ERIC Educational Resources Information Center

    Charron, Camilo

    2002-01-01

    165 students, from the fifth, seventh and ninth grades were asked to solve written problems involving fractions. In the problems a reference quantity (RQ) was multiplied by a fraction (FR), yielding the value of a compared quantity (CQ). The fraction expressed either an part-whole ratio (PW), or a part-part ratio (PP). Six type of problems were…

  12. Improvement of dry fractionation ethanol fermentation by partial germ supplementation

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Ethanol fermentation of dry fractionated grits (corn endosperm pieces) containing different levels of germ was studied using the dry grind process. Partial removal of germ fraction allows for marketing the germ fraction and potentially more efficient fermentation. Grits obtained from a dry milling p...

  13. Fraction Development in Children: Importance of Building Numerical Magnitude Understanding

    ERIC Educational Resources Information Center

    Jordan, Nancy C.; Carrique, Jessica; Hansen, Nicole; Resnick, Ilyse

    2016-01-01

    This chapter situates fraction learning within the integrated theory of numerical development. We argue that the understanding of numerical magnitudes for whole numbers as well as for fractions is critical to fraction learning in particular and mathematics achievement more generally. Results from the Delaware Longitudinal Study, which examined…

  14. Developing Children's Understanding of Fractions: An Intervention Study

    ERIC Educational Resources Information Center

    Gabriel, Florence; Coche, Frederic; Szucs, Denes; Carette, Vincent; Rey, Bernard; Content, Alain

    2012-01-01

    Fractions constitute a stumbling block in mathematics education. To improve children's understanding of fractions, we designed an intervention based on learning-by-doing activities, which focused on the representation of the magnitude of fractions. Participants were 292 Grade 4 and 5 children. Half of the classes received experimental instruction,…

  15. Developing Understanding of Fractions through Pattern: Blocks and Fair Trade

    ERIC Educational Resources Information Center

    Roddick, Cheryl; Silvas-Centeno, Christina

    2007-01-01

    This article describes the process of design and implementation of a hands-on unit on fractions in the sixth grade. The fraction unit, taught by a classroom teacher with the aid of a university professor, uses pattern blocks to help students develop conceptual understanding of fractions. Student misunderstandings and outcomes are presented, as…

  16. Measuring Fraction Comparison Strategies with Eye-Tracking

    ERIC Educational Resources Information Center

    Obersteiner, Andreas; Tumpek, Christine

    2016-01-01

    Research suggests that people use a variety of strategies for comparing the numerical values of two fractions. They use holistic strategies that rely on the fraction magnitudes, componential strategies that rely on the fraction numerators or denominators, or a combination of both. We investigated how mathematically skilled adults adapt their…

  17. 7 CFR 718.5 - Rule of fractions.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 7 2010-01-01 2010-01-01 false Rule of fractions. 718.5 Section 718.5 Agriculture Regulations of the Department of Agriculture (Continued) FARM SERVICE AGENCY, DEPARTMENT OF AGRICULTURE FARM... General Provisions § 718.5 Rule of fractions. (a) Fractions shall be rounded after completion of...

  18. 38 CFR 3.112 - Fractions of one cent.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Fractions of one cent. 3... Pension, Compensation, and Dependency and Indemnity Compensation Administrative § 3.112 Fractions of one cent. In all cases where the amount to be paid under any award involves a fraction of a cent,...

  19. 7 CFR 1405.2 - Basic rule of fractions.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 10 2010-01-01 2010-01-01 false Basic rule of fractions. 1405.2 Section 1405.2 Agriculture Regulations of the Department of Agriculture (Continued) COMMODITY CREDIT CORPORATION, DEPARTMENT... rule of fractions. Fractions shall be rounded in accordance with the provisions of 7 CFR part 718....

  20. 19 CFR 159.3 - Rounding of fractions.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... 19 Customs Duties 2 2010-04-01 2010-04-01 false Rounding of fractions. 159.3 Section 159.3 Customs... (CONTINUED) LIQUIDATION OF DUTIES General Provisions § 159.3 Rounding of fractions. (a) Value. In the... cents or more, the lower fractions shall be dropped, and if it is necessary to take up as whole...