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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. Firing recoilless weapons from enclosures.

    PubMed

    Price, G R

    1991-01-01

    Recoilless weapons commonly release a great deal of energy rearward in the immediate vicinity of the crew. If such weapons are fired from within structures, there is concern that in addition to the acoustic hazard to the ear or other organs, there might be hazard associated with flying debris or even structural collapse. Two studies were conducted to evaluate such hazards by remotely firing a total of 24 rounds from the 90 mm recoilless rifle, LAW, TOW, and DRAGON weapons systems from within enclosures (Price, 1978; Shank & Garinther, 1975). The structures, selected from available buildings, were made of various materials (reinforced concrete, masonry, sandbags, and wood) and ranged in volume from 14m3 to 161 m3 with venting areas from 2.9 m2 to 11 m2. Data included pressure histories, motion pictures of the structures and small objects placed in the room, and physiological data from 32 goats (tissue/organ system damage) and 8 cats (hearing loss measures). At the firer's locations, peak pressures ranged from 178 to 189 dB and B-durations ranged from 28 to 376 msec. Although the firings commonly produced some structural damage, none of the firings caused structural collapse or induced tissue damage to nonauditory organs. Ear drum rupture did occur in 5 goats and the cat ears exposed with no hearing protection did show permanent hearing losses. Of the cat ears exposed with hearing protection (EAR plugs), only one showed a permanent loss.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. Theory of Moessbauer line broadening due to diffusion

    SciTech Connect

    Schroeder, K.; Wolf, D.; Dederichs, P.H.

    1981-12-01

    We have calculated the line broadening of the Moessbauer line due to diffusion of Moessbauer atoms via single vacanices. We take into account the perturbation of vacancy jumps in the neighbourhood of an impurity Moessbauer atom (e.g. Fe in Al) using the 5-frequency model. The anisotropy of the line width is given by the Fourier transform of the final distribution of a Moessbauer atom after an encounter with a vacancy. This distribution is calculated by Monte Carlo computer simulation. 3 figures, 1 tables.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Moessbauer assessment of cation disorder in columbite-tantalite minerals

    SciTech Connect

    Augsburger, M.S.; Pedregosa, J.C.; Sosa, G.M.; Mercader, R.C.

    1999-03-01

    The authors have used X-ray diffraction and Moessbauer spectroscopy to investigate the cationic disorder between crystallographic sites of a columbite-tantalite series of pegmatites. The X-ray results show that the pegmatites have different degrees of crystallographic disorder according to the quarries where the samples come from. Moessbauer spectra allow us to distinguish two Fe{sup 2+} different sites. A simple model assuming equal f-factors and occupation probabilities both for Fe and Mn has been used to turn the relative populations for Fe yielded by Moessbauer spectroscopy into effective site occupancy of the 2+ ions. A well-known empirical formula applied to X-ray results to obtain cationic disorder has been found to correlate within experimental errors with the percentage of cationic ordering obtained by Moessbauer spectroscopy.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. (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.

  5. SEM, optical, and Moessbauer studies of submicrometer chromite in Allende

    NASA Technical Reports Server (NTRS)

    Housley, R. M.

    1982-01-01

    New scanning electron and optical microscope results are presented showing that sub-micrometer chromite is abundant along healed cracks and grain boundaries in Allende chondrule olivine. Some wider healed cracks also contain pentlandite and euhedral Ni3Fe grains. Also reported are Moessbauer measurements on Allende HF-HCl residues confirming a high Fe(+++)/Fe(++) ratio.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. Design of the MsAa-4 Moessbauer Spectrometer

    SciTech Connect

    Blachowski, A.; Ruebenbauer, K.; Zukrowski, J.; Gornicki, R.

    2008-10-28

    An entirely new Moessbauer spectrometer MsAa-4 is currently being under design and construction. New features as compared to the basic features of the previous generation MsAa-3 spectrometer could be summarized as follows. Completely digital processing of the {gamma}-ray detector signal beyond the Gaussian shape filter/amplifier is to be implemented. The spectrometer is going to be able to accommodate external multiple detector heads. Up to 128 {gamma}-ray spectra in 16384 channels of 32-bit each and up to 512 Moessbauer spectra in 4096 channels of 32-bit each could be collected simultaneously, provided the proper external multiple detector head is used. The count-rate per single detector is limited to about 10{sup 5} counts per second in total. Improved precision of the reference function from 12-bit to 16-bit is to be provided. The reference function is stored in 8192 channels per a complete cycle. Addition of the random noise to the reference corner prism of the Michelson-Morley calibration interferometer is to be introduced to avoid spurious fringes due to the phase lock-up. An integrated universal temperature controller being able to use a variety of the temperature sensors is to be interconnected properly with the spectrometer. The spectrometer is now a stand-alone network device as it is equipped with the Ethernet connection to the outside world. Fast and high precision digital oscilloscope is to be incorporated to the spectrometer as the intrinsic unit. This oscilloscope could monitor signals at various crucial points of the internal spectrometer electronics. Modular design and use of the strict standards allows easy reconfiguration for other applications than Moessbauer spectroscopy.

  13. Moessbauer Study of Sphero-Conical Vessels from Bolgar

    NASA Astrophysics Data System (ADS)

    Ivanova, A. G.; Nuretdinova, A. R.; Pyataev, A. V.; Valiulina, S. I.; Voronina, E. V.

    2017-05-01

    Samples of sphero-conical vessels found in mass quantities in the ancient settlement Bolgar were analyzed by Moessbauer spectroscopy. Wares with relatively low annealing temperatures <500°C and having a ratio Fepar/Fe2+ ≤ 1.11 in transmission spectra were differentiated from those with high ones. The detected value of {Fe}_{par}^{3+} /Fe2+ was considerably less than the value of 2.69 that was characteristic of raw materials for pottery production in the vicinity of the selected settlement. This indicated that other non-local sources of raw materials existed in the medieval handicraft center.

  14. Moessbauer Spectroscopy of Soils and Rocks at Gusev Crater and Meridiani Planum

    NASA Technical Reports Server (NTRS)

    Klingelhoefer, G.; Morris, R. V.; Bernhardt, B.; Schroeder, C.; Rodionov, D.; deSouza, P. A., Jr.; Yen, A.; Renz, F.; Wdowiak, T.; Squyres, S.

    2004-01-01

    For the first time in history a Moessbauer spectrometer was placed on the surface of another planet. The miniaturized Moessbauer spectrometer MIMOS II is part of the Athena payload of NASA's twin Mars Exploration Rovers (MER) Spirit,and Opportunity. It determines the Fe-bearing mineralogy of Martian soils and rocks at the Rovers respective landing sites, Gusev crater and Meridiani Planum. First results of soil and rock measurements at both landing sites confirm a generally basaltic composition of Martian surface materials.

  15. 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.

  16. 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.

  17. 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.

  18. 57Fe Moessbauer Study of Localization and Valence Sate of Iron Ions in Granular Nanocomposites (FeCoZr)x(Al2O3)100-x for Spintronic Applications

    SciTech Connect

    Saad, Anis; Fedotova, Julia; Kalinin, Jurii; Sitnikov, Alexander; Fedotov, Alexander; Rudov, Denis

    2005-04-26

    The influence of composition of the composite films, containing distributed fragmented components of amorphous metallic alloy CoFeZr and amorphous alumina with particles dimensions of 6-10 nm, on the Moessbauer spectra and hyperfine parameters was investigated. Moessbauer spectroscopy of the (Co0.45Fe0.45Zr0.10)X(Al2O3)1-X studied films with 30 at. % < X < 65 at. % has revealed that the structure of Fe ions coexisted in two valence states -- Fe2+ and Fe3+, the pronounced tendency for increasing Fe3+ fraction with the X increment, disappearance of the singlet connected with the Fe -- containing nanoparticles for the samples with X > 55 %, and lack of the ferromagnetic state in the metallic nanoparticles.

  19. 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

  20. Moessbauer Study of Electrodeposited Fe/Fe-Oxide Multilayers

    SciTech Connect

    Kuzmann, E.; Homonnay, Z.; Klencsar, Z.; Vertes, A.; Lakatos-Varsanyi, M.; Miko, A.; Varga, L.K.; Kalman, E.; Nagy, F.

    2005-04-26

    Iron has been deposited electrochemically by short current pulses in Na-saccharin containing FeII-chloride and sulphate solution electrolytes. Combined electrochemical techniques with initial pulse plating of iron nanolayer and its subsequent anodic oxidation under potential control have been used for production of Fe/Fe-oxide multilayers. 57Fe CEM spectra of pulse plated iron revealed the presence of a minor doublet attributed mainly to {gamma}-FeOOH in addition to the dominant sextet of {alpha}-iron. In the case of anodically oxidized pulse plated iron and of samples after repeated deposition of anodically oxidized pulse plated iron an additional minor doublet, assigned to ferrous chloride, also appears in the Moessbauer spectra. A significant change in the magnetic anisotropy of {alpha}-iron was observed with the anodic oxidation. The thickness of the layers were estimated from the CEM spectrum data by a modified computer program of the Liljequist method. The coercive field and the power loss versus frequency data showed that the pulse plated iron cores are good inductive elements up to several kHz frequencies.

  1. Moessbauer-Fresnel zone plate as nuclear monochromator

    SciTech Connect

    Mooney, T.M.; Alp, E.E.; Yun, W.B.

    1992-06-01

    Zone plates currently used in x-ray optics derive their focusing power from (a spatial variation of) the electronic refractive index -- that is, from the collective effect of electronic x-ray-scattering amplitudes. Nuclei also scatter x rays, and resonant nuclear-scattering amplitudes, particularly those associated with Moessbauer fluorescence, can dominate the refractive index for x-rays whose energies are very near the nuclear-resonance energy. A zone plate whose Fresnel zones are filled alternately with {sup 57}Fe and {sup 56}Fe ({sup 57}Fe has a nuclear resonance of natural width {Gamma} = 4.8 nano-eV at 14.413 keV; {sup 56}Fe has no such resonance) has a resonant focusing efficiency; it focuses only those x-rays whose energies are within several {Gamma} of resonance. When followed by an absorbing screen with a small pinhole, such a zone plate can function as a synchrotron-radiation monochromator with an energy resolution of a few parts in 10{sup 12}. The energy-dependent focusing efficiency and the resulting time-dependent response of a resonant zone plate are discussed.

  2. 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.

  3. Moessbauer studies of rare earth-iron hydrides, carbides, and nitrides

    SciTech Connect

    Ryan, D.H.; Chen, X.; Altounian, Z. )

    1993-04-01

    The basic principles of Moessbauer spectroscopy are introduced in the context of magnetically ordered alloys. A description of fitting procedures is presented, emphasizing the use of information derived from other techniques and indicating reliability limits. Ways in which the local structural and magnetic information obtained from Moessbauer spectroscopy can be used to probe the effects of hydrogen, carbon, and nitrogen additions in R2Fe17 alloys are presented, as well as how to distinguish local and global changes. Even apparently large-scale effects, such as change in the magnetic easy direction, are shown to have clear local signatures. A new hybrid carbonitride of the 2-17 alloy series is introduced, which combines superior magnetic properties with enhanced thermal stability. The coherent two-phase structure of this material, revealed by Moessbauer spectroscopy, is used to emphasize the different information obtained from local and bulk measurements.

  4. Moessbauer effect measurement in single crystal iron subjected to cyclic stress

    NASA Technical Reports Server (NTRS)

    Singh, J. J.

    1976-01-01

    Backscattered Moessbauer spectra were recorded at different fatigue levels in cyclically fatigued high-purity single-crystal iron specimens in the form of rectangular strips with appropriate concentrators in the midplane. The Moessbauer spectra were submitted to a least-squares analysis to determine the isomer shift, quadrupole shift, hyperfine field, and peak spectral widths in each spectrum. It is shown that the quadrupole shift and the isomer shift changed little with fatigue, whereas the effective internal field and the associate line widths exhibit significant variation as a function of fatigue level. It is concluded that the impurity concentration builds up slowly with increasing fatigue level in the region of stress concentration. Since there is a direct correlation between crack initiation and defect concentration level, it is expected that Moessbauer measurements in the test specimen can provide a means of monitoring the impurity buildup presumed to be the eventual cause of fatigue crack initiation and failure.

  5. 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.

  6. 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.

  7. Thermal Transformations of Iron Cations in the System Metal-Vitreous Enamel Coat. Moessbauer Spectroscopic Study

    SciTech Connect

    Barcova, K.; Mashlan, M.; Zboril, R.; Hrabovska, K.

    2005-04-26

    Vitreous enameling on steel is carried out to provide a protective layer against chemical corrosion from the surrounding environment. The glass bonds with the steel to form a composite material. The Moessbauer spectroscopy was firstly applied to study the vitreous enameling in which the complex of processes, as diffusion of species, adhesion between the glass and the steel, galvanic reactions, plays an important role. The Moessbauer spectroscopy provides unique information about the Fe-phase structure of the vitreous enamel layer and that of the steel-enamel interface. Diffusion of iron from steel surface towards enamel layer and formation of a new Fe2+ phase was proved.

  8. Moessbauer spectroscopy evidence of a spinodal mechanism for the thermal decomposition of fcc FeCu

    SciTech Connect

    Crespo, P. |; Barro, M.J.; Hernando, A.; Escorial, A.G.; Menendez, N.; Tornero, J.D.; Barandiaran, J.M.

    1998-07-24

    Moessbauer spectroscopy shows the existence of compositional fluctuations, where different Fe environments coexist, during decomposition upon heat treatment of metastable f.c.c. FeCu solid solution. The presence of isolated Fe atoms in the Cu matrix, f.c.c. Fe{sub rich}Cu, f.c.c. FeCu{sub rich} and b.c.c. Fe has been detected in early decomposition stages. At later decomposition stages, low temperature Moessbauer spectroscopy indicates the presence of a broad distribution of Curie temperatures, coexisting with isolated Fe atoms in the Cu matrix, f.c.c. Fe and b.c.c. Fe.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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).

  14. 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.

  15. 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.

  16. 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.

  17. 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

  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. 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)

  20. 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.

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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.}

  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. 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.

  8. 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.

  9. 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

  10. Reflectivity (visible and near IR), Moessbauer, static magnetic, and X ray diffraction properties of aluminum-substituted hematites

    NASA Technical Reports Server (NTRS)

    Morris, Richard V.; Schulze, Darrell G.; Lauer, Howard V., Jr.; Agresti, David G.; Shelfer, Tad D.

    1992-01-01

    The effect of substituting iron by aluminum in polymorphs of Fe2O3 and FeOOH on their reflectivity characteristics was investigated by comparing data on visible and NIR reflectivities and on static magnetic, XRD, and Moessbauer properties for a family of aluminum-substituted hematites alpha-(Fe,Al)2O3, with compositions where the values of the Al/(Al+Fe) ratio were up to 0.61. Samples were prepared by oxidation of magnetite, dehydroxylation of goethite, and direct precipitation. The analytical methods used for obtaining diffuse reflectivity spectra (350-2200 nm), Moessbauer spectra, and static magnetic data are those described by Morris et al. (1989).

  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. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Moessbauer studies of exchange-coupled two-iron centers in proteins

    SciTech Connect

    Sage, J.T.

    1986-01-01

    This study reports Moessbauer measurements on three derivatives of the oxygen-transport protein hemerythrin and on the oxidized and reduced forms of uteroferrin, a purple acid phosphatase isolated from porcine uterine fluid. Both proteins contain an exchange-coupled pair of iron atoms coordinated directly to amino acid side chains. A model that takes account of both the exchange coupling and the zero-field splitting at each site is presented and used to describe the magnetic properties of the ground spin multiplet of a pair of coupled spins. One notable feature of the model is the fact that the g- and A-tensors of the coupled system may be quite anisotropic even if the corresponding single-site tensors are not. Preliminary studies of some non-Kramers systems are also presented. The Moessbauer spectrum of an azide derivative of deoxyhemerythrin broadens in a small applied field, indicating the presence of a near degeneracy. The spectrum of oxidized uteroferrin broadens as the temperature is raised, even in the absence of an applied field. No fully adequate explanation for the latter observation is apparent.

  19. 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.

  20. 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.

  1. 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.

  2. Gamma scattering in condensed matter with high intensity Moessbauer radiation. Final technical progress report, January 16, 1993--January 15, 1996

    SciTech Connect

    1997-06-01

    Progress is reported on work with high intensity radiation. Moessbauer radioisotopes of exceptional high intensity have been the source of photons for most experiments. Topics include lattice dynamics, studies of glass forming liquids, and line-shape and it`s role in finding materials and nuclear parameters.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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}.

  9. 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.

  10. 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.

  11. 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].

  12. 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.

  13. 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

  14. 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.

  15. Moessbauer spectra as a 'fingerprint' in tin-lithium compounds: Applications to Li-ion batteries

    SciTech Connect

    Robert, F. Lippens, P.E.; Olivier-Fourcade, J.; Jumas, J.-C.; Gillot, F.; Morcrette, M.; Tarascon, J.-M.

    2007-01-15

    Several Li-Sn crystalline phases, i.e. Li{sub 2}Sn{sub 5}, LiSn, Li{sub 7}Sn{sub 3}, Li{sub 5}Sn{sub 2}, Li{sub 13}Sn{sub 5}, Li{sub 7}Sn{sub 2} and Li{sub 22}Sn{sub 5} were prepared by ball-milling and characterized by X-ray powder diffraction and {sup 119}Sn Moessbauer spectroscopy. The analysis of the Moessbauer hyperfine parameters, i.e. isomer shift ({delta}) and quadrupole splitting ({delta}), made it possible to define two types of Li-Sn compounds: the Sn-richest compounds (Li{sub 2}Sn{sub 5}, LiSn) and the Li-richest compounds (Li{sub 7}Sn{sub 3}, Li{sub 5}Sn{sub 2}, Li{sub 13}Sn{sub 5}, Li{sub 7}Sn{sub 2}, Li{sub 22}Sn{sub 5}). The isomer shift values ranged from 2.56 to 2.38 mm s{sup -1} for Li{sub 2}Sn{sub 5}, LiSn and from 2.07 to 1.83 mm s{sup -1} for Li{sub 7}Sn{sub 3}, Li{sub 5}Sn{sub 2}, Li{sub 13}Sn{sub 5}, Li{sub 7}Sn{sub 2} and Li{sub 22}Sn{sub 5}, respectively. A {delta}-{delta} correlation diagram is introduced in order to identify the different phases observed during the electrochemical process of new Sn-based materials. This approach is illustrated by the identification of the phases obtained at the end of the first discharge of {eta}-Cu{sub 6}Sn{sub 5} and SnB{sub 0.6}P{sub 0.4}O{sub 2.9}. - Graphical abstract: {delta}-{delta} correlation diagram for the different tin sites of the Li-Sn compounds. The symbols denote the different Li-Sn phases and the products obtained at the end of the discharge of {eta}-Cu{sub 6}Sn{sub 5} and SnB{sub 0.6}P{sub 0.4}O{sub 2.9}. The grey and the light-grey areas show Sn-centred polyhedra without and with one Sn first-nearest neighbours, respectively.

  16. Engineering Design Handbook: Recoilless Rifle Weapon Systems.

    DTIC Science & Technology

    1976-01-15

    cannon capable of defeating armor . In early reduced to practice and mounted experimen- 1943, the US Army Chief of Ordnance tally on an airplane (Ref. I...for scrvice use and at the request of the man-portable, infantry-type weapon for de- Army Gruand Forces, the 57 mm rifle was feat of armor ". A program...Rifle and ammunition were never good accuracy at 500 yd and capable of presented for user tests (Ref. 11I). defeating tank armor up to 6 in. thick at a

  17. Safety Evaluation of Cannon and Recoilless Weapons

    DTIC Science & Technology

    1977-07-12

    34. REPORT NUMDER 2. GOVT ACCESSION NO. 3. RIECIPIEIT’S CATALOG NUM TdP-3-2-8051 Ř. TITLE (and Subtia.) T".YPE OF REPORT G Pf.,o1• •l U. S . AMY...TEST AND EVALUA _.---.- ’ P_ E TIONS PROC ’SAFETY .EVALUATION OF FinaL -* .ANON AND .,-OILLESS - APONS, 6. PERFORMING ORG. REPORT NUMBER 7. AUTHOR( s ) ’I...CONTRACT OR GRIANT NUMBER( s ) 9. PERFORMING ORGANIZATION NAME AND AODRESS 10. PROGRAM! ._L-MNT. PROJECT. TASK U. S . ARMY ABERDEEN PROVING GROUND

  18. 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.

  19. Moessbauer study at room temperature of zinc ferrite as sorbent for hot coal gas desulphurization

    SciTech Connect

    Ahmed, M.A.

    2009-07-01

    Abstract: The method of using Moessbauer spectroscopy at room temperature was applied to assign the iron sites in one fresh zinc ferrite sample ZF with (1:1) concentration of their component oxides and calcined at 900C as well as its sulfurization derivatives at 750C in different coal gas of composition 0.5% H{sub 2}S + 0.5% H{sub 2}; 0.5% H{sub 2}S + 10% H{sub 2}; 0.5% H{sub 2}S + 25% H{sub 2}, and 0.5% H{sub 2}S + 10% H{sub 2}O (v). The most important iron phase obtained in the sulfurized samples, was pyrrhotite, Fe1-xS that exhibit three well different ional sextets. From the peak area and the associated magnetic hyperfine fields, the average magnetic field was calculated and indicates lowering in the number of iron vacancies whereas x is close to 0.

  20. 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.

  1. 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.

  2. 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

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

    NASA Astrophysics Data System (ADS)

    Morris, R. V.; Klingelhoefer, G.

    2004-12-01

    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 (~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. Because its structure contains the hydroxide anion, the Moessbauer detection of the hydroxide sulfate jarosite (K,Na)Fe3(SO4)2(OH)6 in outcrops

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. Fractional distillation

    SciTech Connect

    Brand, M. J.; Callejas, R. J.

    1985-10-08

    Process and apparatus are provided for the recovery of low, medium and high boiling components from feed streams containing same wherein reboiler fouling, gumming and the like are minimized, via the control of fractionator reboiler temperatures.

  14. Fractionalize this

    SciTech Connect

    Phillips, Philip

    2010-12-01

    Precisely what are the electrons in a high-temperature superconductor doing before they superconduct? Strong electronic correlations may give rise to composite rather than fractionalized excitations, as is typical in other strongly coupled systems such as quark matter.

  15. Moessbauer spectroscopic study of phase conversions of an iron-containing oxide catalyst for oxidative dehydrogenation of butenes

    SciTech Connect

    Golub'ev, A.V.; Matveev, A.I.; Amirbekov, E.N.; Maksimov, Yu.V.; Suzdalev, I.P.

    1988-06-01

    Moessbauer spectroscopy was used to study the structure of ..gamma..-Al/sub 2/O/sub 3/-supported iron oxide, which is catalytically active in the oxidative dehydrogenation of butenes to divinyl. The phase conversions of the catalyst were investigated after treating it in reducing (butenes) and reaction (butenes + oxygen + water vapor) media and after regeneration in a stream of oxygen. It is shown that the supported phase changes from a structure similar to hematite (..cap alpha..-Fe/sub 2/O/sub 3/) to spinel structure both under the effect of butenes and the reaction mixture. When this happens ion exchange occurs between the spinel and the support, with the formation of partly hydrated complexes of Fe/sup 2 +/ ions in an asymmetric environment of O/sup 2 -/ ions and OH/sup -/ groups of the lattice of the support. These complexes vanish upon reoxidation of the catalyst, and part of the spinel is oxidized to hematite.

  16. 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)

  17. 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.

  18. 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…

  19. 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…

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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].

  6. 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.

  7. 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}.

  8. Moessbauer spectroscopy studies of iron-catalysts used in Fischer-Tropsch (FT) processes. Quarterly technical progress report, January--March, 1994

    SciTech Connect

    Huffman, G.P.; Rao, K.R.P.M.

    1994-12-31

    The objective of this project is to carry out a Moessbauer spectroscopy study of Iron-based catalysts to identify iron phases present and correlate with water gas shift and FT activities. A total of 15 catalysts were evaluated so far. Results are presented on the amounts in each catalyst of the following phases: superparamagnetic phase, hematite ({alpha}-Fe{sub 2}O{sub 3}), magnetite (Fe{sub 3}O{sub 4}), Chi-carbide phase ({chi}-Fe{sub 5}C{sub 2}), and an epsilon-carbide phase ({var_epsilon}-Fe{sub 2.2}C).

  9. 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.

  10. Influence of Ordering Phenomena on the Thermomechanical Processing of High-Si Electrical Steel Studied by Moessbauer Spectroscopy

    SciTech Connect

    Ruiz, Daniel; Ros-Yanez, Tanya; Houbaert, Yvan; Vandenberghe, Robert E.

    2005-04-26

    Fe-Si alloys with Si-contents up to 14 at.%Si (7.6 wt.%Si ) were produced by conventional casting and hot/cold rolled with different conditions of temperatures, pass reductions and cooling rates. The obtained thickness of the final sheet was between 0.5 and 0.7 mm for Si-steel up to 10 at.%Si (5.5 wt.%). Moessbauer spectroscopy was used to characterize the order evolution with the Si-content and the thermomechanical processing of the material. A new fitting program was developed for this purpose due to the known complexity of the Fe-alloys spectra. Results show that there is never complete disorder, i.e. binomial distribution of the atoms, whatever the Si-concentration is. Moreover, a clear tendency towards D03 ordering is observed. The obtained long-range order parameters prove a patent increase of the D03 order above 7 at.%Si (3.6 wt.%) which can be associated to the observed brittleness beyond this Si-amount. Concerning the relationship between order and thermomechanical processing, no big effect was found for low Si-contents (up to 6 at.%Si), while for higher amounts two results are clearly observed: (i) the slower the cooling after the hot rolling is, the higher the order is and (ii) cold deformation removes order in a great way. This agrees with the need of fast cooling after hot rolling in order to increase the cold workability of the Si-steel.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Coordination of Fe, Ga and Ge in high pressure glasses by Moessbauer, Raman and X-ray absorption spectroscopy, and geological implications

    NASA Technical Reports Server (NTRS)

    Fleet, M. E.; Henderson, G. S.; Herzberg, C. T.; Crozier, E. D.; Osborne, M. D.; Scarfe, C. M.

    1984-01-01

    For some time, it has been recognized that the structure of silicate liquids has a great bearing on such magma properties as viscosity, diffusivity, and thermal expansion and on the extrapolation of thermodynamic quantities outside of the experimentally measurable range. In this connection it is vital to know if pressure imposes changes in melt structure similar to the pressure-induced reconstructive transformations in crystals. In the present study on 1 bar and high pressure glasses, an investigation is conducted regarding the coordination of Fe(3+) in Fe silicate glasses by Moessbauer spectroscopy. Raman spectroscopy is employed to explore the coordinations of Ge(4+) in GeO2 glasses and of Ga(3+) in NaGa silicate glasses, while the coordination of Ga(3+) in NaGaSiO4 glasses is studied with the aid of methods of X-ray absorption spectroscopy.

  19. 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.

  20. 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.

  1. 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.

  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. 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

  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. © Hammill Institute on Disabilities 2016.

  5. FRACTIONAL INTEGRATION TOOLBOX.

    PubMed

    Marinov, Toma M; Ramirez, Nelson; Santamaria, Fidel

    2013-09-01

    The problems formulated in the fractional calculus framework often require numerical fractional integration/differentiation of large data sets. Several existing fractional control toolboxes are capable of performing fractional calculus operations, however, none of them can efficiently perform numerical integration on multiple large data sequences. We developed a Fractional Integration Toolbox (FIT), which efficiently performs fractional numerical integration/differentiation of the Riemann-Liouville type on large data sequences. The toolbox allows parallelization and is designed to be deployed on both CPU and GPU platforms.

  6. Ordering and oxygen content effects in YBa sub 2 (Cu sub 1 minus x Fe sub x ) sub 3 O sub 7 samples observed by high-temperature Moessbauer spectroscopy

    SciTech Connect

    Saitovitch, E.B.; Scorzelli, R.B.; Azevedo, I.S.; dos Santos, C.A. )

    1990-05-01

    We report here {ital in} {ital situ} high-temperature {sup 57}Fe Moessbauer measurements on YBa{sub 2}(Cu{sub 1{minus}{ital x}}Fe{sub {ital x}}){sub 3}O{sub 7} samples in controlled oxygen atmosphere, in air, or in vacuum. In these conditions, fundamental information can be obtained related to the thermal stability of the different Fe species, as well as the mechanism of oxygen loss.

  7. Meaning of Fractions

    NASA Astrophysics Data System (ADS)

    Dewi, D. A. K.; Suryadi, D.; Suratno, T.; Mulyana, E.; Kurniawan, H.

    2017-02-01

    Introducing fractions is identical to divide an object. Suppose we divide the apple into two parts. One divided into two parts, the question arises whether one part can be called a half or not. Based on this activity, how can students give meaning to fractions. This study aims at designing a different fractions lesson by applying Didactical Design Research. In doing so, we undertook several research phases: 1) thinking what is fractions and why students should learn this concept; 2) designing didactical situation based on identified learning obstacles; and 3) reflecting retrospectively on the lesson design and its implementation as to redesign the fractions lesson. Our analysis revealed that most students held epistemological obstacles in giving meaning of fractions because they only know fractions as numbers that have numerator and denominator. By positioning ourselves as students, we discuss the ideal design to help students in constructing the meaning of fractions.

  8. 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)

  9. Unfolding Fraction Multiplication

    ERIC Educational Resources Information Center

    Wyberg, Terry; Whitney, Stephanie R.; Cramer, Kathleen A.; Monson, Debra S.; Leavitt, Seth

    2011-01-01

    Students often have difficulty understanding fractions, in general, and understanding how to multiply fractions, in particular. To move past this potential problem area, students need to develop a deeper understanding of multiplication and connect the ideas to fractions. In this article, the authors share their insights into teaching fraction…

  10. 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)

  11. 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.

  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. 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…

  14. 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.

  15. 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

  16. 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.

  17. 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

  18. Phase evolution in {sup 57}Fe/Al multilayers studied through dc magnetization, conversion electron Moessbauer spectroscopy, and transmission electron microscopy

    SciTech Connect

    Jani, Snehal; Lakshmi, N.; Venugopalan, K.; Sebastian, Varkey; Reddy, V. R.; Gupta, Ajay; Lalla, N. P.

    2008-12-15

    Fe/Al multilayer thin films with an overall atomic concentration ratio of Fe:Al=1:2 have been prepared by ion-beam sputtering. Phase formation and microstructural evolution with thermal annealing have been studied by x-ray reflectivity, cross-sectional transmission electron microscopy, dc magnetization, and conversion electron Moessbauer spectroscopy. These studies show that although the starting composition is Al rich, the intermixing of Fe and Al at the interfaces leads to the formation of a magnetic Fe{sub 3}Al-like region at the interface. Thus, the magnetic contribution in the as-deposited multilayer structure (MLS) is not only from pure Fe but also from an Fe{sub 3}Al-like region formed at the interface. On annealing the MLS, a stable nonmagnetic MLS consisting of intermetallic B2Fe{sub 50}Al{sub 50} separated by thin Al layers is formed. Further annealing only induces better ordering of Fe{sub 50}Al{sub 50} and does not destroy the MLS.

  19. 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…

  20. Paper Folding Fractions

    ERIC Educational Resources Information Center

    Pagni, David

    2007-01-01

    In this article, the author presents a paper folding activity that can be used for teaching fractions. This activity can be used to describe areas of folded polygons in terms of a standard unit of measure. A paper folding fractions worksheet and its corresponding solutions are also presented in this article. (Contains 2 figures.)

  1. The Future of Fractions

    ERIC Educational Resources Information Center

    Usiskin, Zalman P.

    2007-01-01

    In the 1970s, the movement to the metric system (which has still not completely occurred in the United States) and the advent of hand-held calculators led some to speculate that decimal representation of numbers would render fractions obsolete. This provocative proposition stimulated Zalman Usiskin to write "The Future of Fractions" in 1979. He…

  2. 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.

  3. 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…

  4. 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…

  5. (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.

  6. 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…

  7. 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.

  8. 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

  9. Fractionation: past, present, future.

    PubMed

    Saedi, Nazanin; Jalian, H Ray; Petelin, Anthony; Zachary, Christopher

    2012-06-01

    The development of fractional photothermolysis is a milestone in the history of laser technology and cutaneous resurfacing. Based on the concept that skin is treated in a fractional manner, where narrow cylinders of tissue are thermally heated and normal adjacent skin is left unaffected, the fractional devices have shown effectiveness in treating a variety of conditions. Since its development, we are becoming more adept at using optimal parameters to induce near carbon dioxide laser benefits with a much more comfortable postoperative period and fewer complications. The future remains bright for fractionated laser devices and with new devices and wavelengths, the applications of this technology continue to grow. Copyright © 2012 Elsevier Inc. All rights reserved.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. Modern plasma fractionation.

    PubMed

    Burnouf, Thierry

    2007-04-01

    Protein products fractionated from human plasma are an essential class of therapeutics used, often as the only available option, in the prevention, management, and treatment of life-threatening conditions resulting from trauma, congenital deficiencies, immunologic disorders, or infections. Modern plasma product production technology remains largely based on the ethanol fractionation process, but much has evolved in the last few years to improve product purity, to enhance the recovery of immunoglobulin G, and to isolate new plasma proteins, such as alpha1-protease inhibitor, von Willebrand factor, and protein C. Because of the human origin of the starting material and the pooling of 10,000 to 50,000 donations required for industrial processing, the major risk associated to plasma products is the transmission of blood-borne infectious agents. A complete set of measures--and, most particularly, the use of dedicated viral inactivation and removal treatments--has been implemented throughout the production chain of fractionated plasma products over the last 20 years to ensure optimal safety, in particular, and not exclusively, against HIV, hepatitis B virus, and hepatitis C virus. In this review, we summarize the practices of the modern plasma fractionation industry from the collection of the raw plasma material to the industrial manufacture of fractionated products. We describe the quality requirements of plasma for fractionation and the various treatments applied for the inactivation and removal of blood-borne infectious agents and provide examples of methods used for the purification of the various classes of plasma protein therapies. We also highlight aspects of the good manufacturing practices and the regulatory environment that govern the whole chain of production. In a regulated and professional environment, fractionated plasma products manufactured by modern processes are certainly among the lowest-risk therapeutic biological products in use today.

  18. 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)

  19. Fractionator feed section

    SciTech Connect

    Sampath, V.R.; Bachmann, D.E.

    1993-07-27

    A fractionator feed section in a fractionator to which is fed a feed mixture comprising a vapor component and a liquid component and which fractionator comprises a tray above said feed section which passes liquid reflux to said feed section, said feed section comprising: (a) a downwardly extending, elongated first baffle; (b) a downwardly extending, elongated second baffle; (c) a seal pan below said first baffle and said second baffle, said seal pan comprising a seal pan mixture of liquids into which a portion of said first baffle and a portion of said second baffle extend to form a mixing zone; (d) a feed nozzle which introduces said liquid component and said vapor component downward into said mixing zone; and, (e) a trough which introduces said liquid reflux to said mixing zone, wherein said liquid component and said liquid reflux mix to form said seal pan mixture of liquids.

  20. Iterated fractional Tikhonov regularization

    NASA Astrophysics Data System (ADS)

    Bianchi, Davide; Buccini, Alessandro; Donatelli, Marco; Serra-Capizzano, Stefano

    2015-05-01

    Fractional Tikhonov regularization methods have been recently proposed to reduce the oversmoothing property of the Tikhonov regularization in standard form, in order to preserve the details of the approximated solution. Their regularization and convergence properties have been previously investigated showing that they are of optimal order. This paper provides saturation and converse results on their convergence rates. Using the same iterative refinement strategy of iterated Tikhonov regularization, new iterated fractional Tikhonov regularization methods are introduced. We show that these iterated methods are of optimal order and overcome the previous saturation results. Furthermore, nonstationary iterated fractional Tikhonov regularization methods are investigated, establishing their convergence rate under general conditions on the iteration parameters. Numerical results confirm the effectiveness of the proposed regularization iterations.

  1. Fractional generalization of Liouville equations.

    PubMed

    Tarasov, Vasily E

    2004-03-01

    In this paper fractional generalization of Liouville equation is considered. We derive fractional analog of normalization condition for distribution function. Fractional generalization of the Liouville equation for dissipative and Hamiltonian systems was derived from the fractional normalization condition. This condition is considered as a normalization condition for systems in fractional phase space. The interpretation of the fractional space is discussed. Copyright 2004 American Institute of Physics.

  2. 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

  3. 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.

  4. 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.

  5. Videodisc Instruction in Fractions.

    ERIC Educational Resources Information Center

    Carnine, Douglas; And Others

    1987-01-01

    How laser videodisc technology can be used to improve mathematics instruction is described, with note of the development of a videodisc curriculum on mastering fractions. Relevant research is reviewed, as well as how teachers can use the technology. The instructional design is described, and field-testing and revision reported. (MNS)

  6. 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…

  7. Fractional charge search

    SciTech Connect

    Innes, W.; Klein, S.; Perl, M.; Price, J.C.

    1982-06-01

    A device to search for fractional charge in matter is described. The sample is coupled to a low-noise amplifier by a periodically varying capacitor and the resulting signal is synchronously detected. The varying capacitor is constructed as a rapidly spinning wheel. Samples of any material in volumes of up to 0.05 ml may be searched in less than an hour.

  8. 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.

  9. Fractions through Fruit Salad.

    ERIC Educational Resources Information Center

    Lincoln, Lisa

    1987-01-01

    The mathematics concept of fractions was taught to a group of learning disabled, dyslexic, and multiply handicapped students (15-20 years old) by preparing a fruit salad. Enthusiastic student participation and enhanced knowledge illustrated the effectiveness of employing several sensory modes in learning activities. (CB)

  10. 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.

  11. 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)

  12. 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…

  13. 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

  14. Hyperfine Field Properties of Amorphous Iron-Germanium Alloys Through Moessbauer Spectroscopy Down to 0.72 K

    NASA Astrophysics Data System (ADS)

    Hamdeh, Hussein Husni

    Sputtered amorphous samples of FexGel-x; 0.12 < x < 0.72 have been studied by 57Fe Mossbauer spectroscopy over a temperature range from 0.72 K to room temperature. The broadening observed in the Mossbauer spectra lines is analyzed in terms of distributions of hyperfine fields. The isomer shift, the quadrupole splitting ((DELTA) Eq)(,eff) and the magnetic hyperfine field H(,eff) have been determined as functions of x and T. Also the magnetic ordering temperatures Tc have been determined for appropriate Fe concentrations. The critical concentration Xc below which magnetic ordering is absent down to 4.2 K has been found by extrapolating H(,eff)(x) or Tc(x) to zero to be around x = 0.43. The resulting analysis of the isomer shift suggests that the reduction of magnetism is caused mainly by the broadening process of the 3d-band and depends on the volume of the metalliod. The isomer shift data has a maximum around x = 0.55, and it is interpreted in terms of charge transfer, intra-atomic s (--->) d charge conversion and hybridization effects by a model proposed by Miedema and van der Woude. At room temperature the onset of long range magnetic order occurs around x = 0.52. Above Tc the observed ((DELTA) Eq)(,eff) is of order 0.45, whereas the average ((DELTA) Eq)(,eff) is zero below Tc. This indicates the random orientation of the electric field axes with respect to the magnetic hyperfine field. Both values show very slight variation with x and T. H(,eff) and Tc rise sharply with Fe concentration near and above Xc. The data are discussed in terms of localized moment and itinerant electron models. The relation between H(,eff) and the isomer shift has been established, and based on the general-band filling relation the isomer shift attains its maximum value when M(,eff) = m - 0.82n. The magnetic hyperfine field distributions P(H) have been determined as a function of T. They exhibit wide structureless shape and are considered to scale directly with the fraction distribution

  15. 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

  16. Goal Sketches in Fraction Learning

    ERIC Educational Resources Information Center

    Sophian, Catherine; Madrid, Samara

    2003-01-01

    To examine how conceptual knowledge about fraction magnitudes changes as students' learning progresses, 5th and 7th-grade students were asked to solve fraction magnitude problems that entailed finding a fraction between two given fractions and then to evaluate solutions for similar problems that were modeled for them. When the given fractions…

  17. 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.)

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. Fractional statistics from gravitation

    SciTech Connect

    Cho, Y.M. ); Park, D.H. )

    1994-06-15

    We show that the solitons of the SO(3) nonlinear sigma model in 2+1 dimensions, when coupled to gravitation with the gravitational Chern-Simons interaction, become anyons in the absence of the Hopf term. In particular we calculate the fractional statistical factor of the gravitating anyons, and prove that the gravitational Chern-Simons term itself can be interpreted as the Hopf term of the topological current of [Pi][sub 2]([ital S][sup 2]).

  5. 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.

  6. Model Fractional Chern Insulators.

    PubMed

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

    2016-05-27

    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 Z_{k} 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.

  7. [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.

  8. Fractional Langevin equation and Riemann-Liouville fractional derivative.

    PubMed

    Sau Fa, Kwok

    2007-10-01

    In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifies the classical Newtonian force, nonlocal dissipative force, and long-time correlation. We investigate the first two moments, variances and position and velocity correlation functions of this system. We also compare them with the results obtained from the same fractional Langevin equation which uses the Caputo fractional derivative.

  9. Preheating with fractional powers

    NASA Astrophysics Data System (ADS)

    Moghaddam, Hossein Bazrafshan; Brandenberger, Robert

    2016-11-01

    We consider preheating in models in which the potential for the inflaton is given by a fractional power, as is the case in axion monodromy inflation. We assume a standard coupling between the inflaton field and a scalar matter field. We find that in spite of the fact that the oscillation of the inflaton about the field value which minimizes the potential is anharmonic, there is nevertheless a parametric resonance instability, and we determine the Floquet exponent which describes this instability as a function of the parameters of the inflaton potential.

  10. 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.

  11. 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.

  12. 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.

  13. Fractional Lindstedt series

    NASA Astrophysics Data System (ADS)

    Gallavotti, G.; Gentile, G.; Giuliani, A.

    2006-01-01

    The parametric equations of the surfaces on which highly resonant quasiperiodic motions develop (lower-dimensional tori) cannot be analytically continued, in general, in the perturbation parameter ɛ, i.e., they are not analytic functions of ɛ. However rather generally quasiperiodic motions whose frequencies satisfy only one rational relation ("resonances of order 1") admit formal perturbation expansions in terms of a fractional power of ɛ depending on the degeneration of the resonance. We find conditions for this to happen, and in such a case we prove that the formal expansion is convergent after suitable resummation.

  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. Fractional Vorticity Equations

    NASA Astrophysics Data System (ADS)

    Schertzer, D.; Tchguirinskaia, I.; Lovejoy, S.; Tuck, A.

    2012-04-01

    As a result of a thorough discussion (Schertzer et al., Atmos. Chem. Phys., 12, 327-336, 2012 ) of the limitations of the quasi-geostrophic approximation and turbulence, fractional vorticity equations were obtained. This was done with the help of an anisotropic scaling analysis, instead of the classical scale analysis, as done to derive the quasi-geostrophic approximation. This breaks the rotational symmetry of the classical 3D vorticity equations and a priori yields a (2 + Hz)-dimensional turbulence (0 ≤ Hz ≤ 1). This corresponds to a first step in the derivation of a dynamical alternative to the quasi-geostrophic approximation and turbulence. The corresponding precise definition of fractional dimensional turbulence already demonstrates that the classical 2-D and 3-D turbulence are not the main options to understand atmospheric and oceanic dynamics. Although (2 + Hz)-dimensional turbulence (with 0 < Hz < 1) has more common features with 3-D turbulence than with 2-D turbulence, it has nevertheless very distinctive features: its scaling anisotropy is in agreement with the layered pancake structure, which is typical of rotating and stratified turbulence, but not of the classical 3-D turbulence. In this presentation, we further discuss the properties of this set of deterministic-like equations, especially how they can generate a statistical scaling anisotropy, as well as the relevance of the theoretical value Hz = 5/9.

  16. [Ablative and fractional lasers].

    PubMed

    Beylot, C

    2008-02-01

    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. The fractional techniques such as Fraxel are used to treat non-adjacent microzones without ablation of the epidermis. Around 25 p. 100 of the affected region is treated per session without ablation of the epidermis. Each fraction is only mini-invasive and is performed under local anesthesia. Social hindrance is minimal. Nonetheless, the results are inferior to those obtained with ablative lasers, especially regarding deep wrinkles. The treatment is costly and four sessions are usually required to treat the whole affected area. Others regions of the face may also be treated. Encouraging results have been obtained with mélasma.

  17. 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 ...

  18. Positive fractional linear electrical circuits

    NASA Astrophysics Data System (ADS)

    Kaczorek, Tadeusz

    2013-10-01

    The positive fractional linear systems and electrical circuits are addressed. New classes of fractional asymptotically stable and unstable electrical circuits are introduced. The Caputo and Riemann-Liouville definitions of fractional derivatives are used to analysis of the positive electrical circuits composed of resistors, capacitors, coils and voltage (current) sources. The positive fractional electrical and specially unstable different types electrical circuits are analyzed. Some open problems are formulated.

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

    PubMed

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

    2017-10-01

    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.

  20. The Small Wonders of Fractions.

    ERIC Educational Resources Information Center

    May, Lola

    1996-01-01

    Presents five math activities designed to help students understand fractions, keep students motivated, and help them maintain their math skills. The activities are "What's in a Name?""Fractured Words,""Egyptian Fractions,""More Fractured Fractions,""Name the Parts," and "Timely Device."…

  1. 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.

  2. Fractional diffusion on bounded domains

    SciTech Connect

    Defterli, Ozlem; D'Elia, Marta; Du, Qiang; Gunzburger, Max Donald; Lehoucq, Richard B.; Meerschaert, Mark M.

    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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. An improved fractional divider for fractional-N frequency synthesizers

    NASA Astrophysics Data System (ADS)

    Zhang, Wei; Liu, Yang; Zhou, Yongqi

    2009-07-01

    This paper presents an improved fractional divider used in 1.8~2GHz fractional-N frequency synthesizers. A new clock setting for delta-sigma modulator (DSM) is proposed to prevent the potential problems of traditional fractional dividers: the DSM output would be wrongly loaded and the action of DSM circuit may affect the phase-detection of phase-frequency-detector (PFD). Simulation result shows the effectiveness of this improvement.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. Dividing Fractions and Problem Solving

    ERIC Educational Resources Information Center

    Cramer, Kathleen; Monson, Debra; Whitney, Stephanie; Leavitt, Seth; Wyberg, Terry

    2010-01-01

    Fraction division is generally introduced in sixth or seventh grade with this rule: "Invert and multiply." The authors examined current commercial curricula and found that few textbooks use context as a way to build meaning for the division of fractions. When context is used, the connection between the invert-and-multiply rule and the context is…

  3. 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…

  4. 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.

  5. 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.

  6. 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…

  7. Fractionated Spacecraft Architectures Seeding Study

    DTIC Science & Technology

    2006-04-03

    Multi-attribute Trade- Space Exploration The fractionated spacecraft concept is investigated using Multi-attribute Trade- Space Exploration . This method...Spacecraft Payload Bus Subsystems Payload Module Infrastructure Modules To the Fractionated Spacecraft Multi-Attribute Trade- Space Exploration 1...spacecraft (white blocks) and additional hardware (blue blocks). III. CONCEPT ASSESSMENT METHOD 1. Multi-attribute Trade- Space Exploration The

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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

  13. Upgrading petroleum and petroleum fractions

    SciTech Connect

    Ferguson, S.; Reese, D.D.

    1988-06-21

    A method is described for neutralizing the organic naphthenic acids acidity present in petroleum and petroleum fractions to produce a neutralization number less than 1.0 whereby they are rendered suitable as lube oil feed stocks which consists essentially of treating the petroleum and petroleum fractions with a neutralizing amount of monoethanolamine to form an amine salt with the organic acids and then heating the thus-neutralized petroleum and petroleum fractions at a temperature at least about 25/sup 0/F greater than the boiling point of water and for a time sufficient to convert the amine salts to amides.

  14. 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.

  15. Weyl quantization of fractional derivatives

    SciTech Connect

    Tarasov, Vasily E.

    2008-10-15

    The quantum analogs of the derivatives with respect to coordinates q{sub k} and momenta p{sub k} are commutators with operators P{sub k} and Q{sub k}. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for analytic functions. To define a quantum analog of the fractional Liouville derivative, which is defined on the real axis, we can use the representation of the Weyl quantization by the Fourier transformation.

  16. 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.

  17. Fractional Transmission Line with Losses

    NASA Astrophysics Data System (ADS)

    Gómez-Aguilar, José Francisco; Dumitru, Baleanu

    2014-11-01

    In this manuscript, the fractional transmission line with losses is presented. The order of the Caputo derivative is considered as 0 < β ≤ 1 and 0 < γ ≤ 1 for the fractional equation in space and time domain, respectively. Two cases are solved, with fractional spatial and fractional temporal derivatives, and also numerical simulations were carried out, where there are taken both derivatives in simultaneous form. Two parameters σx and σt are introduced and a physical relation between these parameters is reported. Solutions in space and time are given in terms of the Mittag-Leffler functions. The classic cases are recovered when β and γ are equal to 1.

  18. Commercial SNF Accident Release Fractions

    SciTech Connect

    J. Schulz

    2004-11-05

    The purpose of this analysis is to specify and document the total and respirable fractions for radioactive materials that could be potentially released from an accident at the repository involving commercial spent nuclear fuel (SNF) in a dry environment. The total and respirable release fractions are used to support the preclosure licensing basis for the repository. The total release fraction is defined as the fraction of total commercial SNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. Radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses; this subset of the total release fraction is referred to as the respirable release fraction. Accidents may involve waste forms characterized as: (1) bare unconfined intact fuel assemblies, (2) confined intact fuel assemblies, or (3) canistered failed commercial SNF. Confined intact commercial SNF assemblies at the repository are contained in shipping casks, canisters, or waste packages. Four categories of failed commercial SNF are identified: (1) mechanically and cladding-penetration damaged commercial SNF, (2) consolidated/reconstituted assemblies, (3) fuel rods, pieces, and debris, and (4) nonfuel components. It is assumed that failed commercial SNF is placed into waste packages with a mesh screen at each end (CRWMS M&O 1999). In contrast to bare unconfined fuel assemblies, the

  19. Concurrent fractional and equilibrium crystallisation

    NASA Astrophysics Data System (ADS)

    Sha, Lian-Kun

    2012-06-01

    This paper proposes the concept of concurrent fractional and equilibrium crystallisation (CFEC) in a multi-phase magmatic system in light of experimental results on diffusivities of elements and other species in minerals and melts. A group of equations are presented to describe how the concentrations of an element or isotope change in fractionated solid, equilibrated solid, melt, liquid, and gas phases, as well as in magma, as a function of distribution coefficients and mass fractions during the CFEC process. CFEC model is a generalised and unified formulation that is valid, not only for pure fractional crystallisation (FC) and perfect equilibrium crystallisation (EC) singly, as two of its limiting end-member cases, but also for the geologically more important process of concurrent fractional and equilibrium crystallisation. The concept that both fractional and equilibrium crystallisation can operate concurrently in a magmatic system, for a given element, among different minerals, and even within different-sized crystal grains of the very same mineral phase, is of fundamental importance in deepening our current understanding of magmatic differentiation processes. CFEC probably occurs more frequently in the natural world than either pure fractional or perfect equilibrium crystallisation alone, as a result of the interplay of varying diffusivities of elements under diverse physicochemical conditions, different residence time and growth rates of mineral phases in magmas, and varying grain sizes within each phase and among different phases. The marked systematic variations in trace element concentrations in the melts of the Bishop Tuff have long been perplexing and difficult to reconcile with existing models of differentiation. CFEC, which is able to better explain the scatter trends in a systematic way than fractional crystallisation, is considered to be the cause.

  20. {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.

  1. Fractional Charge Definitions and Conditions

    SciTech Connect

    Goldhaber, A.S.

    2004-06-04

    Fractional charge is known through theoretical and experimental discoveries of isolable objects carrying fractions of familiar charge units--electric charge Q, spin S, and the difference of baryon and lepton numbers B-L. With a few simple assumptions all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which medium correlations yield familiar adiabatic, continuous renormalization, or sometimes nonadiabatic, discrete renormalization. Fractional charges may be carried by fundamental particles or fundamental solitons. Either picture works for the simplest fractional-quantum-Hall-effect quasiholes, though the particle description is far more general. The only known fundamental solitons in three or fewer space dimensions d are the kink (d = 1), the vortex (d = 2), and the magnetic monopole (d = 3). Further, for a charge not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional values of B-L for electrically charged elementary particles.

  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. 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.

  7. 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)

  8. Ablative and fractional ablative lasers.

    PubMed

    Brightman, Lori A; Brauer, Jeremy A; Anolik, Robert; Weiss, Elliot; Karen, Julie; Chapas, Anne; Hale, Elizabeth; Bernstein, Leonard; Geronemus, Roy G

    2009-10-01

    The field of nonsurgical laser resurfacing for aesthetic enhancement continues to improve with new research and technological advances. Since its beginnings in the 1980s, the laser-resurfacing industry has produced a multitude of devices employing ablative, nonablative, and fractional ablative technologies. The three approaches largely differ in their method of thermal damage, weighing degrees of efficacy, downtime, and side effect profiles against each other. Nonablative technologies generate some interest, although only for those patient populations seeking mild improvements. Fractional technologies, however, have gained dramatic ground on fully ablative resurfacing. Fractional laser resurfacing, while exhibiting results that fall just short of the ideal outcomes of fully ablative treatments, is an increasingly attractive alternative because of its far more favorable side effect profile, reduced recovery time, and significant clinical outcome.

  9. Type-2 fuzzy fractional derivatives

    NASA Astrophysics Data System (ADS)

    Mazandarani, Mehran; Najariyan, Marzieh

    2014-07-01

    In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann-Liouville and Caputo derivative of order β ɛ (0, 1), and based on type-2 Hukuhara difference and H2-differentiability. The existence and uniqueness of the solutions of type-2 fuzzy fractional differential equations (T2FFDEs) under Caputo type-2 fuzzy fractional derivative and the definition of Laplace transform of type-2 fuzzy number-valued functions are also given. Moreover, the approximate solution to T2FFDE by a Predictor-Evaluate-Corrector-Evaluate (PECE) method is presented. Finally, the approximate solutions of two examples of linear and nonlinear T2FFDEs are obtained using the PECE method, and some cases of T2FFDEs applications in some sciences are presented.

  10. 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

  11. 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.

  12. 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…

  13. 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…

  14. 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.

  15. The Future of Fractional Lasers.

    PubMed

    Paasch, Uwe

    2016-06-01

    Recent insights to the potential of fractional skin treatments have established standard laser procedures to treat aged, sun-damaged skin and scars. On top of this, the concept has been extended to fibrosing conditions, to remove foreign bodies and to treat inflammatory skin diseases. The biggest potential, however, is foreseen with the option of a contact-free temporary opening of the epidermal barrier (TOR, German: gate) to promote new and intensified treatment regimen. To date these concepts are predominantly experimental, although first clinical studies already show a better response rate if actinic keratoses are treated by fractional laser-intensified photodynamic therapy (PDT) in comparison to the conventional PDT. Possible risks may arise due to the fact that fractional laser home devices are at hand. Used in conjunction with topicals of all origins, toxic and allergic reactions may occur. Principles of current fractional laser interventions are presented as facts while visions are given as future indications. Thieme Medical Publishers 333 Seventh Avenue, New York, NY 10001, USA.

  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. 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.

  18. Subcellular fractionation of rough microsomes.

    PubMed

    Sabatini, David D

    2014-09-02

    When eukaryotic cells are homogenized, the rough endoplasmic reticula are converted into small vesicles, called rough microsomes. Strategies for the isolation of rough microsomes are introduced here, as are methods for evaluating the purity and intactness of an isolated rough microsomal fraction. © 2014 Cold Spring Harbor Laboratory Press.

  19. 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.

  20. 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…

  1. 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)

  2. 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,…

  3. 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,…

  4. 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.

  5. 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)

  6. 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

  7. 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.; hide

    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.

  8. 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

  9. The radiosurgery fractionation quandary: single fraction or hypofractionation?

    PubMed

    Kirkpatrick, John P; Soltys, Scott G; Lo, Simon S; Beal, Kathryn; Shrieve, Dennis C; Brown, Paul D

    2017-04-01

    Stereotactic radiosurgery (SRS), typically administered in a single session, is widely employed to safely, efficiently, and effectively treat small intracranial lesions. However, for large lesions or those in close proximity to critical structures, it can be difficult to obtain an acceptable balance of tumor control while avoiding damage to normal tissue when single-fraction SRS is utilized. Treating a lesion in 2 to 5 fractions of SRS (termed "hypofractionated SRS" [HF-SRS]) potentially provides the ability to treat a lesion with a total dose of radiation that provides both adequate tumor control and acceptable toxicity. Indeed, studies of HF-SRS in large brain metastases, vestibular schwannomas, meningiomas, and gliomas suggest that a superior balance of tumor control and toxicity is observed compared with single-fraction SRS. Nonetheless, a great deal of effort remains to understand radiobiologic mechanisms for HF-SRS driving the dose-volume response relationship for tumors and normal tissues and to utilize this fundamental knowledge and the results of clinic studies to optimize HF-SRS. In particular, the application of HF-SRS in the setting of immunomodulatory cancer therapies offers special challenges and opportunities.

  10. Galaxy Cluster Baryon Fractions Revisited

    NASA Astrophysics Data System (ADS)

    Gonzalez, Anthony H.; Sivanandam, Suresh; Zabludoff, Ann I.; Zaritsky, Dennis

    2013-11-01

    We measure the baryons contained in both the stellar and hot-gas components for 12 galaxy clusters and groups at z ~ 0.1 with M = 1-5 × 1014 M ⊙. This paper improves upon our previous work through the addition of XMM-Newton X-ray data, enabling measurements of the total mass and masses of each major baryonic component—intracluster medium, intracluster stars, and stars in galaxies—for each system. We recover a mean relation for the stellar mass versus halo mass, M_{\\star }\\propto M_{500}^{-0.52+/- 0.04}, that is 1σ shallower than in our previous result. We confirm that the partitioning of baryons between the stellar and hot-gas components is a strong function of M 500; the fractions of total mass in stars and X-ray gas within a sphere of radius r 500 scale as f_{\\star }\\propto M_{500}^{-0.45+/- 0.04} and f_{gas}\\propto M_{500}^{0.26+/- 0.03}, respectively. We also confirm that the combination of the brightest cluster galaxy and intracluster stars is an increasingly important contributor to the stellar baryon budget in lower halo masses. Studies that fail to fully account for intracluster stars typically underestimate the normalization of the stellar baryon fraction versus M 500 relation by ~25%. Our derived stellar baryon fractions are also higher, and the trend with halo mass weaker, than those derived from recent halo occupation distribution and abundance matching analyses. One difference from our previous work is the weak, but statistically significant, dependence here of the total baryon fraction upon halo mass: f_{bary}\\propto M_{500}^{0.16+/- 0.04}. For M 500 >~ 2 × 1014, the total baryon fractions within r 500 are on average 18% below the universal value from the seven year Wilkinson Microwave Anisotropy Probe (WMAP) analysis, or 7% below for the cosmological parameters from the Planck analysis. In the latter case, the difference between the universal value and cluster baryon fractions is less than the systematic uncertainties associated with

  11. 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…

  12. 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.

  13. 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…

  14. 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…

  15. 12 CFR 5.67 - Fractional shares.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 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 shares...

  16. STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.

    PubMed

    Meerschaert, Mark M; Sabzikar, Farzad

    2014-07-01

    Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.

  17. 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

  18. 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.

  19. Fractional reaction-diffusion equation

    NASA Astrophysics Data System (ADS)

    Seki, Kazuhiko; Wojcik, Mariusz; Tachiya, M.

    2003-07-01

    A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump motion, interferes with the reaction at the encounter distance. Therefore, the reaction term has a memory effect. The derived equation is applied to the geminate recombination problem. The recombination is shown to depend on the intrinsic reaction rate, in contrast with the results of Sung et al. [J. Chem. Phys. 116, 2338 (2002)], which were obtained from the fractional reaction-diffusion equation where the diffusion term has a memory effect but the reaction term does not. The reactivity dependence of the recombination probability is confirmed by numerical simulations.

  20. Astrophysical Applications of Fractional Calculus

    NASA Astrophysics Data System (ADS)

    Stanislavsky, Aleksander A.

    The paradigm of fractional calculus occupies an important place for the macroscopic description of subdiffusion. Its advance in theoretical astrophysics is expected to be very attractive too. In this report we discuss a recent development of the idea to some astrophysical problems. One of them is connected with a random migration of bright points associated with magnetic fields at the solar photosphere. The transport of the bright points has subdiffusive features that require the fractional generalization of the Leighton's model. Another problem is related to the angular distribution of radio beams, being propagated through a medium with random inhomogeneities. The peculiarity of this medium is that radio beams are trapped because of random wave localization. This idea can be useful for the diagnostics of interplanetary and interstellar turbulent media.

  1. 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

  2. Complexity and the Fractional Calculus

    DTIC Science & Technology

    2013-01-01

    interpreted as a form of phase decor- relation process rather than one with friction. The fractional version of the popular Lotka - Volterra ecological...trajectory is an ordinary Lotka - Volterra cycle in the operational time . Transitioning from the operational time to the chronological time spreads...these trajectories over the entire Lotka - Volterra cycle thereby generating the mistaken impression that the resulting average trajectory reaches

  3. Fractional Trajectories: Decorrelation Versus Friction

    DTIC Science & Technology

    2013-07-27

    between trajectories.Weapply the general theory developed herein to the Lotka – Volterra ecological The views, opinions and/or findings contained in...calculus, is shown to be a manifestation of decorrelations between trajectories.Weapply the general theory developed herein to the Lotka – Volterra ...fractional Lotka – Volterra ecological model. a r t i c l e i n f o Article history: Received 17 April 2013 Received in revised form 21 June 2013

  4. Fractional viscoelastic beam under torsion

    NASA Astrophysics Data System (ADS)

    Colinas-Armijo, N.; Cutrona, S.; Di Paola, M.; Pirrotta, A.

    2017-07-01

    This paper introduces a study on twisted viscoelastic beams, having considered fractional calculus to capture the viscoelastic behaviour. Further another novelty of this paper is extending a recent numerical approach, labelled line elementless method (LEM), to viscoelastic beams. The latter does not require any discretization neither in the domain nor in the boundary. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.

  5. 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.

  6. 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.

  7. Fire effects on silica fractionation

    NASA Astrophysics Data System (ADS)

    Unzué-Belmonte, Dácil; Schaller, Jörg; Vandevenne, Floor; Barao, Lúcia; Struyf, Eric; Meire, Patrick

    2015-04-01

    Fire events are expected to increase due to climate change, both in number and intensity Effects range from changes in soil biogeochemistry up to the whole ecosystem functioning and morphology. While N, P and C cycling have received quite some attention, little attention was paid to fire effects on the biogeochemical Si cycle and the consequences after a fire event. The Si cycle is a globally important biogeochemical cycle, with strong connections to other biogeochemical cycles, including C. Dissolved 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…). Biogenic and other pedogenic secondary Si stocks form an important filter between weathering of mineral silicates and eventual transport of dissolved Si to rivers and the coastal zone. We used a new method to analyze the different reactive fractions of silica in the litter layer of 3 ecosystems after different fire treatments. Using a continuous extraction of Si and Al in 0.5M NaOH at 85°C, biogenic and non-biogenic alkaline reactive Si fractions can be separated based on their Si/Al ratios and their reactivity. We analyzed the silica fractionation after two burning treatments (no heating, 350°C and 550°C) from three types of litter (spruce forest, beech forest and Sphagnum peat). Reactive Si from litter of spruce and beech forest was purely biogenic, based on the observed Si/Al ratio. Beech litter (~2.2 % BSi) had two different biogenic silica pools, one reactive and one more refractory. Spruce litter (~1.5% BSi) showed only one fraction of biogenic Si. There was negligible biogenic Si present in the peat samples (<0.1%). While

  8. 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.

  9. Adaptive fractionation therapy: II. Biological effective dose.

    PubMed

    Chen, Mingli; Lu, Weiguo; Chen, Quan; Ruchala, Kenneth; Olivera, Gustavo

    2008-10-07

    Radiation therapy is fractionized to differentiate the cell killing between the tumor and organ at risk (OAR). Conventionally, fractionation is done by dividing the total dose into equal fraction sizes. However, as the relative positions (configurations) between OAR and the tumor vary from fractions to fractions, intuitively, we want to use a larger fraction size when OAR and the tumor are far apart and a smaller fraction size when OAR and the tumor are close to each other. Adaptive fractionation accounts for variations of configurations between OAR and the tumor. In part I of this series, the adaptation minimizes the OAR (physical) dose and maintains the total tumor (physical) dose. In this work, instead, the adaptation is based on the biological effective dose (BED). Unlike the linear programming approach in part I, we build a fraction size lookup table using mathematical induction. The lookup table essentially describes the fraction size as a function of the remaining tumor BED, the OAR/tumor dose ratio and the remaining number of fractions. The lookup table is calculated by maximizing the expected survival of OAR and preserving the tumor cell kill. Immediately before the treatment of each fraction, the OAR-tumor configuration and thus the dose ratio can be obtained from the daily setup image, and then the fraction size can be determined by the lookup table. Extensive simulations demonstrate the effectiveness of our method compared with the conventional fractionation method.

  10. The Codevelopment of Children's Fraction Arithmetic Skill and Fraction Magnitude Understanding

    ERIC Educational Resources Information Center

    Bailey, Drew H.; Hansen, Nicole; Jordan, Nancy C.

    2017-01-01

    The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

  11. 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.

  12. 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.

  13. 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)

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. Fractional dynamics of complex networks

    NASA Astrophysics Data System (ADS)

    Turalska, Malgorzata; West, Bruce J.

    2014-03-01

    The relation between the behavior of a single element and the global dynamics of its host network is an open problem in the science of complex networks. Typically one attempts to infer the global dynamics by combining the behavior of single elements within the system, following a bottom-up approach. Here we address an inverse problem. We show that for a generic model within the Ising universality class it is possible to construct a description of the dynamics of an individual element, given the information about the network's global behavior. We demonstrate that the individual trajectory response to the collective motion of the network is described by a linear fractional differential equation, whose analytic solution is the Mittag-Leffler function. This solution is obtained through a subordination procedure without the necessity of linearizing the underlying dynamics, that is, the solution retains the influence of the nonlinear network dynamics on the individual. Moreover the solutions to the fractional equation of motion suggest a new direction for designing control mechanisms for complex networks. The implications of this new perspective are explored by introducing a control signal into a small number of network elements and analyzing the subsequent change in the network dynamics.

  20. Skin Characteristics after Fractional Photothermolysis

    PubMed Central

    Oh, Byung Ho; Hwang, Young Ji; Choe, Yong Beom; Ahn, Kyu Joong

    2011-01-01

    Background Fractional photothermolysis makes thousands of minute areas called microthermal treatment zones on the skin surface and transmits thermal injury to facilitate heat shock protein formation around the dermis. Potential side effects include acneiform eruption, herpes simplex virus outbreak, erythema, and post-inflammatory hyperpigmentation. Objective To investigate and compare the changes in the skin of Asian patients after two different fractional photothermolysis systems (FPS) on a split face. Methods A half-split face study was performed with 10,600 nm carbon dioxide FPS on the left and 1,550 nm erbium-doped FPS on the right side of the face. Only one session of laser irradiation and several biophysical measurements were done. Results Although both FPS proved to be effective in treating acne scar and wrinkle patients, a slightly higher satisfaction rating was seen with the 10,600 nm FPS treatment. Both types of FPS showed a significant increase in transepidermal water loss which decreased gradually after treatment and returned to pre-treatment level after 1 week. A decreased reviscometer score was sustained for a longer period in wrinkle areas treated with 10,600 nm FPS. Conclusion Even though the changes in skin varied according to different FPS wave-length, adverse outcomes, such as increased erythema and TEWL were entirely subdued within 3 months of treatment. PMID:22148011

  1. Discrete fractional solutions of the radial equation of the fractional Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Yilmazer, Resat; Ozturk, Okkes

    2017-07-01

    One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus (DFC) has also an important position in the fractional calculus. The nabla operator in DFC is practical for the singular differential equations. In this study, we investigated the radial equation of the fractional Schrödinger equation. The particular solutions of this equation was obtained as discrete fractional forms via ∇-discrete fractional operator out of known methods.

  2. 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 ...

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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)

  8. Fractional Levy motion through path integrals

    SciTech Connect

    Calvo, Ivan; Sanchez, Raul; Carreras, Benjamin A

    2009-01-01

    Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The fractional diffusion equation corresponding to fLm is also obtained.

  9. 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…

  10. 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…

  11. 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…

  12. 12 CFR 5.67 - Fractional shares.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... fractional shares. The bank may: (a) Issue scripts or warrants for trading; (b) Make reasonable arrangements... fair price upon the fraction not being issued through its sale, or the purchase of the additional... such stock is available; or (d) Sell full shares representing all the fractions at public auction, or...

  13. 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…

  14. 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…

  15. On Fractional Duffin-Kemmer-Petiau Equation

    NASA Astrophysics Data System (ADS)

    Bouzid, N.; Merad, M.; Baleanu, D.

    2016-04-01

    In this paper we treat a fractional bosonic, scalar and vectorial, time equation namely Duffin-Kemmer-Petiau Equation. The fractional variational principle was used, the fractional Euler-Lagrange equations were presented. The wave functions were determined and expressed in terms of Mittag-Leffler function.

  16. 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…

  17. 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…

  18. 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…

  19. 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…

  20. 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…

  1. 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…

  2. 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…

  3. 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…

  4. 16 CFR 500.17 - Fractions.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 16 Commercial Practices 1 2011-01-01 2011-01-01 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 contain...

  5. 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…

  6. 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…

  7. 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…

  8. 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...

  9. Subordination pathways to fractional diffusion

    NASA Astrophysics Data System (ADS)

    Gorenflo, R.; Mainardi, F.

    2011-03-01

    The uncoupled Continuous Time Random Walk ( CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: ( rw 1), a random walk along the line of natural time, happening in operational time; ( w 2), a random walk along the line of space, happening in operational time; ( rw 3), the inversion of ( rw 1), namely a random walk along the line of operational time, happening in natural time. Via the general integral equation of CTRW and appropriate rescaling, the transition to the diffusion limit is carried out for each of these three random walks. Combining the limits of ( rw 1) and ( rw 2) we get the method of parametric subordination for generating particle paths, whereas combination of ( rw 2) and ( rw 3) yields the subordination integral for the sojourn probability density in space - time fractional diffusion.

  10. Fractional relaxations in photonic crystals

    NASA Astrophysics Data System (ADS)

    Giraldi, Filippo; Petruccione, Francesco

    2014-10-01

    A quantum dot interacting with the radiation field of a photonic crystal is considered. An analytical description of the dynamics and the coherence between the two states of the quantum dot is provided. Besides the well-known trapping, a fractional nature of the dynamics appears via relaxations of the Mittag-Leffler type. Furthermore, coherence exhibits a transition from the decay {{t}-3/2} to {{t}-1/2} if the transition frequency of the quantum dot is exactly in the middle of the band gap. Similarly, the population of the excited level undergoes a transition from the relaxation 1/{{t}3} to 1/t. These resonances and transitions belong also to the context of matter-wave emissions in optical lattices.

  11. Copolyamino acid fractionation and protobiochemistry

    NASA Technical Reports Server (NTRS)

    Fox, S. W.

    1981-01-01

    Investigation of the origins of living things by the uniquely appropriate method of successive approximation in attempted retracement of steps in molecular evolution has yielded: a comprehensive theoretical flowsheet from archaic inanimate matter to an infrastructured, microscopic, protoreproductive, protometabolic protocell; a laboratory model of the same; and an explanatory assessment of the natural variation component of Darwinian evolution. For each of these, the significance is dependent upon awareness of the intrinsic tendency of amino acids, in mixed sets, to order themselves. Without such awareness, it is believed these vistas would have been delayed for decades. Selfordering would have in turn been difficult to recognize and support were it not for the chromatographic developments in fractionation of copolyamino acids.

  12. Fractional Differential Equations and Multifractality

    NASA Astrophysics Data System (ADS)

    Larcheveque, M.; Schertzer, D. J.; Schertzer, D. J.; Duan, J.; Lovejoy, S.

    2001-12-01

    There has been a mushrooming interest in the linear Fokker-Planck Equation (FPPE) which corresponds to the generating equation of Lévy's anomalous diffusion. We already pointed out some theoretical and empirical limitations of the linear FPPE for various geophysical problems: the medium is in fact considered as homogeneous and the exponent of the power law of the pdf tails should be smaller than 2. We showed that a nonlinear extension based on a nonlinear Langevin equation forced by a Lévy stable motion overcomes these limitations. We show that in order to generate multifractal diffusion, and more generally multifractal fields, we need to furthermore consider fractional time derivatives in the Langevin equation and in FPPE. We compare our approach with the Continuous-Time Random Walk (CTWR) approach.

  13. Fractional-calculus diffusion equation

    PubMed Central

    2010-01-01

    Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

  14. 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

  15. Fractionation: a new era in laser resurfacing.

    PubMed

    Saedi, Nazanin; Petelin, Anthony; Zachary, Christopher

    2011-07-01

    Fractional photothermolysis combines the benefits of fully ablative lasers with significantly reduced downtime and fewer complications. Skin is treated in a fractional manner, with narrow cylinders of tissue being thermally heated and normal adjacent skin left unaffected, and the fractional devices have shown effectiveness in treating a variety of conditions, especially scarring and photodamage. There are many devices that use fractional photothermolysis, and practitioners are becoming more adept at using optimal parameters to induce near CO(2) laser benefits. Fractionated lasers have become the cornerstone of a minimally invasive treatment regimen and have ushered in a new era of laser skin rejuvenation. Copyright © 2011. Published by Elsevier Inc.

  16. 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.

  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. 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.

  19. Hydrologic transport and partitioning of phosphorus fractions

    NASA Astrophysics Data System (ADS)

    Berretta, C.; Sansalone, J.

    2011-06-01

    SummaryPhosphorus (P) in rainfall-runoff partitions between dissolved and particulate matter (PM) bound phases. This study investigates the transport and partitioning of P to PM fractions in runoff from a landscaped and biogenically-loaded carpark in Gainesville, FL (GNV). Additionally, partitioning and concentration results are compared to a similarly-sized concrete-paved source area of a similar rainfall depth frequency distribution in Baton Rouge, LA (BTR), where in contrast vehicular traffic represents the main source of pollutants. Results illustrate that concentrations of P fractions (dissolved, suspended, settleable and sediment) for GNV are one to two orders of magnitude higher than BTR. Despite these differences the dissolved fraction ( f d) and partitioning coefficient ( K d) distributions are similar, illustrating that P is predominantly bound to PM fractions. Examining PM size fractions, specific capacity for P (PSC) indicates that the P concentration order is suspended > settleable > sediment for GNV, similarly to BTR. For GNV the dominant PM mass fraction is sediment (>75 μm), while the mass of P is distributed predominantly between sediment and suspended (<25 μm) fractions since these PM mass fractions dominated the settleable one. With respect to transport of PM and P fractions the predominance of events for both areas is mass-limited first-flush, although each fraction illustrated unique washoff parameters. However, while transport is predominantly mass-limited, the transport of each PM and P fraction is influenced by separate hydrologic parameters.

  20. Control of a fractional distillation process

    SciTech Connect

    Skraba, F.W.; Tuck, L.

    1983-03-22

    In a fractional distillation process in which a heating fluid and waste heat stream are utilized to supply heat to a fractional distillation column and in which the heat supplied from the waste heat stream is not controllable, control of the liquid level in the fractional distillation column is accomplished by manipulating the flow rate of the heating fluid so as to maintain a desired liquid level until such time as the flow rate of the heating fluid becomes zero at which time the flow rate of the external reflux to the fractional distillation column is manipulated to maintain a desired liquid level in the fractional distillation column. A switching of control of the liquid level provides a means by which an uncontrollable heat input may be provided to the fractional distillation column without losing control of the liquid level in the fractional distillation column.

  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. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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

  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. 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.

  10. 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.

  11. 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.…

  12. 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.…

  13. 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.

  14. Thermomechanical Fractional Model of TEMHD Rotational Flow.

    PubMed

    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.

  15. 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.

  16. On the entangled fractional squeezing transformation

    NASA Astrophysics Data System (ADS)

    Fan, Hong-Yi; Chen, Jun-Hua; Zhang, Peng-Fei

    2015-04-01

    We propose an entangled fractional squeezing transformation (EFrST) generated by using two mutually conjugate entangled state representations with the following operator: ; this transformation sharply contrasts the complex fractional Fourier transformation produced by using (see Front. Phys. DOI: 10.1007/s11467-014-0445-x). The EFrST is obtained by converting the triangular functions in the integration kernel of the usual fractional Fourier transformation into hyperbolic functions, i.e., tan α → tanh α and sin α → sinh α. The fractional property of the EFrST can be well described by virtue of the properties of the entangled state representations.

  17. 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.

  18. 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.

  19. 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.

  20. Controllability of Nonlinear Fractional Delay Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Nirmala, R. Joice; Balachandran, K.; Rodríguez-Germa, L.; Trujillo, J. J.

    2016-02-01

    This paper is concerned with controllability of nonlinear fractional delay dynamical systems with delay in state variables. The solution representations of fractional delay differential equations have been established by using the Laplace transform technique and the Mittag-Leffler function. Necessary and sufficient conditions for the controllability criteria of linear fractional delay systems are established. Further sufficient condition for the controllability of nonlinear fractional delay dynamical system are obtained by using the fixed point argument. Examples and numerical simulation are presented to illustrate the results.

  1. 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

  2. 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.

  3. 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.

  4. Synchronization of fractional order complex dynamical networks

    NASA Astrophysics Data System (ADS)

    Wang, Yu; Li, Tianzeng

    2015-06-01

    In this letter the synchronization of complex dynamical networks with fractional order chaotic nodes is studied. A fractional order controller for synchronization of complex network is presented. Some new sufficient synchronization criteria are proposed based on the Lyapunov stability theory and the LaSalle invariance principle. These synchronization criteria can apply to an arbitrary fractional order complex network in which the coupling-configuration matrix and the inner-coupling matrix are not assumed to be symmetric or irreducible. It means that this method is more general and effective. Numerical simulations of two fractional order complex networks demonstrate the universality and the effectiveness of the proposed method.

  5. 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.

  6. 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.

  7. 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

  8. 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

  9. A computer program for Moessbauer data processing

    NASA Technical Reports Server (NTRS)

    Howser, L. M.; Singh, J. J.; Smith, R. E., Jr.

    1972-01-01

    A computer program to analyze Mossbauer data is presented in detail. The least-squares curve fitting techniques described apply to single line spectra, single hyperfine spectra, or when the constituent spectra are separated well enough to let the individual absorption peaks stand alone. The present program is not adapted for complex spectra resulting from the existence of several local environments in the absorber iron alloy. Sample problems are presented to aid the user in setting up and running the program. The program is written in FORTRAN 4 language for the Control Data 6000 series digital computer with the SCOPE 3.0 operating system and requires approximately 115,000 octal locations of core storage. A typical case with one absorption peak runs in 20 seconds, and a typical problem with six absorption peaks requires 50 seconds.

  10. 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.

  11. Moessbauer mineralogy of calcined Murchison meteorite

    NASA Technical Reports Server (NTRS)

    Morris, Richard V.; Zolensky, M. E.; Hiroi, T.; Lipschutz, M. E.

    1994-01-01

    The three Antarctic meteorites B7904, Y82162, and Y86720 are unusual because they have characteristics in common with both CI and CM groups and because they apparently underwent thermal alteration after hydrous alteration on their parent body. They are also spectrally similar (visible and near-IR) to C, G, B, and F asteroids, which may imply that the surface materials on those asteroids may have undergone thermal alteration. Based on the reflectance spectra of samples of Murchison (CM2 carbonaceous chondrite) that were thermally altered in the laboratory (cryopumped and initial 10(exp -5) atm H2), Hiroi et al. concluded that putative thermal alteration occurred at temperatures of 600 to 1000 C. Similar experiments have been done on Murchison and reported mineralogical changes based on data from transmission electron diffraction microscopy, electron diffraction, and analytical electron microscopy. We report here the Mossbauer mineralogy of the same samples of thermally-altered Murchison. Mossbauer mineralogy gives the molar distribution of Fe among its oxidation states and iron-bearing mineralogies.

  12. 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.

  13. 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…

  14. Homotopy analysis method for fractional IVPs

    NASA Astrophysics Data System (ADS)

    Hashim, I.; Abdulaziz, O.; Momani, S.

    2009-03-01

    In this paper, the homotopy analysis method is applied to solve linear and nonlinear fractional initial-value problems (fIVPs). The fractional derivatives are described by Caputo's sense. Exact and/or approximate analytical solutions of the fIVPs are obtained. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.

  15. 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…

  16. 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…

  17. 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.

  18. 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

  19. 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…

  20. 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.

  1. A Computational Model of Fraction Arithmetic

    ERIC Educational Resources Information Center

    Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.

    2017-01-01

    Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

  2. 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…

  3. 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…

  4. 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…

  5. 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)

  6. 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.

  7. Modular polynomial arithmetic in partial fraction decomposition

    NASA Technical Reports Server (NTRS)

    Abdali, S. K.; Caviness, B. F.; Pridor, A.

    1977-01-01

    Algorithms for general partial fraction decomposition are obtained by using modular polynomial arithmetic. An algorithm is presented to compute inverses modulo a power of a polynomial in terms of inverses modulo that polynomial. This algorithm is used to make an improvement in the Kung-Tong partial fraction decomposition algorithm.

  8. 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,…

  9. 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…

  10. 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…

  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: 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…

  13. 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…

  14. 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…

  15. 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…

  16. 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…

  17. 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…

  18. 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…

  19. 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…

  20. 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.

  1. 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…

  2. 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…

  3. 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.

  4. 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,…

  5. 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…

  6. 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,…

  7. [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.

  8. 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…

  9. 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.

  10. 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).

  11. Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

    PubMed Central

    Hilton, Harry H.

    2012-01-01

    Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated. PMID:28817038

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. The Effects of LAP Fractions on Addition and Subtraction Of Fractions with Students with Mild Disabilities

    ERIC Educational Resources Information Center

    Test, David W.; Ellis, Michael F.

    2005-01-01

    One of the hardest math skills for students to learn is fractions. This study used a multiple probe across participants to evaluate the effectiveness of a mnemonic strategy called LAP Fractions on six middle school students' ability to add and subtract fractions. Five of six participants were able to achieve mastery, and all six students…

  19. CCII based fractional filters of different orders.

    PubMed

    Soltan, Ahmed; Radwan, Ahmed G; Soliman, Ahmed M

    2014-03-01

    This paper aims to generalize the design of continuous-time filters to the fractional domain with different orders and validates the theoretical results with two different CCII based filters. In particular, the proposed study introduces the generalized formulas for the previous fractional-order analysis of equal orders. The fractional-order filters enhance the design flexibility and prove that the integer-order performance is a very narrow subset from the fractional-order behavior due to the extra degrees of freedom. The general fundamentals of these filters are presented by calculating the maximum and minimum frequencies, the half power frequency and the right phase frequency which are considered a critical issue for the filter design. Different numerical solutions for the generalized fractional order low pass filters with two different fractional order elements are introduced and verified by the circuit simulations of two fractional-order filters: Kerwin-Huelsman-Newcomb (KHN) and Tow-Tomas CCII-based filters, showing great matching.

  20. 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.

  1. SPECIFIC FRACTIONATION OF HUMAN ANTIDEXTRAN ANTIBODIES

    PubMed Central

    Gelzer, Justus; Kabat, Elvin A.

    1964-01-01

    Human antidextran of one individual, absorbed specifically on sephadex, was fractionated into two populations of antibody molecules by successive elution with oligosaccharides of the isomaltose series of increasing size. The purified antibody fractions and some whole antidextran sera were found to fix complement with dextrans of molecular weight of 195,000 and above. It could be demonstrated by quantitative microcomplement fixation inhibition assays that the antibody eluted with isomaltotriose had a higher affinity for smaller oligosaccharides relative to isomaltohexaose, indicating a high content of antibody molecules with smaller combining sites, while with the second fraction, eluted with isomaltohexaose, the small haptens were very poor inhibitors and the larger oligosaccharides inhibited readily, presumably due to a higher proportion of molecules with larger combining site size. Assays of similarly prepared fractions, obtained from earlier bleedings of the same individual (1), with inhibition of complement fixation were in good agreement with those obtained by inhibition of precipitation. The two purified antidextran fractions were shown to differ with respect to their complement-fixing capacity. The fraction with molecules with smaller size-combining sites fixed only about half as much complement per unit antibody N as did the fraction containing largely molecules with larger combining sites suggesting that the strength of complement fixation is affected by the strength of the antigen-antibody interaction. PMID:14176295

  2. Fractional thermal diffusion and the heat equation

    NASA Astrophysics Data System (ADS)

    Gómez, Francisco; Morales, Luis; González, Mario; Alvarado, Victor; López, Guadalupe

    2015-02-01

    Fractional calculus is the branch of mathematical analysis that deals with operators interpreted as derivatives and integrals of non-integer order. This mathematical representation is used in the description of non-local behaviors and anomalous complex processes. Fourier's lawfor the conduction of heat exhibit anomalous behaviors when the order of the derivative is considered as 0 < β,ϒ ≤ 1 for the space-time domain respectively. In this paper we proposed an alternative representation of the fractional Fourier's law equation, three cases are presented; with fractional spatial derivative, fractional temporal derivative and fractional space-time derivative (both derivatives in simultaneous form). In this analysis we introduce fractional dimensional parameters σx and σt with dimensions of meters and seconds respectively. The fractional derivative of Caputo type is considered and the analytical solutions are given in terms of the Mittag-Leffler function. The generalization of the equations in spacetime exhibit different cases of anomalous behavior and Non-Fourier heat conduction processes. An illustrative example is presented.

  3. GOLGI FRACTIONS PREPARED FROM RAT LIVER HOMOGENATES

    PubMed Central

    Ehrenreich, J. H.; Bergeron, J. J. M.; Siekevitz, P.; Palade, G. E.

    1973-01-01

    In devising a new procedure for the isolation of Golgi fractions from rat liver homogenates, we have taken advantage of the overloading with very low density lipoprotein (VLDL) particles that occurs in the Golgi elements of hepatocytes ∼90 min after ethanol is administered (0.6 g/100 g body weight) by stomach tube to the animals. The VLDLs act as morphological markers as well as density modifiers of these elements. The starting preparation is a total microsomal fraction prepared from liver homogenized (1:5) in 0.25 M sucrose. This fraction is resuspended in 1.15 M sucrose and loaded at the bottom of a discontinuous sucrose density gradient. Centrifugation at ∼13 x 106 g·min yields by flotation three Golgi fractions of density >1.041 and <1.173. The light and intermediate fractions consist essentially of VLDL-loaded Golgi vacuoles and cisternae. Nearly empty, often collapsed, Golgi cisternae are the main component of the heavy fraction. A procedure which subjects the Golgi fractions to hypotonic shock and shearing in a French press at pH 8.5 allows the extraction of the content of the Golgi elements and the subsequent isolation of their membranes by differential centrifugation. PMID:4356571

  4. 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.

  5. 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.

  6. 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

  7. State space realization of fractional order systems

    SciTech Connect

    Djamah, T.; Mansouri, R.; Djennoune, S.; Bettayeb, M.

    2009-03-05

    In the past few years, fractional calculus appeared to be a useful tool for the modeling and control of dynamic systems. Although, some methods of the control theory have been developed for the commensurate case, the difficulties of the non commensurate called generalized fractional systems still remain unsolved. In this paper, a method is presented for obtaining the state space model of a generalized fractional system starting from its transfer function. The method remains valid for the particular cases of commensurate and integer systems. An application to some examples illustrates the algorithm.

  8. Behavior of fractional diffusion at the origin.

    PubMed

    Ryabov, Ya E

    2003-09-01

    The present work discusses the fractional diffusion equation based on the Riemann-Liouville fractional time derivatives. It was shown that the normalization conservation constraint leads to the divergency of diffusive agent concentration at the origin. This divergency implies an external source of the diffusive agent at r-->0. Thus, the Riemann-Liouville fractional time derivative implies a loss of diffusive agent mass, which is compensated for by the source of this agent at the origin. In contrast, the absence of the normalization conservation constraint does not lead to any divergences in the limit r-->0 and at the same time provides the decay of normalization.

  9. 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.

  10. The Fractions SNARC Revisited: Processing Fractions on a Consistent Mental Number Line.

    PubMed

    Toomarian, Elizabeth Y; Hubbard, Edward M

    2017-07-12

    The ability to understand fractions is key to establishing a solid foundation in mathematics, yet children and adults struggle to comprehend them. Previous studies have suggested that these struggles emerge because people fail to process fraction magnitude holistically on the mental number line (MNL), focusing instead on fraction components (Bonato et al. 2007). Subsequent studies have produced evidence for default holistic processing (Meert et al., 2009; 2010), but examined only magnitude processing, not spatial representations. We explored the spatial representations of fractions on the MNL in a series of three experiments: Experiment 1 replicated Bonato et al. (2007); 30 naïve undergraduates compared unit fractions (1/1-1/9) to 1/5, resulting in a reverse SNARC effect. Experiment 2 countered potential strategic biases induced by the limited set of fractions used by Bonato et al. by expanding the stimulus set to include all irreducible, single-digit proper fractions, and asked participants to compare them against 1/2. We observed a classic SNARC effect, completely reversing the pattern from Experiment 1. Together, Experiments 1 and 2 demonstrate that stimulus properties dramatically impact spatial representations of fractions. In Experiment 3, we demonstrated within-subjects reliability of the SNARC effect across both a fractions and whole number comparison task. Our results suggest that adults can indeed process fraction magnitudes holistically, and that their spatial representations occur on a consistent MNL for both whole numbers and fractions.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. Early Predictors of Middle School Fraction Knowledge

    PubMed Central

    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 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. PMID:24576209

  17. 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.

  18. 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.

  19. Fractional differentiation by neocortical pyramidal neurons

    PubMed Central

    Lundstrom, Brian Nils; Higgs, Matthew H; Spain, William J; Fairhall, Adrienne L

    2008-01-01

    Neural systems adapt to changes in stimulus statistics. However, it is not known how stimuli with complex temporal dynamics drive the dynamics of adaptation and the resulting firing rate. For single neurons, it has often been assumed that adaptation has a single time scale. Here, we show that single rat neocortical pyramidal neurons adapt with a time scale that depends on the time scale of changes in stimulus statistics. This multiple time scale adaptation is consistent with fractional order differentiation, such that the neuron’s firing rate is a fractional derivative of slowly varying stimulus parameters. Biophysically, even though neuronal fractional differentiation effectively yields adaptation with many time scales, we find that its implementation requires only a few, properly balanced known adaptive mechanisms. Fractional differentiation provides single neurons with a fundamental and general computation that can contribute to efficient information processing, stimulus anticipation, and frequency independent phase shifts of oscillatory neuronal firing. PMID:18931665

  20. Bio-oil fractionation and condensation

    DOEpatents

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

    2017-04-04

    The present invention relates to a method of fractionating bio-oil vapors which involves providing bio-oil vapors comprising bio-oil constituents. 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 disclosed are steps for subsequently recovering further liquid fractions of liquefied bio-oil constituents. Particular compositions of bio-oil condensation products are also described.

  1. Synthetic Division, Taylor Polynomials, Partial Fractions.

    ERIC Educational Resources Information Center

    Lambert, Howard B.

    1989-01-01

    Reviews the underpinnings of synthetic division. Shows how to quickly obtain the coefficients of the Taylor expansion of a polynomial about a point, and a partial fraction decomposition of a polynomial. (MVL)

  2. Exact solution to fractional logistic equation

    NASA Astrophysics Data System (ADS)

    West, Bruce J.

    2015-07-01

    The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.

  3. 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.

  4. [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

  5. 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

  6. 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.

  7. Stochastic Evolution Equations Driven by Fractional Noises

    DTIC Science & Technology

    2016-11-28

    Stochastic Evolution Equations Driven by Fractional Noises We have introduced a modification of the classical Euler numerical scheme for stochastic...of Papers published in peer-reviewed journals: Final Report: Stochastic Evolution Equations Driven by Fractional Noises Report Title We have introduced...case the evolution form of the equation will involve a Stratonovich integral (or path-wise Young integral). The product can also be interpreted as a

  8. 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…

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. Wave function methods for fractional electrons

    NASA Astrophysics Data System (ADS)

    Steinmann, Stephan N.; Yang, Weitao

    2013-08-01

    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

  14. 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.

  15. Generalized continued fractions and ergodic theory

    NASA Astrophysics Data System (ADS)

    Pustyl'nikov, L. D.

    2003-02-01

    In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest.

  16. 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.

  17. Oscillator with fraction order restoring force

    NASA Astrophysics Data System (ADS)

    Cveticanin, L.

    2009-03-01

    In this paper a new analytical method for solving the differential equations which describe the motion of the oscillator with fraction order elastic force is introduced. Using the first integral of motion the exact period of vibration in the form of the Euler beta function is obtained. Based on that value the approximate solution of the strong nonlinear fraction order differential equation is formed. The suggested procedure is applied for various fraction values, but also for the pure quadratic, cubic and quintic oscillators. The advantage of the suggested method is that is valid for all fraction values α⩾1, the accuracy of the approximate solution is very high as the period of vibration is exactly analytically determined and is independent on the time. In the paper the fraction order differential equation with small linear and nonlinear terms is also considered. The Krylov-Bogolubov method is extended due to the fact that frequency of vibration depends on the amplitude of vibration. The approximate solution is with time variable amplitude, phase and frequency. The linear damped fraction order oscillator is widely discussed. The approximate solution of the differential equation which describes the vibrations of such oscillator is compared with exact numerical one and shows a good agreement.

  18. 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.

  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. 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.

  1. 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

  2. Characterization of Coconut Oil Fractions Obtained from Solvent Fractionation Using Acetone.

    PubMed

    Sonwai, Sopark; Rungprasertphol, Poonyawee; Nantipipat, Nantinee; Tungvongcharoan, Satinee; Laiyangkoon, Nantikan

    2017-09-01

    This work was aimed to study the solvent fraction of coconut oil (CNO). The fatty acid and triacylglycerol compositions, solid fat content (SFC) and the crystallization properties of CNO and its solid and liquid fractions obtained from fractionation at different conditions were investigated using various techniques. CNO was dissolved in acetone (1:1 w/v) and left to crystallize isothermally at 10°C for 0.5, 1 and 2 h and at 12°C for 2, 3 and 6 h. The solid fractions contained significantly lower contents of saturated fatty acids of ≤ 10 carbon atoms but considerably higher contents of saturated fatty acids with > 12 carbon atoms with respect to those of CNO and the liquid fractions. They also contained higher contents of high-melting triacylglycerol species with carbon number ≥ 38. Because of this, the DSC crystallization onset temperatures and the crystallization peak temperatures of the solid fractions were higher than CNO and the liquid fractions. The SFC values of the solid fractions were significantly higher than CNO at all measuring temperatures before reaching 0% just below the body temperature with the fraction obtained at 12°C for 2 h exhibiting the highest SFC. On the contrary, the SFC values of the liquid fractions were lower than CNO. The crystallization duration exhibited strong influence on the solid fractions. There was no effect on the crystal polymorphic structure possibly because CNO has β'-2 as a stable polymorph. The enhanced SFC of the solid fractions would allow them to find use in food applications where a specific melting temperature is desired such as sophisticated confectionery fats, and the decreased SFC of the liquid fractions would provide them with a higher cold stability which would be useful during extended storage time.

  3. 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..

  4. 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.

  5. Fractional formalism to DNA chain and impact of the fractional order on breather dynamics.

    PubMed

    Mvogo, Alain; Kofané, Timoléon Crépin

    2016-12-01

    We have investigated the impact of the fractional order derivative on the dynamics of modulated waves of a homogeneous DNA chain that is based on site-dependent finite stacking and pairing enthalpies. We have reformulated the classical Lagrangian of the system by including the coordinates depending on the Riemann-Liouville time derivative of fractional order γ. From the Lagrange equation, we derived the fractional nonlinear equation of motion. We obtained the fractional breather as solutions by means of a fractional perturbation technique. The impact of the fractional order is investigated and we showed that depending on the values of γ, there are three types of waves that propagate in DNA. We have static breathers, breathers of small amplitude and high velocity, and breathers of high amplitude and small velocity.

  6. Impact of variable RBE on proton fractionation

    SciTech Connect

    Dasu, Alexandru; Toma-Dasu, Iuliana

    2013-01-15

    Purpose: To explore the impact of variable proton relative biological effectiveness (RBE) on dose fractionation for clinically relevant situations. A generic RBE = 1.1 is generally used for isoeffect calculations, while experimental studies showed that proton RBE varies with tissue type, dose, and linear energy transfer (LET). Methods: An analytical expression for the LET and {alpha}/{beta} dependence of the linear-quadratic (LQ) model has been used for proton simulations in parallel with the assumption of a generic RBE = 1.1. Calculations have been performed for ranges of LET values and fractionation sensitivities to describe clinically relevant cases, such as the treatment of head and neck and prostate tumors. Isoeffect calculations were compared with predictions from a generic RBE value and reported clinical results. Results: The generic RBE = 1.1 appears to be a reasonable estimate for the proton RBE of rapidly growing tissues irradiated with low LET radiation. However, the use of a variable RBE predicts larger differences for tissues with low {alpha}/{beta} (both tumor and normal) and at low doses per fraction. In some situations these differences may appear in contrast to the findings from photon studies highlighting the importance of accurate accounting for the radiobiological effectiveness of protons. Furthermore, the use of variable RBE leads to closer predictions to clinical results. Conclusions: The LET dependence of the RBE has a strong impact on the predicted effectiveness of fractionated proton radiotherapy. The magnitude of the effect is modulated by the fractionation sensitivity and the fractional dose indicating the need for accurate analyses both in the target and around it. Care should therefore be employed for changing clinical fractionation patterns or when analyzing results from clinical studies for this type of radiation.

  7. Exploring fractionation models for Martian magmas

    NASA Astrophysics Data System (ADS)

    Udry, Arya; Balta, J. Brian; McSween, Harry Y.

    2014-01-01

    primary compositions, i.e., magmas that did not experience fractionation and/or contamination after extraction from the mantle, occur as a subset of Martian meteorites and a few lavas analyzed on the planet's surface by rovers. Eruptions of primary magmas are rare on Earth and presumably on Mars. Previous studies of fractional crystallization of Martian primary magmas have been conducted under isobaric conditions, simulating idealized crystallization in magma chambers. Polybaric fractionation, which occurs during magma ascent, has not been investigated in detail for Martian magmas. Using the MELTS algorithm and the pMELTS revision, we present comprehensive isobaric and polybaric thermodynamic calculations of the fractional crystallization of four primary or parental Martian magmas (Humphrey, Fastball, Y-980459 shergottite, and nakhlite parental melts) using various pressure-temperature paths, oxygen fugacities, and water contents to constrain how these magmas might evolve. We then examine whether known Martian alkaline rock compositions could have formed through fractional crystallization of these magmas under the simulated conditions. We find that isobaric and polybaric crystallization paths produce similar residual melt compositions, but given sufficient details, we may be able to distinguish between them. We calculate that Backstay (Gusev Crater) likely formed by fractionation of a primary magma under polybaric conditions, while Jake_M (Gale Crater) may have formed through melting of a metasomatized mantle, crustal assimilation, or fractional crystallization of an unknown primary magma. The best fits for the Backstay composition indicate that consideration of polybaric crystallization paths can help improve the quality of fit when simulating liquid lines of descent.

  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. 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 t τ 0 CD u (x , t) = g (t ; u), τ ∈ (0 , 1 ], where t τ 0 CD #x03c4; 0 C 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.

  10. Tests of equal effect per fraction in microcolony assays of survival after fractionated irradiations

    SciTech Connect

    Taylor, J.M.G.

    1985-01-01

    H.D Thames, Jr. and H.R. Withers 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.

  11. 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.

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Proteome analysis of human nuclear insoluble fractions.

    PubMed

    Takata, Hideaki; Nishijima, Hitoshi; Ogura, Shun-Ichiro; Sakaguchi, Takehisa; Bubulya, Paula A; Mochizuki, Tohru; Shibahara, Kei-Ichi

    2009-08-01

    The interphase nucleus is a highly ordered and compartmentalized organelle. Little is known regarding what elaborate mechanisms might exist to explain these properties of the nucleus. Also unresolved is whether some architectural components might facilitate the formation of functional intranuclear compartments or higher order chromatin structure. As the first step to address these questions, we performed an in-depth proteome analysis of nuclear insoluble fractions of human HeLa-S3 cells prepared by two different approaches: a high-salt/detergent/nuclease-resistant fraction and a lithium 3,5-diiodosalicylate/nuclease-resistant fraction. Proteins of the fractions were analyzed by liquid chromatography electrospray ionization tandem mass spectrometry, identifying 333 and 330 proteins from each fraction respectively. Among the insoluble nuclear proteins, we identified 37 hitherto unknown or functionally uncharacterized proteins. The RNA recognition motif, WD40 repeats, HEAT repeats and the SAP domain were often found in these identified proteins. The subcellular distribution of selected proteins, including DEK protein and SON protein, demonstrated their novel associations with nuclear insoluble materials, corroborating our MS-based analysis. This study establishes a comprehensive catalog of the nuclear insoluble proteins in human cells. Further functional analysis of the proteins identified in our study will significantly improve our understanding of the dynamic organization of the interphase nucleus.

  19. Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction.

    PubMed

    Liu, Yingyi

    2017-09-08

    Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. © 2017 The British Psychological Society.

  20. 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.