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https://www.physicsforums.com/threads/magnetic-pinches-and-mhd.366912/
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# Magnetic pinches and MHD
1. Jan 3, 2010
### Crusoe
Can someone give me an intuitive explanation why plasmas or conductive fluids tend to follow magnetic flux lines?
E.g. http://en.wikipedia.org/wiki/Magnetohydrodynamics" [Broken] entry on this says:
If I take a stab at a qualitative explanation, is it because magnetic flux lines are equipotential lines, therefore if the conductor deviates from the flux lines, induced currents are produced which oppose the motion in accordance with Lenz's law?
Also, I know the explanation for Lenz's law is conservation of energy, but it just seems odd that induced currents so happen to be set up to precisely keep energy conserved.
What causes magnetic pinching, e.g. in lightning bolts or even lightning rods (below) then? I would have thought an axial current along a conductive fluid would cause charged particles within it to follow a circular orbit. Where do they get the centripetal force to both follow such an orbit, and in fact exceed that for a stable orbit, and end up reducing their orbital radii?
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https://www.maplesoft.com/support/help/AddOns/view.aspx?path=BlockImporter/setup
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Setting up BlockImporter - BlockImporter Help
Home : Support : Online Help : Toolboxes : BlockImporter : BlockImporter/setup
Setting up BlockImporter
Description
• To use the BlockImporter Import command, the Maple-MATLAB® link must be set up and functioning correctly.
• To test the link between MATLAB®/Simulink® and Maple, execute, in Maple, the command $\mathrm{Matlab:-openlink}\left(\right)$. Success is indicated by a NULL return, failure raises an error or a warning. If the test is not successful, follow the instructions in Matlab[setup] to configure the link.
> $\mathrm{Matlab}:-\mathrm{openlink}\left(\right)$
> $\mathrm{Matlab}:-\mathrm{evalM}\left("version"\right)$
> $\mathrm{Matlab}:-\mathrm{getvar}\left("ans"\right)$
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http://wicomdsp.blogspot.com/2015/03/frequency-error-estimation-range-and.html
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## Pages
### Frequency Error Estimate Range and Resolution Determination
Frequency Error Estimation Range and Resolution Determination Frequency error estimation in IEEE 802.11 systems is done over preamble Short Training Field (STF) and Long Training Field (LTF) signals.
Time domain signal of STF and LTF has period 0.8us and 3.2us respectively. With this knowledge, frequency error can be computed through shifted cross-correlation operation.
STF signal assist in computing coarse estimate of frequency error and a fine estimate can be obtained from LTF.
Frequency Error Estimate Range
Range of frequency errors that can be computed from STF will be [-1/(2*0.8u) to 1/(2*0.8u)] or [-625khz to +625khz]
Range of frequency errors that can be computed from LTF will be [-1/(2*3.2u) to 1/(2*3.2u)] or [-156.25khz to +156.25khz]
Above ranges can be obtained by equating the angle of $e^{j2\pi f T_p}$ to $+/- \pi$. Where $T_p$ is the period of STF or LTF.
Frequency Error Estimate Resolution
Resolution of frequency error estimate has significance in real time systems. Resolution of fixed point implemenation determine the resolution of the frequency error estimation algorithm.
A $'n'$ bit precision fixed point implementation will have an ampitude resolution of $2^{-n}$. To know the resolution of frequency error estimate, it is required to know the smallest possible phase represented in the implemented fixed point.
Let us say $\cos\left(x\right)$ is well represented by the fixed point. If $\Delta = (2 \pi f T_p)$ be the possible phase resolution by the fixed point, then $\cos\left(x +\Delta\right)~ - ~\cos\left(x\right) = -2^{-n}$ gives rise to $\Delta \sin\left(x\right) = 2^{-n}$.
Similarly, Let us say $\sin\left(x\right)$ is well represented by the fixed point, then $\sin\left(x +\Delta\right)~ - ~\sin\left(x\right) = 2^{-n}$ gives rise to $\Delta \cos\left(x\right) = 2^{-n}$.
From the above $\Delta = +/- \sqrt{2} . 2^{-n}$ or $f = +/- \sqrt{2} . 2^{-n} . \frac{1}{2 \pi T_p}$
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http://www.science.gov/topicpages/s/saturation+vapor+pressure.html
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#### Sample records for saturation vapor pressure
1. Improved Magnus form approximation of saturation vapor pressure
SciTech Connect
Alduchov, O.A.; Eskridge, R.E.
1997-11-01
Relative humidity is usually measured in aerological observations and dew point depression is usually reported in upper-air reports. These variables must frequently be converted to other moisture variables in meteorological analysis. If relative humidity is converted to vapor pressure, most humidity variables can then be determined. Elliott and Gaffen reviewed the practices and procedures of the US radiosonde system. In their paper, a comparison of the relative errors was made between the saturation vapor pressure formulations of Tetens (1930), Goff-Gratch (1946), Wexler (1976), and Buck (1981). In this paper, the authors will expand the analysis of Elliott and Gaffen by deriving several new saturation vapor pressure formulas, and reviewing the various errors in these formulations. They will show that two of the new formulations of vapor pressure over water and ice are superior to existing formulas. Upper air temperature data are found to vary from about +50 C to {minus}80 C. This large variation requires a saturation vapor pressure equation to be accurate over a large temperature range. While the errors introduced by the use of relatively inaccurate conversion equations are smaller than the errors due to the instruments, dewpoint coding errors, and dewpoint conversion algorithms (Elliott and Gaffen, 1993); they introduce additional systematic errors in humidity data. The most precise formulation of vapor pressure over a plane surface of water was given by Wexler (1976). The relative errors of Tetens (1930) formula and one due to Buck (1981) (Buck`s equation is recommended in the Federal Meteorological Handbook No. 3, 1991) are shown. The relative errors in this table are the predicted value minus the Wexler value divided by the Wexler value.
2. Adipic and malonic acid aqueous solutions: surface tensions and saturation vapor pressures.
PubMed
Riipinen, Ilona; Koponen, Ismo K; Frank, Gran P; Hyvrinen, Antti-Pekka; Vanhanen, Joonas; Lihavainen, Heikki; Lehtinen, Kari E J; Bilde, Merete; Kulmala, Markku
2007-12-20
The surface tension of adipic aqueous solutions was measured as a function of temperature (T=278-313 K) and adipic acid mole fraction (X=0.000-0.003) using the Wilhelmy plate method. A parametrization fitted to these data is presented. The evaporation rates of binary water-malonic and water-adipic acid droplets were measured with a TDMA technique at different temperatures (T=293-300 K) and relative humidities (58-80%), and the saturation vapor pressures of subcooled liquid malonic and adipic acids were derived from the data using a binary evaporation model. The temperature dependence of the vapor pressures was obtained as least-squares fits to the derived vapor pressures: ln(Psat,l) (Pa)=220.2389-22634.96/T (K)-26.66767 ln T (K) for malonic acid and ln(Psat,l) (Pa)=140.6704-18230.97/T (K)-15.48011 ln T (K) for adipic acid. PMID:18044850
3. Determination of saturation pressure and enthalpy of vaporization of semi-volatile aerosols: the integrated volume mentod
EPA Science Inventory
This study presents the integrated volume method for estimating saturation pressure and enthalpy of vaporization of a whole aerosol distribution. We measure the change of total volume of an aerosol distribution between a reference state and several heated states, with the heating...
4. Evaluation of saturation vapor pressure over hypersaline water bodies at the southern edge of the Dead Sea, Jordan
SciTech Connect
Oroud, I.M. )
1994-12-01
The activity coefficient and saturation vapor pressure for hypersaline solutions located at the southern edge of the Dead Sea are computed analytically. The collected data consist of temperature and evaporation rates measured for a freshwater pan and three other hypersaline solutions with specific gravities of 1.26, 1.31, and 1.34, respectively. The activity coefficients of the three saline pans were computed after accounting for the effect of buoyancy, which was included in the computations because of consistently large, positive virtual temperature differences between the saline pans and the ambient air. The ratios of saline to fresh pan evaporation (Es/Ef: the [alpha] ratio) of the present study are also compared to data reported for the Bonneville Salt Brines, Utah. It is found that the a ratios of the present study, although conducted over an extended period of time, are larger than those reported for the Bonneville Brines. Results of the present study imply that evaporation from the various brine-concentrated, shallow lakes at the southern edge of the Dead Sea is likely to proceed during the entire year, and water vapor deposition from the atmosphere, due to an inverted vapor pressure, is less likely to occur particularly for brines with specific gravities of less than 1.3.
5. Persistent Water-Nitric Acid Condensate with Saturation Water Vapor Pressure Greater than That of Hexagonal Ice.
PubMed
Gao, Ru-Shan; Gierczak, Tomasz; Thornberry, Troy D; Rollins, Andrew W; Burkholder, James B; Telg, Hagen; Voigt, Christiane; Peter, Thomas; Fahey, David W
2016-03-10
A laboratory chilled mirror hygrometer (CMH), exposed to an airstream containing water vapor (H2O) and nitric acid (HNO3), has been used to demonstrate the existence of a persistent water-nitric acid condensate that has a saturation H2O vapor pressure greater than that of hexagonal ice (Ih). The condensate was routinely formed on the mirror by removing HNO3 from the airstream following the formation of an initial condensate on the mirror that resembled nitric acid trihydrate (NAT). Typical conditions for the formation of the persistent condensate were a H2O mixing ratio greater than 18 ppm, pressure of 128 hPa, and mirror temperature between 202 and 216 K. In steady-state operation, a CMH maintains a condensate of constant optical diffusivity on a mirror through control of only the mirror temperature. Maintaining the persistent condensate on the mirror required that the mirror temperature be below the H2O saturation temperature with respect to Ih by as much as 3 K, corresponding to up to 63% H2O supersaturation with respect to Ih. The condensate was observed to persist in steady state for up to 16 h. Compositional analysis of the condensate confirmed the co-condensation of H2O and HNO3 and thereby strongly supports the conclusion that the Ih supersaturation is due to residual HNO3 in the condensate. Although the exact structure or stoichiometry of the condensate could not be determined, other known stable phases of HNO3 and H2O are excluded as possible condensates. This persistent condensate, if it also forms in the upper tropical troposphere, might explain some of the high Ih supersaturations in cirrus and contrails that have been reported in the tropical tropopause region. PMID:26447682
6. Glow Discharge Formation over Water Surface at Saturated Water Vapor Pressure and Its Application to Wastewater Treatment
Sugama, Chie; Tochikubo, Fumiyoshi; Uchida, Satoshi
2006-11-01
With the aim of wastewater treatment using the active reaction of OH radicals generated in gas discharges, DC, low frequency (LF, 100 kHz) and RF (13.56 MHz) glow discharges were generated over the water surface at saturated water vapor pressure. Low-pressure glow discharge over the water surface has an advantage of uniform OH radical production near the water surface. A very stable and uniform glow discharge was obtained with an RF power source, whereas the discharges obtained with the DC and LF power sources were sometimes localized. The effective OH radical production was confirmed from the strong optical emission of OH(A{2}?+-X{2}\\Pi) near the water surface. The OH(A{2}?+-X{2}\\Pi) emission intensity near the water surface increased almost linearly with an increase in discharge power. N,N-Dimethyl- p-nitrosoaniline (RNO) solution as a persistent test pollutant was treated by RF glow discharge over the water surface. We confirmed that the RNO solution was certainly decolorized by OH radicals generated in the RF glow discharge. It was found that the degradation of target compounds by OH radicals was concentrated near the water surface in the solution because very slow diffusion of target compounds limited the reaction rate.
7. Saturation vapor pressure and critical constants of H2O, D2O, T2O, and their isotopic mixtures
Matsunaga, N.; Nagashima, A.
1987-11-01
Reliable data on the vapor pressure and critical constants of H2O isotopes and their isotopic mixtures are required for the generation of thermophysical properties data over a wide range of temperatures and pressures. In this study, vapor pressure equations for D2O and T2O have been developed based on the latest experimental and theoretical information. Considering the similarity among H2O isotopes, the functional form of the Saul and Wagner equation, fully proven for H2O, has been employed. The present equation for D2O shows a lower trend by up to 0.09% than the widely used Hill and MacMillan equation at temperatures below 150C. For the vapor pressure of the isotopic mixtures, the available experimental data have been examined for the validity of Raoult's law. Then it has been shown that the critical temperature and the critical pressure of the isotopic mixture can also be predicted as simple mole-fraction average values.
8. Progress of serpentinization in olivine-H2O system at 250 C and vapor-saturated pressure
Okamoto, A.; Ogasawara, Y.; Tsuchiya, N.
2011-12-01
Fluids play a crucial role in global-scale mass transfer, metamorphism, volcanism, and seismic processes in subduction zones. Serpentine minerals, which are produced by interaction between ultramafic rocks and fluids, contain about 13% water and are the greatest carrier of H2O into the deep interior of Earth. Therefore, the volume and distribution of hydrated oceanic mantle are of special interest in evaluating the effects of fluids on subduction zone processes. We conducted hydrothermal experiments in olivine (Ol; Fo91)-H2O and orthopyroxenite (Opx; composed of 95% of orthopyroxene, En66)-H2O systems under conditions of 250 C and vapor-saturated pressure (Psat) to examine the temporal evolution of the solution chemistry and products in runs of up to 1008 h in duration. The maximal degree of hydration (i.e., H2O content in the solid sample) in the Ol-H2O experiments (3.6 wt.%) was much higher than that in the Opx-H2O experiments (0.4 wt.%). In the Ol-H2O experiments, Mg and Si in solution showed an initial increase (stage 1) before decreasing (stage 2) and finally attaining a steady state after 504 h (stage 3). Following a drop in silica activity toward the level of brucite stability filed, the products also changed from serpentine + magnetite (stages 1 and 2) to serpentine + brucite + magnetite (stage 3). Serpentine minerals also changed from lizardite (stages 1 and 2) to lizardite + chrysotile (stage 3). The textures observed in this study were similar to those observed in partly serpentinized dunites. In the Opx-H2O experiments, chlorite formed after orthopyroxene grains, which differs from the formation of talc and serpentine after orthopyroxene (bastite), as observed in natural hydrated harzburgites. The Opx-H2O system maintained 10-103 times higher silica activity than Ol-H2O system, suggesting that brucite does not form after olivine during hydration of peridotites when the Ol-H2O system is linked to the Opx-H2O system. The progress of hydration reactions is affected by mechanical properties of host rocks. The hydration reactions observed in this study produced hierarchical fractures in the reactants, which became filled with reaction products, similar to mesh textures after olivine in natural peridotites. This reaction-induced fracturing produced new reaction surfaces and fluid pathways that enhanced the hydration reactions. The overall reaction producing serpentine+brucite in the Ol-H2O experiments showed the large volume expansion (V/V0 = 1.38 at stage 3), whereas that producing only serpentine proceeded with near constant volume (V/V0 = 1.09 at stage 1). The volume expansion is more difficult to occur in the oceanic lithosphere than in our experiments during serpentinization. Thus, in the case that volume expansion is prevented at reaction sites, one of the following outcomes occurs: (1) the hydration reaction stops until new fractures form, or (2) the reaction proceeds with low volume expansion (absence of brucite) by removing Mg from the system. These two outcomes would produce contrasting distributions or extent of hydration in oceanic lithosphere.
9. Mass spectrometric determination of partial pressures of ions in the saturated vapor over the NaF-Na3AlF6 system
Abramov, S. V.; Chilingarov, N. S.; Borshchevsky, A. Ya; Sidorov, L. N.
2004-01-01
Mass spectrometric determination of absolute partial pressures of basic charged species Na2F+ and AlF4- in the saturated vapor over the NaF-Na3AlF6 system (1:1 molar ratio) was carried out in the 974-1090 K temperature range. The ion pressures were 5-8 orders of magnitude lower than the pressures of basic molecular components NaAlF4 and NaF. Particular attention was given to the equality of device sensitivity constants for positive and negative ions. Absolute device calibration was carried out using the measured ion currents Na2F+ and AlF4- and the equilibrium constant of heterolytic dissociation available in the literature.
10. The vapor pressures of explosives
SciTech Connect
Ewing, Robert G.; Waltman, Melanie J.; Atkinson, David A.; Grate, Jay W.; Hotchkiss, Peter
2013-01-05
The vapor pressures of many explosive compounds are extremely low and thus determining accurate values proves difficult. Many researchers, using a variety of methods, have measured and reported the vapor pressures of explosives compounds at single temperatures, or as a function of temperature using vapor pressure equations. There are large variations in reported vapor pressures for many of these compounds, and some errors exist within individual papers. This article provides a review of explosive vapor pressures and describes the methods used to determine them. We have compiled primary vapor pressure relationships traceable to the original citations and include the temperature ranges for which they have been determined. Corrected values are reported as needed and described in the text. In addition, after critically examining the available data, we calculate and tabulate vapor pressures at 25 °C.
11. Saturation vapor pressure and critical constants of H/sub 2/O, D/sub 2/O, T/sub 2/O, and their isotopic mixtures
SciTech Connect
Matsunaga, N.; Nagashima, A.
1987-11-01
Reliable data on the vapor pressure and critical constants of H/sub 2/O isotopes and their isotopic mixtures are required for the generation of thermophysical properties data over a wide range of temperatures and pressures. In this study, vapor pressure equations for D/sub 2/O and T/sub 2/O have been developed based on the latest experimental and theoretical information. Considering the similarity among H/sub 2/O isotopes, the functional form of the Saul and Wagner equation, fully proven for H/sub 2/O, has been employed. The present equation for D/sub 2/O shows a lower trend by up to 0.09% than the widely used Hill and MacMillan equation at temperatures below 150/sup 0/C. For the vapor pressure of the isotopic mixtures, the available experimental data have been examined for the validity of Raoult's law. Then it has been shown that the critical temperature and the critical pressure of the isotopic mixture can also be predicted as simple mole-fraction average values.
12. Dynamics of viscous coalescing droplets in a saturated vapor phase
Baroudi, Lina; Nagel, Sidney R.; Morris, Jeffrey F.; Lee, Taehun
2015-12-01
The dynamics of two liquid droplets coalescing in their saturated vapor phase are investigated by Lattice Boltzmann numerical simulations. Attention is paid to the effect of the vapor phase on the formation and growth dynamics of the liquid bridge in the viscous regime. We observe that the onset of the coalescence occurs earlier and the expansion of the bridge initially proceeds faster when the coalescence takes place in a saturated vapor compared to the coalescence in a non-condensable gas. We argue that the initially faster evolution of the coalescence in the saturated vapor is caused by the vapor transport through condensation during the early stages of the coalescence.
13. Precision ozone vapor pressure measurements
NASA Technical Reports Server (NTRS)
Hanson, D.; Mauersberger, K.
1985-01-01
The vapor pressure above liquid ozone has been measured with a high accuracy over a temperature range of 85 to 95 K. At the boiling point of liquid argon (87.3 K) an ozone vapor pressure of 0.0403 Torr was obtained with an accuracy of + or - 0.7 percent. A least square fit of the data provided the Clausius-Clapeyron equation for liquid ozone; a latent heat of 82.7 cal/g was calculated. High-precision vapor pressure data are expected to aid research in atmospheric ozone measurements and in many laboratory ozone studies such as measurements of cross sections and reaction rates.
14. Measurements on the flow of vapors near saturation through porous Vycor glass membranes
Loimer, Thomas; Reznickova, Jirina; Uchytil, Petr; Setnickova, Katerina
2012-05-01
We present experimental data of the flow of butane and isobutane vapors through porous Vycor glass membranes. The pressure driven flow of vapors near and far from saturation through membranes with pore diameters of 20 and 33 nm is investigated. The upstream pressures lie between the saturation pressure at the upstream temperature to approximately half that value. The pressure differences are between a few kPa to about 100 kPa. From an adiabatic description of the flow process, we expect condensation of a vapor close enough to saturation and hence, due to the action of capillary forces, an increase in mass flux with respect to the mass flux of a vapor that remains in a gaseous state. According to the adiabatic description, a vapor that flows through a porous membrane may condense for two reason: One reason is capillary condensation in the pores of the membrane, the second reason is heat conduction from the upstream to the downstream side of the membrane due to the Joule-Thomson effect. If the flux of heat in downstream direction is large enough, a vapor near saturation at the upstream side of the membrane may only release sufficient heat by condensation. Describing the flow in terms of dimensionless groups recovered from an adiabatic description of the flow process, we find that a vapor condenses and the mass flux is increased if (i) a dimensionless permeability of the membrane is larger than one and (ii) if the vapor at the upstream side is close enough to saturation such that a dimensionless group involving the upstream pressure and the pressure difference is also larger than one. Experimental data corroborates condition (i) above and indicates that condition (ii) might be valid.
15. Vapor pressure measured with inflatable plastic bag
NASA Technical Reports Server (NTRS)
1965-01-01
Deflated plastic bag in a vacuum chamber measures initial low vapor pressures of materials. The bag captures the test sample vapors and visual observation of the vapor-inflated bag under increasing external pressures yields pertinent data.
16. Water vapor pressure gauge
SciTech Connect
Edwards, D Jr; Gillette, D
1980-01-01
An inexpensive pressure gauge, able to measure the N/sub 2/ and H/sub 2/O components within a vacuum system in the pressure range 1..mu.. to 400..mu.. is described and results of tests of the device are reported.
17. Vapor Pressure Measurements in a Closed System
ERIC Educational Resources Information Center
Iannone, Mark
2006-01-01
An alternative method that uses a simple apparatus to measure vapor pressure versus temperature in a closed system, in which the total pressure is the vapor pressure of the liquid sample, is described. The use of this apparatus gives students a more direct picture of vapor pressure than the isoteniscope method and results have generally been quite
18. Vapor Pressure Measurements in a Closed System
ERIC Educational Resources Information Center
Iannone, Mark
2006-01-01
An alternative method that uses a simple apparatus to measure vapor pressure versus temperature in a closed system, in which the total pressure is the vapor pressure of the liquid sample, is described. The use of this apparatus gives students a more direct picture of vapor pressure than the isoteniscope method and results have generally been quite…
19. Enthalpy of Vaporization and Vapor Pressures: An Inexpensive Apparatus
ERIC Educational Resources Information Center
Battino, Rubin; Dolson, David A.; Hall, Michael A.; Letcher, Trevor M.
2007-01-01
A simple and inexpensive method to determine the enthalpy of vaporization of liquids by measuring vapor pressure as a function of temperature is described. The vapor pressures measured with the stopcock cell were higher than the literature values and those measured with the sidearm rubber septum cell were both higher and lower than literature…
20. Enthalpy of Vaporization and Vapor Pressures: An Inexpensive Apparatus
ERIC Educational Resources Information Center
Battino, Rubin; Dolson, David A.; Hall, Michael A.; Letcher, Trevor M.
2007-01-01
A simple and inexpensive method to determine the enthalpy of vaporization of liquids by measuring vapor pressure as a function of temperature is described. The vapor pressures measured with the stopcock cell were higher than the literature values and those measured with the sidearm rubber septum cell were both higher and lower than literature
1. VAPOR PRESSURES AND HEATS OF VAPORIZATION OF PRIMARY COAL TARS
SciTech Connect
Eric M. Suuberg; Vahur Oja
1997-07-01
This project had as its main focus the determination of vapor pressures of coal pyrolysis tars. It involved performing measurements of these vapor pressures and from them, developing vapor pressure correlations suitable for use in advanced pyrolysis models (those models which explicitly account for mass transport limitations). This report is divided into five main chapters. Each chapter is a relatively stand-alone section. Chapter A reviews the general nature of coal tars and gives a summary of existing vapor pressure correlations for coal tars and model compounds. Chapter B summarizes the main experimental approaches for coal tar preparation and characterization which have been used throughout the project. Chapter C is concerned with the selection of the model compounds for coal pyrolysis tars and reviews the data available to us on the vapor pressures of high boiling point aromatic compounds. This chapter also deals with the question of identifying factors that govern the vapor pressures of coal tar model materials and their mixtures. Chapter D covers the vapor pressures and heats of vaporization of primary cellulose tars. Chapter E discusses the results of the main focus of this study. In summary, this work provides improved understanding of the volatility of coal and cellulose pyrolysis tars. It has resulted in new experimentally verified vapor pressure correlations for use in pyrolysis models. Further research on this topic should aim at developing general vapor pressure correlations for all coal tars, based on their molecular weight together with certain specific chemical characteristics i.e. hydroxyl group content.
2. Saturated Vapour Pressure and Refrigeration - Part I
ERIC Educational Resources Information Center
Bunker, C. A.
1973-01-01
The first part of a two-part article describes an experimental approach that can be used in teaching the concept of saturated vapour pressure. This leads to a discussion of refrigeration cycles in the second part of the article. (JR)
3. Enthalpy of Vaporization and Vapor Pressures: An Inexpensive Apparatus
Battino, Rubin; Dolson, David A.; Hall, Michael R.; Letcher, Trevor M.
2007-05-01
An inexpensive apparatus is described for the determination of the vapor pressure of a liquid as a function of temperature for the purpose of calculating enthalpy changes of vaporization. The solid-state pressure transducer is linear above 100 torr, is useful in the range -40 to 85 C, and is calibrated using pure water. The experimental enthalpies of vaporization for ten solvents are within ca. 0 to 13% of literature values. Two different versions of the static vapor pressure apparatus are described. Also described are a simple air thermostat and an inexpensive temperature controller (0.1 K) based on an integrated temperature sensor. The measurement time is under three hours.
4. Investigation on high temperature vapor pressure of UO 2 containing simulated fission-product elements
Yano, T.; Ohtsubo, A.; Ishii, T.
1984-06-01
During the hypothetical core disruptive accident (HCDA) of a fast breeder reactor (FBR), the temperature of the fuel would rise above 3000 K. The experimental data concerning the saturated fuel vapor pressure are necessary for the analysis of the HCDA. In this study, the UO 2 containing Cs, Ba, Ag, or Sn was used to simulate the irradiated fuel in the FBR. The saturated vapor pressure of pure UO 2 and UO 2 containing Cs, Ba, Ag, or Sn at 3000 to 5000 K was measured dynamically with a pulse laser and a torsion pendulum. The surface of a specimen on the pendulum was heated to eject vapor by the injection of a giant pulse ruby laser beam. The pressure of the ejected vapor was measured by both the maximum rotation angle of the pendulum and the duration of vapor ejection. The saturated vapor pressure was theoretically calculated by using the ejected vapor pressure. The surface temperature of the specimen was estimated from the irradiated energy density measured with a laser energy meter. The saturated vapor pressure of UO 2 at 3640 to 5880 K measured in this study was near the extrapolated value of Ackermann's low temperature data. The vapor pressure of UO 2 containing Cs, Ba, Ag or Sn was higher than that of UO 2. The saturated vapor pressure of UO 2 and a solid fission products system was calculated by using these experimental data.
5. 40 CFR 796.1950 - Vapor pressure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 32 2011-07-01 2011-07-01 false Vapor pressure. 796.1950 Section 796.1950 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) TOXIC SUBSTANCES CONTROL ACT (CONTINUED) CHEMICAL FATE TESTING GUIDELINES Physical and Chemical Properties § 796.1950 Vapor pressure. (a) Introduction—(1) Background...
6. An Interpolation Method for Obtaining Thermodynamic Properties Near Saturated Liquid and Saturated Vapor Lines
NASA Technical Reports Server (NTRS)
Nguyen, Huy H.; Martin, Michael A.
2004-01-01
The two most common approaches used to formulate thermodynamic properties of pure substances are fundamental (or characteristic) equations of state (Helmholtz and Gibbs functions) and a piecemeal approach that is described in Adebiyi and Russell (1992). This paper neither presents a different method to formulate thermodynamic properties of pure substances nor validates the aforementioned approaches. Rather its purpose is to present a method to generate property tables from existing property packages and a method to facilitate the accurate interpretation of fluid thermodynamic property data from those tables. There are two parts to this paper. The first part of the paper shows how efficient and usable property tables were generated, with the minimum number of data points, using an aerospace industry standard property package. The second part describes an innovative interpolation technique that has been developed to properly obtain thermodynamic properties near the saturated liquid and saturated vapor lines.
7. Multicomponent fuel vaporization at high pressures.
SciTech Connect
Torres, D. J.; O'Rourke, P. J.
2002-01-01
We extend our multicomponent fuel model to high pressures using a Peng-Robinson equation of state, and implement the model into KIVA-3V. Phase equilibrium is achieved by equating liquid and vapor fugacities. The latent heat of vaporization and fuel enthalpies are also corrected for at high pressures. Numerical simulations of multicomponent evaporation are performed for single droplets for a diesel fuel surrogate at different pressures.
8. The vapor pressure of iron pentacarbonyl
NASA Technical Reports Server (NTRS)
Gilbert, A. G.; Sulzmann, K. G. P.
1974-01-01
Vapor pressure measurements have been made on pure iron pentacarbonyl between +31 and -19 C. The experimental results may be expressed by the logarithm of pressure (mm Hg) to the base 10 equals -(2096.7 K/T) + 8.4959, which corresponds to a heat of vaporization for the liquid carbonyl of delta H ? (9.588 plus or minus 0.12) kcal/mole. This result confirms and extends the earlier measurements made by Trautz and Badstuebner between 0 and 140 C. The need for careful purification of commercially available iron pentacarbonyl is emphasized, particularly for establishing the correct vapor pressure below 45 C.
9. Predicting vapor pressures using neural networks
Potukuchi, Sudhakar; Wexler, Anthony S.
Calculating surface vapor pressures of volatile inorganic components, nitric acid, hydrochloric acid and ammonia, is essential for modeling condensation and evaporation processes occurring in atmospheric aerosols. The vapor pressure of these compounds depends on temperature, relative humidity, phase state, and particle composition, and their calculation consumes an enormous amount of computer time in Eulerian photochemical/aerosol models. Here we use a thermodynamic model to generate a large set of vapor pressure data as a function of aerosol composition, relative humidity, and temperature. These data are then used as a training set for neural networks. Once the networks memorize the data, interpolation of vapor pressures for intermediate compositions, temperatures and relative humidities is automatic. The neural network models are able to reproduce the values predicted by the thermodynamic models accurately and are 4-1200 times faster depending on atmospheric conditions and the assumptions employed in the thermodynamic calculations.
10. Vapor pressure and thermodynamics of actinide metals
SciTech Connect
Ward, J.W.; Kleinschmidt, P.D.; Haire, R.G.; Brown, D.
1980-01-01
Precise vapor pressure measurements by target collection/mass spectrometric Knudsen effusion techniques were combined with crystal entropy estimates to produce self-consistent free-enrgy functions, permitting calculation of heats, entropies and free energies from 298/sup 0/K to the highest temperatures of measurement. The vapor pressures and thermodyamics of vaporization of americium, curium, berkelium, and californium are compared in terms of electronic structure and bonding trends in the trans-plutonium elements. These resuslts are contrasted with the behavior of the early actinides, with attention to energy states and possible effects of f-electron bonding. 9 figures, 4 tables.
11. An Interpolation Method for Obtaining Thermodynamic Properties Near Saturated Liquid and Saturated Vapor Lines
NASA Technical Reports Server (NTRS)
Nguyen, Huy H.; Martin, Michael A.
2003-01-01
The availability and proper utilization of fluid properties is of fundamental importance in the process of mathematical modeling of propulsion systems. Real fluid properties provide the bridge between the realm of pure analytiis and empirical reality. The two most common approaches used to formulate thermodynamic properties of pure substances are fundamental (or characteristic) equations of state (Helmholtz and Gibbs functions) and a piecemeal approach that is described, for example, in Adebiyi and Russell (1992). This paper neither presents a different method to formulate thermodynamic properties of pure substances nor validates the aforementioned approaches. Rather its purpose is to present a method to be used to facilitate the accurate interpretation of fluid thermodynamic property data generated by existing property packages. There are two parts to this paper. The first part of the paper shows how efficient and usable property tables were generated, with the minimum number of data points, using an aerospace industry standard property package (based on fundamental equations of state approach). The second part describes an innovative interpolation technique that has been developed to properly obtain thermodynamic properties near the saturated liquid and saturated vapor lines.
12. Melt-vapor phase transition in the lead-selenium system at atmospheric and low pressure
Volodin, V. N.; Burabaeva, N. M.; Trebukhov, S. A.
2016-03-01
The boiling temperature and the corresponding vapor phase composition in the existence domain of liquid solutions were calculated from the partial pressures of saturated vapor of the components and lead selenide over liquid melts in the lead-selenium system. The phase diagram was complemented with the liquid-vapor phase transition at atmospheric pressure and in vacuum of 100 Pa, which allowed us to judge the behavior of the components during the distillation separation.
13. Clausius-Clapeyron Equation and Saturation Vapour Pressure: Simple Theory Reconciled with Practice
ERIC Educational Resources Information Center
Koutsoyiannis, Demetris
2012-01-01
While the Clausius-Clapeyron equation is very important as it determines the saturation vapour pressure, in practice it is replaced by empirical, typically Magnus-type, equations which are more accurate. It is shown that the reduced accuracy reflects an inconsistent assumption that the latent heat of vaporization is constant. Not only is this
14. Clausius-Clapeyron Equation and Saturation Vapour Pressure: Simple Theory Reconciled with Practice
ERIC Educational Resources Information Center
Koutsoyiannis, Demetris
2012-01-01
While the Clausius-Clapeyron equation is very important as it determines the saturation vapour pressure, in practice it is replaced by empirical, typically Magnus-type, equations which are more accurate. It is shown that the reduced accuracy reflects an inconsistent assumption that the latent heat of vaporization is constant. Not only is this…
15. 40 CFR 796.1950 - Vapor pressure.
Code of Federal Regulations, 2012 CFR
2012-07-01
...) “Pascal” (Pa) is the standard international unit of vapor pressure and is defined as newtons per square meter (N/m2). A newton is the force necessary to give acceleration of one meter per second squared to one kilogram of mass. (iii) The “torr” is a unit of pressure which equals 133.3 pascals or 1 mm Hg...
16. Vapor pressures of acetylene at low temperatures
NASA Technical Reports Server (NTRS)
Masterson, C. M.; Allen, John E., Jr.; Kraus, G. F.; Khanna, R. K.
1990-01-01
The atmospheres of many of the outer planets and their satellites contain a large number of hydrocarbon species. In particular, acetylene (C2H2) has been identified at Jupiter, Saturn and its satellite Titan, Uranus and Neptune. In the lower atmospheres of these planets, where colder temperatures prevail, the condensation and/or freezing of acetylene is probable. In order to obtain accurate models of the acetylene in these atmospheres, it is necessary to have a complete understanding of its vapor pressures at low temperatures. Vapor pressures at low temperatures for acetylene are being determined. The vapor pressures are measured with two different techniques in order to cover a wide range of temperatures and pressures. In the first, the acetylene is placed in a sample tube which is immersed in a low temperature solvent/liquid nitrogen slush bath whose temperature is measured with a thermocouple. The vapor pressure is then measured directly with a capacitance manometer. For lower pressures, a second technique which was called the thin-film infrared method (TFIR) was developed. It involves measuring the disappearance rate of a thin film of acetylene at a particular temperature. The spectra are then analyzed using previously determined extinction coefficient values, to determine the disappearance rate R (where R = delta n/delta t, the number of molecules that disappear per unit time). This can be related to the vapor pressure directly. This technique facilitates measurement of the lower temperatures and pressures. Both techniques have been calibrated using CO2, and have shown good agreement with the existing literature data.
17. Vapor pressures of the aqueous desiccants
SciTech Connect
Chung, T.W.; Luo, C.M.
1999-09-01
The vapor pressures of the aqueous desiccants lithium chloride, lithium bromide, calcium chloride, ethylene glycol, propylene glycol, and their mixtures were measured at their typical operating concentrations and at temperatures from 298 K to 313 K. The experimental data were fitted to an Antoine type of equation, ln[P(kPa)] = A {minus} B/[T(K) + C], where A, B, and C are constants and are concentration dependent. Vapor pressure data were further used to predict the effectiveness of dehumidification in liquid desiccant dehumidifiers.
18. Toward Carbon Dioxide Vapor-Pressure Thermometer
Dogan, A. Kartal; Bonnier, G.; Uytun, A.; Kocas, I.; Durgut, Y.
2011-12-01
The Temperature Group Laboratory of the National Metrology Institute of Turkey (TUBITAK UME) has realized the scale in the range from the argon triple point (83.8058 K) to the copper freezing point (1357.77 K) and also constructed the International Temperature Scale of 1990 (ITS-90) defining fixed points (Preston-Thomas, Metrologia 27, 3 (1990)). The scale is realized in the low-temperature sub-range by interpolation between the triple points of water, mercury, and argon. The calibration of thermometers below the temperature of the triple point of mercury requires the realization of the argon triple point. Since calibration laboratories are asking for references down to -60 C, a triple point of carbon dioxide (CO2) gives this opportunity to be used as a secondary fixed point. Another aim of this work is to study the ability of CO2 vapor pressure to realize a vapor-pressure thermometer for covering the range from 216 K up to room temperature. This realization is intended to provide an approximation of the international temperature scale in this temperature range. The vapor-pressure thermometer is intended to be assessed by using the triple point of carbon dioxide and by measuring the pressure values at the temperatures of the triple points of mercury and water. Realization of the triple-point temperature of carbon dioxide and the development of the vapor-pressure thermometer will be investigated and presented in this article.
19. MISTING OF LOW VAPOR PRESSURE HALOCARBONS
EPA Science Inventory
The paper gives results of a laboratory-scale study of the use of misting systems to provide total-flood fire protection with lower vapor pressure halocarbons. (NOTE: Several candidate Halon 1301 replacements with a low ozone-depletion potential have higher boiling points (usuall...
20. Heating of a fully saturated darcian half-space: Pressure generation, fluid expulsion, and phase change
USGS Publications Warehouse
Delaney, P.
1984-01-01
Analytical solutions are developed for the pressurization, expansion, and flow of one- and two-phase liquids during heating of fully saturated and hydraulically open Darcian half-spaces subjected to a step rise in temperature at its surface. For silicate materials, advective transfer is commonly unimportant in the liquid region; this is not always the case in the vapor region. Volume change is commonly more important than heat of vaporization in determining the position of the liquid-vapor interface, assuring that the temperatures cannot be determined independently of pressures. Pressure increases reach a maximum near the leading edge of the thermal front and penetrate well into the isothermal region of the body. Mass flux is insensitive to the hydraulic properties of the half-space. ?? 1984.
1. Vapor Pressure, Vapor Composition and Fractional Vaporization of High Temperature Lavas on Io
NASA Technical Reports Server (NTRS)
Fegley, B., Jr.; Schaefer, L.; Kargel, J. S.
2003-01-01
Observations show that Io's atmosphere is dominated by SO2 and other sulfur and sulfur oxide species, with minor amounts of Na, K, and Cl gases. Theoretical modeling and recent observations show that NaCl, which is produced volcanically, is a constituent of the atmosphere. Recent Galileo, HST and ground-based observations show that some volcanic hot spots on Io have extremely high temperatures, in the range 1400-1900 K. At similar temperatures in laboratory experiments, molten silicates and oxides have significant vapor pressures of Na, K, SiO, Fe, Mg, and other gases. Thus vaporization of these species from high temperature lavas on Io seems likely. We therefore modeled the vaporization of silicate and oxide lavas suggested for Io. Our results for vapor chemistry are reported here. The effects of fractional vaporization on lava chemistry are given in a companion abstract by Kargel et al.
2. On the propagation of a coupled saturation and pressure front
SciTech Connect
Vasco, D. W.
2010-12-01
Using an asymptotic technique, valid for a medium with smoothly varying heterogeneity, I derive an expression for the velocity of a propagating, coupled saturation and pressure front. Due to the nonlinearity of the governing equations, the velocity of the propagating front depends upon the magnitude of the saturation and pressure changes across the front in addition to the properties of the medium. Thus, the expression must be evaluated in conjunction with numerical reservoir simulation. The propagation of the two-phase front is governed by the background saturation distribution, the saturation-dependent component of the fluid mobility, the porosity, the permeability, the capillary pressure function, the medium compressibility, and the ratio of the slopes of the relative permeability curves. Numerical simulation of water injection into a porous layer saturated with a nonaqueous phase liquid indicates that two modes of propagation are important. The fastest mode of propagation is a pressure-dominated disturbance that travels through the saturated layer. This is followed, much later, by a coupled mode with a large saturation change. These two modes are also observed in a simulation using a heterogeneous porous layer. A comparison between the propagation times estimated from the results of the numerical simulation and predictions from the asymptotic expression indicates overall agreement.
3. Oxidation of trichloroethylene, toluene, and ethanol vapors by a partially saturated permeable reactive barrier
Mahmoodlu, Mojtaba G.; Hassanizadeh, S. Majid; Hartog, Niels; Raoof, Amir
2014-08-01
The mitigation of volatile organic compound (VOC) vapors in the unsaturated zone largely relies on the active removal of vapor by ventilation. In this study we considered an alternative method involving the use of solid potassium permanganate to create a horizontal permeable reactive barrier for oxidizing VOC vapors. Column experiments were carried out to investigate the oxidation of trichloroethylene (TCE), toluene, and ethanol vapors using a partially saturated mixture of potassium permanganate and sand grains. Results showed a significant removal of VOC vapors due to the oxidation. We found that water saturation has a major effect on the removal capacity of the permeable reactive layer. We observed a high removal efficiency and reactivity of potassium permanganate for all target compounds at the highest water saturation (Sw = 0.6). A change in pH within the reactive layer reduced oxidation rate of VOCs. The use of carbonate minerals increased the reactivity of potassium permanganate during the oxidation of TCE vapor by buffering the pH. Reactive transport of VOC vapors diffusing through the permeable reactive layer was modeled, including the pH effect on the oxidation rates. The model accurately described the observed breakthrough curve of TCE and toluene vapors in the headspace of the column. However, miscibility of ethanol in water in combination with produced water during oxidation made the modeling results less accurate for ethanol. A linear relationship was found between total oxidized mass of VOC vapors per unit volume of permeable reactive layer and initial water saturation. This behavior indicates that pH changes control the overall reactivity and longevity of the permeable reactive layer during oxidation of VOCs. The results suggest that field application of a horizontal permeable reactive barrier can be a viable technology against upward migration of VOC vapors through the unsaturated zone.
4. Oxidation of trichloroethylene, toluene, and ethanol vapors by a partially saturated permeable reactive barrier.
PubMed
Mahmoodlu, Mojtaba G; Hassanizadeh, S Majid; Hartog, Niels; Raoof, Amir
2014-08-01
The mitigation of volatile organic compound (VOC) vapors in the unsaturated zone largely relies on the active removal of vapor by ventilation. In this study we considered an alternative method involving the use of solid potassium permanganate to create a horizontal permeable reactive barrier for oxidizing VOC vapors. Column experiments were carried out to investigate the oxidation of trichloroethylene (TCE), toluene, and ethanol vapors using a partially saturated mixture of potassium permanganate and sand grains. Results showed a significant removal of VOC vapors due to the oxidation. We found that water saturation has a major effect on the removal capacity of the permeable reactive layer. We observed a high removal efficiency and reactivity of potassium permanganate for all target compounds at the highest water saturation (Sw=0.6). A change in pH within the reactive layer reduced oxidation rate of VOCs. The use of carbonate minerals increased the reactivity of potassium permanganate during the oxidation of TCE vapor by buffering the pH. Reactive transport of VOC vapors diffusing through the permeable reactive layer was modeled, including the pH effect on the oxidation rates. The model accurately described the observed breakthrough curve of TCE and toluene vapors in the headspace of the column. However, miscibility of ethanol in water in combination with produced water during oxidation made the modeling results less accurate for ethanol. A linear relationship was found between total oxidized mass of VOC vapors per unit volume of permeable reactive layer and initial water saturation. This behavior indicates that pH changes control the overall reactivity and longevity of the permeable reactive layer during oxidation of VOCs. The results suggest that field application of a horizontal permeable reactive barrier can be a viable technology against upward migration of VOC vapors through the unsaturated zone. PMID:24992709
5. Pore scale mechanisms for enhanced vapor transport through partially saturated porous media
Shahraeeni, Ebrahim; Or, Dani
2012-05-01
Recent theoretical and experimental studies of vapor transport through porous media question the existence and significance of vapor transport enhancement mechanisms postulated by Philip and de Vries. Several enhancement mechanisms were proposed to rectify shortcomings of continuum models and to reconcile discrepancies between predicted and observed vapor fluxes. The absence of direct experimental and theoretical confirmation of these commonly invoked pore scale mechanisms prompted alternate explanations considering the (often neglected) role of transport via capillary connected pathways. The objective of this work was to quantify the specific roles of liquid bridges and of local thermal and capillary gradients on vapor transport at the pore scale. We considered a mechanistic pore scale model of evaporation and condensation dynamics as a building block for quantifying vapor diffusion through partially saturated porous media. Simulations of vapor diffusion in the presence of isolated liquid phase bridges reveal that the so-called enhanced vapor diffusion under isothermal conditions reflects a reduced gaseous diffusion path length. The presence of a thermal gradient may augment or hinder this effect depending on the direction of thermal relative to capillary gradients. As liquid phase saturation increases, capillary transport becomes significant and pore scale vapor enhancement is limited to low water contents as postulated by Philip and deVries. Calculations show that with assistance of a mild thermal gradient water vapor flux could be doubled relative to diffusion of an inert gas through the same system.
6. Notes on Vapor Pressure Equilibria Measurements
Krieger, Albert G.; Henderson, John W.
1996-11-01
After reading the article in this Journal (1), we would like to share our experience with a similar experiment based on an earlier article in this Journal (2). Freshman students at our institution use manometers and 24/40 ground-glass distillation apparatus (abandoned by our organic chemistry classes) to measure boiling points at reduced pressures. Distilled water and 2-methyl-1-propanol are typical liquids of interest. Students enter their collected data into an Excel template which generates graphs of P vs. T and log P vs 1/T to demonstrate the nonlinear and linear relationships that exist between vapor pressures and temperatures. The templates use the Clausius-Clapeyron equation to determine the normal boiling point and the enthalpy of vaporization of the liquid studies. The boiling point determined for water is 100 oC and for 2-methyl-1-propanol is 106 oC, within 2 o of the CRC Handbook data. We have found that the availability of state-of-the-art equipment need not limit the ability to teach and demonstrate fundamental principles. The Excel template (Macintosh) is available upon request domestically and for the cost of international postage for others. Literature Cited 1. Kidahl, N.; Berka, L. H. J. Chem. Educ. 1995, 72, 258. 2. Schaber, P. M. J. Chem. Educ. 1985, 62, 345.
7. 46 CFR 154.451 - Design vapor pressure.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 5 2010-10-01 2010-10-01 false Design vapor pressure. 154.451 Section 154.451 Shipping... FOR SELF-PROPELLED VESSELS CARRYING BULK LIQUEFIED GASES Design, Construction and Equipment Independent Tank Type C and Process Pressure Vessels § 154.451 Design vapor pressure. The Po (kPa) of...
8. 46 CFR 154.451 - Design vapor pressure.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 5 2011-10-01 2011-10-01 false Design vapor pressure. 154.451 Section 154.451 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type C and Process Pressure Vessels § 154.451 Design vapor pressure. The Po (kPa) of...
9. 46 CFR 154.451 - Design vapor pressure.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 5 2012-10-01 2012-10-01 false Design vapor pressure. 154.451 Section 154.451 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type C and Process Pressure Vessels § 154.451 Design vapor pressure. The Po (kPa) of...
10. 46 CFR 154.451 - Design vapor pressure.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 5 2013-10-01 2013-10-01 false Design vapor pressure. 154.451 Section 154.451 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type C and Process Pressure Vessels § 154.451 Design vapor pressure. The Po (kPa) of...
11. 46 CFR 154.451 - Design vapor pressure.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 5 2014-10-01 2014-10-01 false Design vapor pressure. 154.451 Section 154.451 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type C and Process Pressure Vessels § 154.451 Design vapor pressure. The Po (kPa) of...
12. Fuel Vapor Pressures and the Relation of Vapor Pressure to the Preparation of Fuel for Combustion in Fuel Injection Engines
NASA Technical Reports Server (NTRS)
Joachim, William F; Rothrock, A M
1930-01-01
This investigation on the vapor pressure of fuels was conducted in connection with the general research on combustion in fuel injection engines. The purpose of the investigation was to study the effects of high temperatures such as exist during the first stages of injection on the vapor pressures of several fuels and certain fuel mixtures, and the relation of these vapor pressures to the preparation of the fuel for combustion in high-speed fuel injection engines.
13. Coal reservoir saturation: Impact of temperature and pressure
SciTech Connect
Bustin, A.M.M.; Bustin, R.M.
2008-01-15
Methane adsorption isotherms measured for a series of coals with varying rank at a wide range of temperatures and pressures allows the prediction of the change in sorption capacity as a function of tectonic history. Changes in sorption capacity in response to declining pressure and temperature associated with uplift may increase or decrease the capacity of the coal and, if the coal is initially saturated, result in excess gas or a deficiency of gas (undersaturation). Assuming reasonable geothermal and pressure gradients, our data indicate that the sorption capacity will generally decrease with uplift and associated exhumation, suggesting that an initially gas-saturated coal will desorb gas during uplift of the reservoir. The desorbed gas would be available for migration and/or, potentially, resaturation of an undersaturated coal. Our results argue against the generally accepted theory that undersaturation of coal reservoirs results from an increase in the sorption capacity with uplift except for coals at such high pressures that the isotherms are essentially flat or for very high pressure and geothermal gradients.
14. 46 CFR 154.438 - Design vapor pressure.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 5 2010-10-01 2010-10-01 false Design vapor pressure. 154.438 Section 154.438 Shipping... FOR SELF-PROPELLED VESSELS CARRYING BULK LIQUEFIED GASES Design, Construction and Equipment Independent Tank Type A § 154.438 Design vapor pressure. (a) If the surface of an independent tank type A...
15. 46 CFR 154.426 - Design vapor pressure.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 5 2010-10-01 2010-10-01 false Design vapor pressure. 154.426 Section 154.426 Shipping... FOR SELF-PROPELLED VESSELS CARRYING BULK LIQUEFIED GASES Design, Construction and Equipment Membrane Tanks § 154.426 Design vapor pressure. The Po of a membrane tank must not exceed 24.5 kPa gauge...
16. 46 CFR 154.436 - Design vapor pressure.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 5 2010-10-01 2010-10-01 false Design vapor pressure. 154.436 Section 154.436 Shipping... FOR SELF-PROPELLED VESSELS CARRYING BULK LIQUEFIED GASES Design, Construction and Equipment Semi-Membrane Tanks § 154.436 Design vapor pressure. The Po of a semi-membrane tank must not exceed 24.5...
17. 46 CFR 154.419 - Design vapor pressure.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 5 2010-10-01 2010-10-01 false Design vapor pressure. 154.419 Section 154.419 Shipping... FOR SELF-PROPELLED VESSELS CARRYING BULK LIQUEFIED GASES Design, Construction and Equipment Integral Tanks § 154.419 Design vapor pressure. The Po of an integral tank must not exceed 24.5 kPa gauge...
18. 46 CFR 154.445 - Design vapor pressure.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 5 2010-10-01 2010-10-01 false Design vapor pressure. 154.445 Section 154.445 Shipping... FOR SELF-PROPELLED VESSELS CARRYING BULK LIQUEFIED GASES Design, Construction and Equipment Independent Tank Type B § 154.445 Design vapor pressure. If the surfaces of an independent tank type B...
19. 46 CFR 154.445 - Design vapor pressure.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 5 2014-10-01 2014-10-01 false Design vapor pressure. 154.445 Section 154.445 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type B § 154.445 Design vapor pressure. If the surfaces of an independent tank type B...
20. 46 CFR 154.438 - Design vapor pressure.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 5 2014-10-01 2014-10-01 false Design vapor pressure. 154.438 Section 154.438 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type A § 154.438 Design vapor pressure. (a) If the surface of an independent tank type A...
1. 46 CFR 154.438 - Design vapor pressure.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 5 2011-10-01 2011-10-01 false Design vapor pressure. 154.438 Section 154.438 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type A § 154.438 Design vapor pressure. (a) If the surface of an independent tank type A...
2. 46 CFR 154.419 - Design vapor pressure.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 5 2013-10-01 2013-10-01 false Design vapor pressure. 154.419 Section 154.419 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Tanks § 154.419 Design vapor pressure. The Po of an integral tank must not exceed 24.5 kPa gauge...
3. 46 CFR 154.436 - Design vapor pressure.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 5 2012-10-01 2012-10-01 false Design vapor pressure. 154.436 Section 154.436 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS...-Membrane Tanks § 154.436 Design vapor pressure. The Po of a semi-membrane tank must not exceed 24.5...
4. 46 CFR 154.438 - Design vapor pressure.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 5 2013-10-01 2013-10-01 false Design vapor pressure. 154.438 Section 154.438 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type A § 154.438 Design vapor pressure. (a) If the surface of an independent tank type A...
5. 46 CFR 154.436 - Design vapor pressure.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 5 2014-10-01 2014-10-01 false Design vapor pressure. 154.436 Section 154.436 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS...-Membrane Tanks § 154.436 Design vapor pressure. The Po of a semi-membrane tank must not exceed 24.5...
6. 46 CFR 154.419 - Design vapor pressure.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 5 2012-10-01 2012-10-01 false Design vapor pressure. 154.419 Section 154.419 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Tanks § 154.419 Design vapor pressure. The Po of an integral tank must not exceed 24.5 kPa gauge...
7. 46 CFR 154.426 - Design vapor pressure.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 5 2011-10-01 2011-10-01 false Design vapor pressure. 154.426 Section 154.426 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Tanks § 154.426 Design vapor pressure. The Po of a membrane tank must not exceed 24.5 kPa gauge...
8. 46 CFR 154.419 - Design vapor pressure.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 5 2011-10-01 2011-10-01 false Design vapor pressure. 154.419 Section 154.419 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Tanks § 154.419 Design vapor pressure. The Po of an integral tank must not exceed 24.5 kPa gauge...
9. 46 CFR 154.419 - Design vapor pressure.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 5 2014-10-01 2014-10-01 false Design vapor pressure. 154.419 Section 154.419 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Tanks § 154.419 Design vapor pressure. The Po of an integral tank must not exceed 24.5 kPa gauge...
10. 46 CFR 154.445 - Design vapor pressure.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 5 2011-10-01 2011-10-01 false Design vapor pressure. 154.445 Section 154.445 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type B § 154.445 Design vapor pressure. If the surfaces of an independent tank type B...
11. 46 CFR 154.436 - Design vapor pressure.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 5 2011-10-01 2011-10-01 false Design vapor pressure. 154.436 Section 154.436 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS...-Membrane Tanks § 154.436 Design vapor pressure. The Po of a semi-membrane tank must not exceed 24.5...
12. 46 CFR 154.438 - Design vapor pressure.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 5 2012-10-01 2012-10-01 false Design vapor pressure. 154.438 Section 154.438 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type A § 154.438 Design vapor pressure. (a) If the surface of an independent tank type A...
13. 46 CFR 154.426 - Design vapor pressure.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 5 2014-10-01 2014-10-01 false Design vapor pressure. 154.426 Section 154.426 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Tanks § 154.426 Design vapor pressure. The Po of a membrane tank must not exceed 24.5 kPa gauge...
14. 46 CFR 154.445 - Design vapor pressure.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 5 2013-10-01 2013-10-01 false Design vapor pressure. 154.445 Section 154.445 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type B § 154.445 Design vapor pressure. If the surfaces of an independent tank type B...
15. 46 CFR 154.426 - Design vapor pressure.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 5 2013-10-01 2013-10-01 false Design vapor pressure. 154.426 Section 154.426 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Tanks § 154.426 Design vapor pressure. The Po of a membrane tank must not exceed 24.5 kPa gauge...
16. 46 CFR 154.445 - Design vapor pressure.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 5 2012-10-01 2012-10-01 false Design vapor pressure. 154.445 Section 154.445 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Independent Tank Type B § 154.445 Design vapor pressure. If the surfaces of an independent tank type B...
17. 46 CFR 154.436 - Design vapor pressure.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 5 2013-10-01 2013-10-01 false Design vapor pressure. 154.436 Section 154.436 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS...-Membrane Tanks § 154.436 Design vapor pressure. The Po of a semi-membrane tank must not exceed 24.5...
18. 46 CFR 154.426 - Design vapor pressure.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 5 2012-10-01 2012-10-01 false Design vapor pressure. 154.426 Section 154.426 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) CERTAIN BULK DANGEROUS CARGOES SAFETY STANDARDS... Tanks § 154.426 Design vapor pressure. The Po of a membrane tank must not exceed 24.5 kPa gauge...
19. Thermogravimetric study of vapor pressure of TATP synthesized without recrystallization.
PubMed
Mbah, Jonathan; Knott, Debra; Steward, Scott
2014-11-01
This study aims at characterizing the vapor pressure signatures generated by triacetone triperoxide (TATP) that was synthesized without recrystallization by thermogravimmetric analysis (TGA) for exploitation by standoff detection technologies of explosive devices. The thermal behavior of the nonrecrystallized sample was compared with reported values. Any phase change, melting point and decomposition identification were studied by differential scanning calorimeter. Vapor pressures were estimated by the Langmuir method of evaporation from an open surface in a vacuum. Vapor pressures of TATP at different temperatures were calculated using the linear logarithmic relationship obtained from benzoic acid reference standard. Sublimation of TATP was found to follow apparent zero-order kinetics and sublimes at steady rates at 298 K and above. While the enthalpy of sublimation found, 71.7 kJ mol(-1), is in agreement with reported values the vapor pressures deviated significantly. The differences in the vapor pressures behavior are attributable to the synthesis pathway chosen in this study. PMID:25127637
20. Experimental critical constants, vapor pressures, and vapor and liquid densities for pentafluoroethane (R-125)
SciTech Connect
Duarte-Garza, H.A.; Stouffer, C.E.; Hall, K.R.; Holste, J.C.; Marsh, K.N.; Gammon, B.E.
1997-07-01
This paper presents measurements of vapor pressure from 220 K to 338 K, liquid density from 180 K to 350 K and up to 70 MPa and vapor density from 310 K to 480 K and up to 12 MPa for pentafluoroethane (R-125). Extrapolating the observed vapor pressures to the measured critical temperature (339.41 {+-} 0.01) K provides a critical pressure of (3.6391 {+-} 0.002) MPa. Using these values with the law of rectilinear diameters indicates a critical density of (4,768{+-} 7) mol/m{sup 3}. Correlations provide values which agree with the measured values for the vapor densities within {+-}0.05%, the liquid densities within {+-}0.1%, and the vapor pressures within {+-}0.05%. The results are compared with values from the literature.
1. LOX vaporization in high-pressure, hydrogen-rich gas
NASA Technical Reports Server (NTRS)
Litchford, Ron J.; Jeng, San-Mou
1990-01-01
LOX droplet vaporization in high-pressure hydrogen-rich gas is analyzed, with special attention to thermodynamic effects which compel the surface to heat to the critical state and to supercritical vaporization processes on heating to criticality. Subcritical vaporization is modeled using a quasi-steady diffusion-controlled gas-phase transport formulation coupled to an effective-conductivity internal-energy-transport model accounting for circulation effects. It is demonstrated how the droplet surface might heat to the critical state, for ambient pressures slightly greater than the critical pressure of oxygen, such that the bulk of propellant within the droplet remains substantially below the critical mixing temperature.
2. Controlling the vapor pressure of a mercury lamp
DOEpatents
Grossman, Mark W. (Belmont, MA); George, William A. (Rockport, MA)
1988-01-01
The invention described herein discloses a method and apparatus for controlling the Hg vapor pressure within a lamp. This is done by establishing and controlling two temperature zones within the lamp. One zone is colder than the other zone. The first zone is called the cold spot. By controlling the temperature of the cold spot, the Hg vapor pressure within the lamp is controlled. Likewise, by controlling the Hg vapor pressure of the lamp, the intensity and linewidth of the radiation emitted from the lamp is controlled.
3. Controlling the vapor pressure of a mercury lamp
DOEpatents
Grossman, M.W.; George, W.A.
1988-05-24
The invention described herein discloses a method and apparatus for controlling the Hg vapor pressure within a lamp. This is done by establishing and controlling two temperature zones within the lamp. One zone is colder than the other zone. The first zone is called the cold spot. By controlling the temperature of the cold spot, the Hg vapor pressure within the lamp is controlled. Likewise, by controlling the Hg vapor pressure of the lamp, the intensity and linewidth of the radiation emitted from the lamp is controlled. 2 figs.
4. 46 CFR 30.10-59 - Reid vapor pressure-TB/ALL.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 1 2012-10-01 2012-10-01 false Reid vapor pressure-TB/ALL. 30.10-59 Section 30.10-59...-59 Reid vapor pressure—TB/ALL. The term Reid vapor pressure means the vapor pressure of a liquid at a....01-3), Method of Test for Vapor Pressure of Petroleum Products. This Standard is available...
5. 46 CFR 30.10-59 - Reid vapor pressure-TB/ALL.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false Reid vapor pressure-TB/ALL. 30.10-59 Section 30.10-59...-59 Reid vapor pressure—TB/ALL. The term Reid vapor pressure means the vapor pressure of a liquid at a....01-3), Method of Test for Vapor Pressure of Petroleum Products. This Standard is available...
6. 46 CFR 30.10-59 - Reid vapor pressure-TB/ALL.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 1 2014-10-01 2014-10-01 false Reid vapor pressure-TB/ALL. 30.10-59 Section 30.10-59...-59 Reid vapor pressure—TB/ALL. The term Reid vapor pressure means the vapor pressure of a liquid at a....01-3), Method of Test for Vapor Pressure of Petroleum Products. This Standard is available...
7. 46 CFR 30.10-59 - Reid vapor pressure-TB/ALL.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 1 2011-10-01 2011-10-01 false Reid vapor pressure-TB/ALL. 30.10-59 Section 30.10-59...-59 Reid vapor pressure—TB/ALL. The term Reid vapor pressure means the vapor pressure of a liquid at a....01-3), Method of Test for Vapor Pressure of Petroleum Products. This Standard is available...
8. 46 CFR 30.10-59 - Reid vapor pressure-TB/ALL.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 1 2013-10-01 2013-10-01 false Reid vapor pressure-TB/ALL. 30.10-59 Section 30.10-59...-59 Reid vapor pressure—TB/ALL. The term Reid vapor pressure means the vapor pressure of a liquid at a....01-3), Method of Test for Vapor Pressure of Petroleum Products. This Standard is available...
9. A Simple Experiment for Determining Vapor Pressure and Enthalpy of Vaporization of Water.
ERIC Educational Resources Information Center
Levinson, Gerald S.
1982-01-01
Laboratory procedures, calculations, and sample results are described for a freshman chemistry experiment in which the Clausius-Clapeyron equation is introduced as a means of describing the variation of vapor pressure with temperature and for determining enthalpy of vaporization. (Author/SK)
10. Using Dalton's Law of Partial Pressures to Determine the Vapor Pressure of a Volatile Liquid
ERIC Educational Resources Information Center
Hilgeman, Fred R.; Bertrand, Gary; Wilson, Brent
2007-01-01
This experiment, designed for a general chemistry laboratory, illustrates the use of Dalton's law of partial pressures to determine the vapor pressure of a volatile liquid. A predetermined volume of air is injected into a calibrated tube filled with a liquid whose vapor pressure is to be measured. The volume of the liquid displaced is greater than
11. Using Dalton's Law of Partial Pressures to Determine the Vapor Pressure of a Volatile Liquid
ERIC Educational Resources Information Center
Hilgeman, Fred R.; Bertrand, Gary; Wilson, Brent
2007-01-01
This experiment, designed for a general chemistry laboratory, illustrates the use of Dalton's law of partial pressures to determine the vapor pressure of a volatile liquid. A predetermined volume of air is injected into a calibrated tube filled with a liquid whose vapor pressure is to be measured. The volume of the liquid displaced is greater than…
12. Evidence of water vapor in excess of saturation in the atmosphere of Mars.
PubMed
Maltagliati, L; Montmessin, F; Fedorova, A; Korablev, O; Forget, F; Bertaux, J-L
2011-09-30
The vertical distribution of water vapor is key to the study of Mars' hydrological cycle. To date, it has been explored mainly through global climate models because of a lack of direct measurements. However, these models assume the absence of supersaturation in the atmosphere of Mars. Here, we report observations made using the SPICAM (Spectroscopy for the Investigation of the Characteristics of the Atmosphere of Mars) instrument onboard Mars Express that provide evidence of the frequent presence of water vapor in excess of saturation, by an amount far surpassing that encountered in Earth's atmosphere. This result contradicts the widespread assumption that atmospheric water on Mars cannot exist in a supersaturated state, directly affecting our long-term representation of water transport, accumulation, escape, and chemistry on a global scale. PMID:21960630
13. Structural rearrangements in a lamellar diblock copolymer thin film during treatment with saturated solvent vapor
PubMed Central
Di, Zhenyu; Posselt, Dorthe; Smilgies, Detlef-M.; Papadakis, Christine M.
2010-01-01
We have investigated the structural changes in thin films of lamellar poly(styrene-b-butadiene) diblock copolymers during treatment with saturated cyclohexane vapor, a solvent slightly selective for polybutadiene. Using real-time, in-situ grazing-incidence small-angle X-ray scattering (GISAXS), the swelling and the rearrangement of the lamellae were investigated with a time resolution of a few seconds, and the underlying processes on the molecular level were identified. After a few minutes in vapor, a transient state with a more well-defined and more long-range ordered lamellar orientation was encountered. Additional parallel lamellae formed which we attribute to the increased degree of coiling of the polymers in the swollen state. Eventually, the film became disordered. These changes are attributed to the increased mobility of the swollen polymers and the gradually decreasing segment-segment interaction parameter in the film as solvent is absorbed. PMID:20305742
14. Vapor pressures of a homologous series of polyethylene glycols as a reference data set for validating vapor pressure measurement techniques.
Krieger, Ulrich; Marcolli, Claudia; Siegrist, Franziska
2015-04-01
The production of secondary organic aerosol (SOA) by gas-to-particle partitioning is generally represented by an equilibrium partitioning model. A key physical parameter which governs gas-particle partitioning is the pure component vapor pressure, which is difficult to measure for low- and semivolatile compounds. For typical atmospheric compounds like e.g. citric acid or tartaric acid, vapor pressures have been reported in the literature which differ by up to six orders of magnitude [Huisman et al., 2013]. Here, we report vapor pressures of a homologous series of polyethylene glycols (triethylene glycol to octaethylene glycol) determined by measuring the evaporation rate of single, levitated aerosol particles in an electrodynamic balance. We propose to use those as a reference data set for validating different vapor pressure measurement techniques. With each addition of a (O-CH2-CH2)-group the vapor pressure is lowered by about one order of magnitude which makes it easy to detect the lower limit of vapor pressures accessible with a particular technique down to a pressure of 10-8 Pa at room temperature. Reference: Huisman, A. J., Krieger, U. K., Zuend, A., Marcolli, C., and Peter, T., Atmos. Chem. Phys., 13, 6647-6662, 2013.
15. 40 CFR 796.1950 - Vapor pressure.
Code of Federal Regulations, 2014 CFR
2014-07-01
... surface. Volatilization is an important source of material for airborne transport and may lead to the... adsorptivity onto solids, or high solubility in water are less likely to vaporize and become airborne than... during the course of the test. (2) Definitions and units. (i) “Desorption efficiency” of a...
16. Subatmospheric vapor pressures evaluated from internal-energy measurements
Duarte-Garza, H. A.; Magee, J. W.
1997-01-01
Vapor pressures were evaluated from measured internal-energy changes in the vapor+liquid two-phase region, ? U (2). The method employed a thermodynamic relationship between the derivative quantity (? U (2)/? V) T and the vapor pressure ( p ?) and its temperature derivative (? p/? T)?. This method was applied at temperatures between the triple point and the normal boiling point of three substances: 1,1,1,2-tetrafluoroethane (R134a), pentafluoroethane (R125), and difluoromethane (R32). Agreement with experimentally measured vapor pressures near the normal boiling point (101.325 kPa) was within the experimental uncertainty of approximately 0.04 kPa (0.04%). The method was applied to R134a to test the thermodynamic consistency of a published p-p-T equation of state with an equation for p ? for this substance. It was also applied to evaluate published p ? data which are in disagreement by more than their claimed uncertainty.
17. Electronic absorption band broadening and surface roughening of phthalocyanine double layers by saturated solvent vapor treatment
SciTech Connect
Kim, Jinhyun; Yim, Sanggyu
2012-10-15
Variations in the electronic absorption (EA) and surface morphology of three types of phthalocyanine (Pc) thin film systems, i.e. copper phthalocyanine (CuPc) single layer, zinc phthalocyanine (ZnPc) single layer, and ZnPc on CuPc (CuPc/ZnPc) double layer film, treated with saturated acetone vapor were investigated. For the treated CuPc single layer film, the surface roughness slightly increased and bundles of nanorods were formed, while the EA varied little. In contrast, for the ZnPc single layer film, the relatively high solubility of ZnPc led to a considerable shift in the absorption bands as well as a large increase in the surface roughness and formation of long and wide nano-beams, indicating a part of the ZnPc molecules dissolved in acetone, which altered their molecular stacking. For the CuPc/ZnPc film, the saturated acetone vapor treatment resulted in morphological changes in mainly the upper ZnPc layer due to the significantly low solubility of the underlying CuPc layer. The treatment also broadened the EA band, which involved a combination of unchanged CuPc and changed ZnPc absorption.
18. Extrapolation of the Goff-Gratch formula for vapor pressure of liquid water at temperatures below 0/sup 0/C
SciTech Connect
Detwiler, A.
1983-03-01
Indirect justification for extrapolating the Goff-Gratch formula for saturation vapor pressure over liquid water to temperatures as low as -60/sup 0/C has been obtained during a recent study of ice nucleation on aerosol particles in a laboratory cloud chamber.
19. Water-vapor pressure control in a volume
NASA Technical Reports Server (NTRS)
Scialdone, J. J.
1978-01-01
The variation with time of the partial pressure of water in a volume that has openings to the outside environment and includes vapor sources was evaluated as a function of the purging flow and its vapor content. Experimental tests to estimate the diffusion of ambient humidity through openings and to validate calculated results were included. The purging flows required to produce and maintain a certain humidity in shipping containers, storage rooms, and clean rooms can be estimated with the relationship developed here. These purging flows are necessary to prevent the contamination, degradation, and other effects of water vapor on the systems inside these volumes.
20. Evaporation rate and vapor pressure of selected polymeric lubricating oils.
NASA Technical Reports Server (NTRS)
Gardos, M. N.
1973-01-01
A recently developed ultrahigh-vacuum quartz spring mass sorption microbalance has been utilized to measure the evaporation rates of several low-volatility polymeric lubricating oils at various temperatures. The evaporation rates are used to calculate the vapor pressures by the Langmuir equation. A method is presented to accurately estimate extended temperature range evaporation rate and vapor pressure data for polymeric oils, incorporating appropriate corrections for the increases in molecular weight and the change in volatility of the progressively evaporating polymer fractions. The logarithms of the calculated data appear to follow linear relationships within the test temperature ranges, when plotted versus 1000/T. These functions and the observed effusion characteristics of the fluids on progressive volatilization are useful in estimating evaporation rate and vapor pressure changes on evaporative depletion.
1. Resonance ionization spectroscopy measurement of vapor pressure of rubidium iodide
SciTech Connect
Capelle, G.A.; Jessup, D.A.; Borella, H.M.; Franks, L.A.
1984-01-15
Resonance ionization spectroscopy has been used to measure vapor pressure data for a solid (RbI) to very low pressures. A pulsed UV laser was used to dissociate RbI molecules in the vapor phase established over a sample at known temperature. The rubidium atoms were then ionized by a two-step process using a dye laser tuned to either of two allowed transitions in the ground-state atomic Rb system. These measurements have extended the RbI vapor pressure versus temperature curve approximatelly 10 orders of magnitude below previously reported experimental data. Although this experiment is limited to RbI, the technique is applicable to a wide variety of solids, both atomic and molecular.
2. Sound propagation in saturated gas-vapor-droplet suspensions with droplet evaporation and nonlinear relaxation.
PubMed
Kandula, Max
2012-06-01
The Sound attenuation and dispersion in saturated gas-vapor-droplet mixture in the presence of evaporation has been investigated theoretically. The theory is based on an extension of the work of Davidson [J. Atmos. Sci. 32(11), 2201-2205 (1975)] to accommodate the effects of nonlinear particle relaxation processes of mass, momentum and energy transfer on sound attenuation and dispersion. The results indicate the existence of a spectral broadening effect in the attenuation coefficient (scaled with respect to the peak value) with a decrease in droplet mass concentration. It is further shown that for large values of the droplet concentration the scaled attenuation coefficient is characterized by a universal spectrum independent of droplet mass concentration. PMID:22713018
3. Ice Nucleation of Snomax Particles below Water Vapor Saturation: Immersion Freezing in Concentrated Solution Droplets
Kanji, Z. A.; Boose, Y.; Augustin, S.; Wex, H.
2014-12-01
Heterogeneous ice nucleation in the atmosphere is important and has received an increasing amount of interest in the past years, as it initiates the ice phase in mixed phase clouds and, to some extent, also in cirrus clouds. The presence of ice influences cloud radiative properties and, for mixed phase clouds, also the formation of precipitation and cloud lifetime. Immersion freezing has been in the focus of ice nucleation research in recent years. Here, we examine ice nucleation activity of biological ice nuclei (IN) derived from bacteria, namely of particles generated from a suspensions of Snomax, both above and below water vapor saturation. Measurements were done with PINC (Portable Ice Nucleus Counter, Chou et al., 2011) during a measurement campaign at LACIS (Leipzig Aerosol Cloud Interaction Simulator, see e.g. Wex et al., 2014) in Leipzig. Immersion freezing measurements from PINC and LACIS were in agreement in the temperature regime for which both instruments operate reliably. Here, we will show that measurements done below water vapor saturation follow what would be expected for immersion freezing in concentrated solutions, similar to what was suggested for coated kaolinite particles in Wex et al. (2014). Chou, C., O. Stetzer, E. Weingartner, Z. Juranyi, Z. A. Kanji, and U. Lohmann (2011), Ice nuclei properties within a Saharan dust event at the Jungfraujoch in the Swiss Alps, Atmos. Chem. Phys., 11(10), 4725-4738, doi:10.5194/acp-11-4725-2011. Wex, H., P. J. DeMott, Y. Tobo, S. Hartmann, M. Rsch, T. Clauss, L. Tomsche, D. Niedermeier, and F. Stratmann (2014), Kaolinite particles as ice nuclei: learning from the use of different kaolinite samples and different coatings, Atmos. Chem. Phys., 14, doi:10.5194/acp-14-5529-2014.
4. Microwave measurements of water vapor partial pressure at high temperatures
SciTech Connect
Latorre, V.R.
1991-02-01
One of the desired parameters in the Yucca Mountain Project is the capillary pressure of the rock comprising the repository. This parameter is related to the partial pressure of water vapor in the air when in equilibrium with the rock mass. Although there are a number of devices that will measure the relative humidity (directly related to the water vapor partial pressure), they generally will fail at temperatures on the order of 150C. Since thee author has observed borehole temperatures considerably in excess of this value in G-Tunnel at the Nevada Test Site (NTS), a different scheme is required to obtain the desired partial pressure data at higher temperatures. This chapter presents a microwave technique that has been developed to measure water vapor partial pressure in boreholes at temperatures up to 250C. The heart of the system is a microwave coaxial resonator whose resonant frequency is inversely proportional to the square root of the real part of the complex dielectric constant of the medium (air) filling the resonator. The real part of the dielectric constant of air is approximately equal to the square of the refractive index which, in turn, is proportional to the partial pressure of the water vapor in the air. Thus, a microwave resonant cavity can be used to measure changes in the relative humidity or partial pressure of water vapor in the air. Since this type of device is constructed of metal, it is able to withstand very high temperatures. The actual limitation is the temperature limit of the dielectric material in the cable connecting the resonator to its driving and monitoring equipment-an automatic network analyzer in our case. In the following sections, the theory of operation, design, construction, calibration and installation of the microwave diagnostics system is presented. The results and conclusions are also presented, along with suggestions for future work.
5. New class of compounds have very low vapor pressures
NASA Technical Reports Server (NTRS)
Angell, C. A.; Gruen, D. M.
1967-01-01
Magnesium hexahydrate tetrachlorometallates are 50-volume-percent water, have a high melting point and possess a low vapor pressure. These new compounds are relatively noncorrosive, thermally stable, and water soluble but not hygroscopic. They may have potential applications as cooling fluids.
6. Vapor pressures and gas-film coefficients for ketones
USGS Publications Warehouse
Rathbun, R.E.; Tai, D.Y.
1987-01-01
Comparison of handbook vapor pressures for seven ketones with more recent literature data showed large differences for four of the ketones. Gas-film coefficients for the volatilization of these ketones from water determined by two different methods were in reasonable agreement. ?? 1987.
7. Distillation device supplies cesium vapor at constant pressure
NASA Technical Reports Server (NTRS)
Basiulis, A.; Shefsiek, P. K.
1968-01-01
Distillation apparatus in the form of a U tube supplies small amounts of pure cesium vapor at constant pressure to a thermionic converter. The upstream leg of the U tube is connected to a vacuum pump to withdraw noncondensable impurities, the bottom portion serves as a reservoir for the liquid cesium.
8. Pump for Saturated Liquids
NASA Technical Reports Server (NTRS)
Elliott, D. G.
1986-01-01
Boiling liquids pumped by device based on proven components. Expanding saturated liquid in nozzle and diverting its phases along separate paths in liquid/vapor separator raises pressure of liquid. Liquid cooled in process. Pump makes it unnecessary to pressurize cryogenic liquids in order to pump them. Problems of introducing noncondensable pressurizing gas avoided.
9. Vapor pressure of perfluoroalkylalkanes: the role of the dipole.
PubMed
Morgado, Pedro; Das, Gaurav; McCabe, Clare; Filipe, Eduardo J M
2015-01-29
The vapor pressure of four liquid perfluoroalkylalkanes (CF3(CF2)n(CH2)mCH3; n = 3, m = 4,5,7; n = 5, m = 5) was measured as a function of temperature between 278 and 328 K. Molar enthalpies of vaporization were calculated from the experimental data, and the results were compared with data from the literature for the corresponding alkanes and perfluoroalkanes. The heterosegmented statistical associating fluid theory was used to interpret the results at the molecular level both with and without the explicit inclusion of the dipolar nature of the molecules. Additionally, ab initio calculations were performed for all perfluoroalkylalkanes studied to determine the dipole moment to be used in the theoretical calculations. We demonstrate that the inclusion of a dipolar term is essential for describing the vapor-liquid equilibria of perfluoroalkylalkanes. It is also shown that vapor-liquid equilibria in these compounds result from a subtle balance between dipolar interactions, which decrease the vapor pressure, and the relatively weak dispersive interactions between the hydrogenated and fluorinated segments. PMID:25526174
10. Subatmospheric vapor pressures evaluated from internal-energy measurements
SciTech Connect
Duarte-Garza, H.A. |; Magee, J.W.
1997-01-01
Vapor pressures were calculated from measured internal-energy changes in the vapor + liquid two-phase region, {Delta}U{sup (2)}. The method employed a thermodynamic relationship between the derivative quantity ({partial_derivative}U{sup (2)}/{partial_derivative}V){sub T} and the vapor pressure (p{sub {sigma}}) and its temperature derivative ({partial_derivative}p/{partial_derivative}T){sub {sigma}}. This method was applied at temperatures between the triple point and the normal boiling point of three substances: 1,1,1,2-tetrafluoroethane (R134a), pentafluoroethane (R125), and difluoromethane (R32). Agreement with experimentally measured vapor pressures near the normal boiling point (101.325 kPa) was within the experimental uncertainty of approximately {+-}0.04 kPa ({+-}0.04%). The method was applied to R134a to test the thermodynamic consistency of a published p-p-T equation of state with an equation for p{sub {sigma}} for this substance. It was also applied to evaluate published p{sub {sigma}} data which are in disagreement by more than their claimed uncertainty.
11. Controlling Vapor Pressure In Hanging-Drop Crystallization
NASA Technical Reports Server (NTRS)
Carter, Daniel C.; Smith, Robbie
1988-01-01
Rate of evaporation adjusted to produce larger crystals. Device helps to control vapor pressure of water and other solvents in vicinity of hanging drop of solution containing dissolved enzyme protein. Well of porous frit (sintered glass) holds solution in proximity to drop of solution containing protein or enzyme. Vapor from solution in frit controls evaporation of solvent from drop to control precipitation of protein or enzyme. With device, rate of nucleation limited to decrease number and increase size (and perhaps quality) of crystals - large crystals of higher quality needed for x-ray diffraction studies of macromolecules.
12. Low temperature measurement of the vapor pressures of planetary molecules
NASA Technical Reports Server (NTRS)
Kraus, George F.
1989-01-01
Interpretation of planetary observations and proper modeling of planetary atmospheres are critically upon accurate laboratory data for the chemical and physical properties of the constitutes of the atmospheres. It is important that these data are taken over the appropriate range of parameters such as temperature, pressure, and composition. Availability of accurate, laboratory data for vapor pressures and equilibrium constants of condensed species at low temperatures is essential for photochemical and cloud models of the atmospheres of the outer planets. In the absence of such data, modelers have no choice but to assume values based on an educated guess. In those cases where higher temperature data are available, a standard procedure is to extrapolate these points to the lower temperatures using the Clausius-Clapeyron equation. Last summer the vapor pressures of acetylene (C2H2) hydrogen cyanide (HCN), and cyanoacetylene (HC3N) was measured using two different methods. At the higher temperatures 1 torr and 10 torr capacitance manometers were used. To measure very low pressures, a technique was used which is based on the infrared absorption of thin film (TFIR). This summer the vapor pressure of acetylene was measured the TFIR method. The vapor pressure of hydrogen sulfide (H2S) was measured using capacitance manometers. Results for H2O agree with literature data over the common range of temperature. At the lower temperatures the data lie slightly below the values predicted by extrapolation of the Clausius-Clapeyron equation. Thin film infrared (TFIR) data for acetylene lie significantly below the values predicted by extrapolation. It is hoped to bridge the gap between the low end of the CM data and the upper end of the TFIR data in the future using a new spinning rotor gauge.
13. Vapor saturation of sodium: Key to unlocking the origin of chondrules
Fedkin, Alexei V.; Grossman, Lawrence
2013-07-01
Sodium saturation of the vapor coexisting with chondrules at their liquidus temperatures implies that vapor-condensed phase equilibrium was reached at those temperatures for all elements more refractory than sodium. In order to investigate the possibility that chondrules formed in impact-generated plumes, equilibrium calculations were applied to droplets made from two different target compositions. Combinations of dust enrichment and Ptot were found that lead to sodium saturation, and the subsequent chemical and mineralogical evolution of the droplets was explored at those conditions. If an impact on a body of CI composition caused instantaneous heating, melting and devolatilization of the target rock and ejection of a plume of gaseous, liquid and solid matter that mixed with residual nebular gas at conditions where 50% or 90% of the sodium was retained by the resulting droplets at their liquidus temperature, their mineralogical and chemical properties would strongly resemble those of Type II chondrules. If the droplets cooled and equilibrated with the mixture of residual nebular gas and their devolatilized water, sulfur and alkalis, the fayalite content of the olivine and the chemical compositions of the bulk droplets and their glasses would closely resemble those of Types IIA and IIAB chondrules at CI dust enrichments between 400 and 800. For 50% sodium retention, the corresponding values of Ptot are 2 bars (for 400) and 1 bar (for 800). For 90% retention, they are 25 and 10 bars, respectively. If, instead, the target has an anhydrous, ordinary chondrite-like composition, called H', the ejected droplets are bathed in a gas mix consisting mostly of devolatilized sulfur and alkalis with residual nebular gas, a much more reducing plume. If the conditions were such that sodium were retained by the resulting droplets at their liquidus temperature, the fayalite contents of the olivine and the chemical compositions of the bulk droplets and their glasses would closely resemble those of Types IA and IAB chondrules at H' dust enrichments between 103 and 4 103. For 90% sodium retention, the corresponding values of Ptot are 15 bars (for 103) and 2 bars (for 4 103). For 50% retention, they are 2 and 8 10-2 bars, respectively.
14. Effects of vapor pressure/velocity and concentration on condensation heat transfer for steam-ethanol vapor mixture
Yan, Junjie; Yang, Yusen; Hu, Shenhua; Zhen, Kejian; Liu, Jiping
2007-11-01
When a steam-ethanol vapor mixture condenses on a vertical flat plate, the form of the condensate film changes and many drops are created. This non-film condensation is called pseudo-dropwise or Marangoni condensation. This paper aims to study the main influencing factors on the Marangoni condensation of steam-ethanol vapor.The factors include the ethanol concentration, vapor pressure, vapor velocity and vapor-to-surface temperature difference. The experiments show that the heat transfer coefficient has a maximum value of approximately 42 kW/m2 K when the ethanol concentration is 1%. At the low concentrations of 0.5, 1, 5.1 and 9.8%, the condensation heat transfer is greater than for pure steam. In addition, the heat transfer for all vapor mixtures increases with both the rise of vapor pressure and vapor velocity.
15. Vapor-Saturated Melting of Fertile Peridotite Revisited: A new Experimental Approach and Re-evaluation of the Hydrous Peridotite Solidus
Grove, T. L.
2001-12-01
The vapor-saturated melting relations of peridotite have been determined for a fertile mantle composition of Hart and Zindler (1986, Chem Geol 57: 247) over the pressure range of 1.2 to 2.4 GPa. For example, at 1.2 GPa melt is present at a temperature of 980 C and at 2.4 GPa melt is present at 920 C. These temperatures should be viewed as maximum values for the vapor-saturated solidus (although see below) because the initial melting temperature of multi-phase, multicomponent systems can often be difficult to detect. At 2.4 GPa the melt composition is highly silica-undersaturated and very aluminous ( ~ 21 wt. % Al2O3). Wet mantle melts are thought to be high in silica, but this is not the case for these hydrous melts. At 1.2 GPa, melt fractions are too small to allow reliable analysis. The experiments have been carried out in a piston cylinder apparatus using Au capsules. The starting material is an oxide mixture containing 14.5 wt. % H2O added as brucite. Free water present in the experiment after quenching indicates subsolidus conditions. The absence of fluid in experiments above the vapor-saturated solidus shows that all of the free H2O is dissolved in the melt. The high H2O content of the starting material moves the bulk composition close to the vapor-saturated melt composition, therefore increasing the amount of melt produced close to the solidus and making detection of low melt fraction possible. Studies of the hydrous peridotite solidus carried out between 1970 and 1975 by Mysen and Boettcher, Kushiro and others, Green and Millhollen and others at 2.0 GPa ranged from < 800 to ~ 1000 C, a variation of over 200 degrees. In a subduction zone environment a fluid-rich component released from the slab ascends into hotter overlying mantle and melting initiates at the vapor-saturated solidus. Melting would begin at a depth of ~ 75 km in the mantle wedge, for a realistic thermal structure. Melting would continue as these initial H2O-rich buoyant melts ascend into hotter, shallower mantle and re-equilibrate with their surroundings. The initiation of melting deep in the mantle wedge has implications for both chemical and mechanical processes in the subduction zone environment.
16. Vapor pressure and vapor fractionation of silicate melts of tektite composition
USGS Publications Warehouse
Walter, Louis S.; Carron, M.K.
1964-01-01
The total vapor pressure of Philippine tektite melts of approximately 70 per cent silica has been determined at temperatures ranging from 1500 to 2100??C. This pressure is 190 ?? 40 mm Hg at 1500??C, 450 ?? 50 mm at 1800??C and 850 ?? 70 mm at 2100?? C. Determinations were made by visually observing the temperature at which bubbles began to form at a constant low ambient pressure. By varying the ambient pressure, a boiling point curve was constructed. This curve differs from the equilibrium vapor pressure curve due to surface tension effects. This difference was evaluated by determining the equilibrium bubble size in the melt and calculating the pressure due to surface tension, assuming the latter to be 380 dyn/cm. The relative volatility from tektite melts of the oxides of Na, K, Fe, Al and Si has been determined as a function of temperature, total pressure arid roughly, of oxygen fugacity. The volatility of SiO2 is decreased and that of Na2O and K2O is increased in an oxygen-poor environment. Preliminary results indicate that volatilization at 2100??C under atmospheric pressure caused little or no change in the percentage Na2O and K2O. The ratio Fe3 Fe2 of the tektite is increased in ambient air at a pressure of 9 ?? 10-4 mm Hg (= 106.5 atm O2, partial pressure) at 2000??C. This suggests that tektites were formed either at lower oxygen pressures or that they are a product of incomplete oxidation of parent material with a still lower ferricferrous ratio. ?? 1964.
17. Method and apparatus to measure vapor pressure in a flow system
DOEpatents
Grossman, Mark W. (Belmont, MA); Biblarz, Oscar (Swampscott, MA)
1991-01-01
The present invention is directed to a method for determining, by a condensation method, the vapor pressure of a material with a known vapor pressure versus temperature characteristic, in a flow system particularly in a mercury isotope enrichment process.
18. Pressure sensitivity of the vapor-cell atomic clock.
PubMed
Iyanu, Gebriel; Wang, He; Camparo, James
2009-06-01
Although atomic clocks have very low levels of frequency instability, they are nonetheless sensitive (albeit slightly) to various environmental parameters, including temperature, power supply voltage, and dc magnetic fields. In the terrestrial environment, however, atmospheric pressure (i.e., the air's molecular density) is not generally included in this list, because the air's density variations near the surface of the earth will typically have a negligible effect on the clock's performance. The situation is different, however, for clocks onboard satellites like Galileo, where manufacturing and testing are done at atmospheric pressure, while operation is in vacuum. The pressure sensitivity of atomic clocks, in particular vapor-cell atomic clocks, can therefore be of significance. Here, we discuss some of the ways in which changes in atmospheric pressure affect vapor-cell atomic clocks, and we demonstrate that, for one device, the pressure-sensitivity traces back to a pressure-induced change in the temperature of the clock's filter and resonance cells. PMID:19574121
19. Vapor pressure measurements of LaGd alloys
Shoji, Yoshiyuki; Matsui, Tsuneo; Nakamura, Kinya; Inoue, Tadashi
1997-08-01
The vapor pressures of La(g) and Gd(g) over La xGd 1- x alloys ( x = 0.00, 0.12, 0.22, 0.45, 0.70, 0.74, 0.85, 1.00) were measured with a time-of-flight mass spectrometer equipped with a tungsten Knudsen cell over the temperature range 1588 to 1797 K. The chemical activities of lanthanum and gadolinium in the alloys were determined by comparing the vapor pressures of La(g) and Gd(g) over the alloys with those over the pure metals. The chemical activities, thus obtained, showed positive deviations from Raoult's law over the entire compositional range. The interatomic force between gadolinium and lanthanum was thought to be repulsive. The partial molar Gibbs free energy and the Gibbs free energy, enthalpy and entropy of formation were calculated from the activity values.
20. Low vapor pressure braze alloys for thermionic energy converters
NASA Technical Reports Server (NTRS)
Bair, V. L.
1976-01-01
The evaluation of cesium diode electrode materials called for braze fillers with very low vapor pressures and a wide range of melting points. Binary alloys of low vapor pressure refractory metals were chosen to fill this need. These alloys of Th, Zr, Hf, Ru, Nb, Ir, Mo, Ta, Os, Re, and W have reported melting point minima or eutectics from 1,510 K to above 3,000 K. Preliminary data are compiled on the use of several of these braze alloys. Melting points and surface wetting on a Ta base are given. Results of brazing Ir, LaB6, Nb, Re, W, and Zr-22 wt % ZrO2 materials into Ta and Nb-1% Zr bases are presented. Current braze usage is summarized.
1. Water vapor pressure should be addressed in Potomac study
Egan, Walter G.
In Bruce Doe's article, “A Potomac Perspective on the Growing Global Greenhouse” (Eos, January 5,1999), a statement is made in the next to last paragraph that “other climatic parameters such as precipitation can correlate better than temperature among the five sites.” It would be expected that precipitation, and in particular the partial pressure of water vapor, should correlate with the carbon dioxide greenhouse effect. It was pointed out by W. G. Egan and coworkers in 1991 that there is an inverse relationship between carbon dioxide and water vapor partial pressure, seen both in laboratory experiments and at all worldwide Global Monitoring for Climate Change monitoring stations. Specific examples were presented for Cold Bay, Alaska and Palmer Station, Antarctica monthly and annually
2. Low vapor pressure braze alloys for thermionic energy converters
NASA Technical Reports Server (NTRS)
Bair, V. L.
1976-01-01
Preliminary results in the use of some low-vapor-pressure braze alloys are reported; these are binary alloys of refractory metals (Th, Zr, Hf, Ru, Nb, Ir, Mo, Ta, Os, Re, W) with vapor pressures below 0.1 nanotorr at 1500 K or 10 microtorr at 2000 K. The melting point minima or eutectics of the alloys range from 1510 K to above 3000 K. Melting points and surface wetting on a Ta base are given. Results are presented on brazing of Ir, LaB6, Nb, Re, W, and ZrO2 (with 22 wt % Zr) into a Ta base or a Nb-1% Zr base. The results are applicable in electrode screening programs for thermionic cesium diodes.
3. A survey and new measurements of ice vapor pressure at temperatures between 170 and 250K
NASA Technical Reports Server (NTRS)
1993-01-01
New measurements of ice vapor pressures at temperatures between 170 and 250 K are presented and published vapor pressure data are summarized. An empirical vapor pressure equation was derived and allows prediction of vapor pressures between 170 k and the triple point of water with an accuracy of approximately 2 percent. Predictions obtained agree, within experimental uncertainty, with the most reliable equation derived from thermodynamic principles.
4. Pressure (Or No Royal Road)
ERIC Educational Resources Information Center
1973-01-01
Discusses how difficult the various problems of pressure, partial pressure, gas laws, and vapor pressure are for students. Outlines the evolution of the concept of pressure, the gas equation for a perfect gas, partial pressures, saturated vapor pressure, Avogadro's hypothesis, Raoult's law, and the vapor pressure of ideal solutions. (JR)
5. A nonlinear regression analysis for estimating low-temperature vapor pressures and enthalpies of vaporization applied to refrigerants
Tillner-Roth, R.
1996-11-01
A new method is presented to extrapolate experimental vapor pressures down to the triple Point. The method involves a nonlinear regression analysis based on the Clausius Clapeyron equation and a simple relation for the enthalpy of vaporization Triple-point pressures and vapor pressures up to 0.1 0.2 MPa are estimated for R125, R32, R143a, R134a, R152a, R123, R124, and ammonia; they generally agree with available experimental data within their uncertainty, Equations for the enthalpy of vaporization which describe this property fairly well at low temperatures are obtained as a byproduct.
6. 46 CFR 154.405 - Design vapor pressure (Po) of a cargo tank.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 5 2012-10-01 2012-10-01 false Design vapor pressure (Po) of a cargo tank. 154.405... Equipment Cargo Containment Systems § 154.405 Design vapor pressure (Po) of a cargo tank. (a) The design vapor pressure (Po) of a cargo tank must be equal to or greater than the MARVS. (b) The Po of a...
7. 46 CFR 154.405 - Design vapor pressure (Po) of a cargo tank.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 5 2011-10-01 2011-10-01 false Design vapor pressure (Po) of a cargo tank. 154.405... Equipment Cargo Containment Systems § 154.405 Design vapor pressure (Po) of a cargo tank. (a) The design vapor pressure (Po) of a cargo tank must be equal to or greater than the MARVS. (b) The Po of a...
8. 46 CFR 154.405 - Design vapor pressure (Po) of a cargo tank.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 5 2013-10-01 2013-10-01 false Design vapor pressure (Po) of a cargo tank. 154.405... Equipment Cargo Containment Systems § 154.405 Design vapor pressure (Po) of a cargo tank. (a) The design vapor pressure (Po) of a cargo tank must be equal to or greater than the MARVS. (b) The Po of a...
9. 46 CFR 154.405 - Design vapor pressure (Po) of a cargo tank.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 5 2014-10-01 2014-10-01 false Design vapor pressure (Po) of a cargo tank. 154.405... Equipment Cargo Containment Systems § 154.405 Design vapor pressure (Po) of a cargo tank. (a) The design vapor pressure (Po) of a cargo tank must be equal to or greater than the MARVS. (b) The Po of a...
10. 46 CFR 154.405 - Design vapor pressure (Po) of a cargo tank.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 5 2010-10-01 2010-10-01 false Design vapor pressure (Po) of a cargo tank. 154.405... Equipment Cargo Containment Systems § 154.405 Design vapor pressure (Po) of a cargo tank. (a) The design vapor pressure (Po) of a cargo tank must be equal to or greater than the MARVS. (b) The Po of a...
11. Acoustic and mechanical response of reservoir rocks under variable saturation and effective pressure.
PubMed
Ravazzoli, C L; Santos, J E; Carcione, J M
2003-04-01
We investigate the acoustic and mechanical properties of a reservoir sandstone saturated by two immiscible hydrocarbon fluids, under different saturations and pressure conditions. The modeling of static and dynamic deformation processes in porous rocks saturated by immiscible fluids depends on many parameters such as, for instance, porosity, permeability, pore fluid, fluid saturation, fluid pressures, capillary pressure, and effective stress. We use a formulation based on an extension of Biot's theory, which allows us to compute the coefficients of the stress-strain relations and the equations of motion in terms of the properties of the single phases at the in situ conditions. The dry-rock moduli are obtained from laboratory measurements for variable confining pressures. We obtain the bulk compressibilities, the effective pressure, and the ultrasonic phase velocities and quality factors for different saturations and pore-fluid pressures ranging from normal to abnormally high values. The objective is to relate the seismic and ultrasonic velocity and attenuation to the microstructural properties and pressure conditions of the reservoir. The problem has an application in the field of seismic exploration for predicting pore-fluid pressures and saturation regimes. PMID:12703693
12. Chemical Vapor Deposition at High Pressure in a Microgravity Environment
NASA Technical Reports Server (NTRS)
McCall, Sonya; Bachmann, Klaus; LeSure, Stacie; Sukidi, Nkadi; Wang, Fuchao
1999-01-01
In this paper we present an evaluation of critical requirements of organometallic chemical vapor deposition (OMCVD) at elevated pressure for a channel flow reactor in a microgravity environment. The objective of using high pressure is to maintain single-phase surface composition for materials that have high thermal decomposition pressure at their optimum growth temperature. Access to microgravity is needed to maintain conditions of laminar flow, which is essential for process analysis. Based on ground based observations we present an optimized reactor design for OMCVD at high pressure and reduced gravity. Also, we discuss non-intrusive real-time optical monitoring of flow dynamics coupled to homogeneous gas phase reactions, transport and surface processes. While suborbital flights may suffice for studies of initial stages of heteroepitaxy experiments in space are essential for a complete evaluation of steady-state growth.
13. New doser for chemical vapor deposition of low vapor-pressure solid precursors
Serghini-Monim, S.; Coatsworth, L. L.; Norton, P. R.; Puddephatt, R. J.
1996-10-01
In this article we describe a new ultrahigh vacuum compatible device to maximize the volatilization of low vapor-pressure precursors used in chemical vapor deposition processes while minimizing their dissociation. A differentially pumped system that places the precursor close to the target substrate was adopted to achieve this configuration; it also allows loading and unloading of the precursor reservoir without breaking vacuum. The device permits the volatilization of low vapor-pressure solid precursors by passing a preheated carrier gas through the precursor which is placed between two fritted disks. This device was also used without a carrier gas and proved its efficiency. The complexes (1,1,1,5,5,5-hexafluoropentanedionato)(1,5-cyclooctadiene) copper (I), [(hfac)Cu(COD)], and (1,1,1,2,2,3,3-heptafluoro-7, 7-dimethyl-4, 6-octanedionato) (trimethylphosphine) silver (I), [(fod)AgPMe3], proved the efficacy of this doser in delivering intact precursors to the substrate using reflection-absorption infrared spectroscopy and mass spectrometry techniques during the adsorption of these precursors on polished Al disks and on polyurethane thin films spun cast onto similar polished Al disks.
14. Vapor pressures and heats of vaporization of primary coal tars. Quarterly technical progress report, July 1 - September 31, 1996
SciTech Connect
Suuberg, E.M.; Oja, V.; Lilly, W.D.
1996-12-31
The vapor pressure correlations that exist at present for coal tars are very crude and they are not considered reliable to even an order of magnitude. This project seeks to address this important gap in the near term by direct measurement of vapor pressures of coal tar fractions, by application of well-established techniques and modifications thereof. The principal objectives of the program are to: (1) obtain data on the vapor pressures and heats of vaporization of tars from a range of ranks of coal; (2) develop correlations based on a minimum set of conveniently measurable characteristics of the tars; and (3) develop equipment that would allow performing such measurements in a reliable, straightforward fashion. During this quarter we have extended the work on measurements of vapor pressures of coal tars, using the continuous Knudsen effusion technique. These results need further analysis and therefore in this report we describe only the general idea behind the technique, and also show some typical results.
15. Vapor pressures and vapor compositions in equilibrium with hypostoichiometric uranium dioxide at high temperatures
SciTech Connect
Green, D.W.; Leibowitz, L.
1981-06-01
Thermodynamic functions of the gaseous species, thermodynamic functions of the condensed phase, and an oxygen-potential model have been combined to calculate the vapor pressures and vapor compositions in equilibrium with condensed-phase UO/sub 2-x/ for 1500 less than or equal to T less than or equal to 6000 K and 0 less than or equal to x less than or equal to 0.5. A method for extending the oxygen-potential model of Blackburn to the liquid region has been derived and evaluated. New thermodynamic functions of the UO/sub 2/ condensed phase have been derived from the best available data, including the heat capacity recommended by Fink.
16. Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell
Andreeva, C.; Cartaleva, S.; Petrov, L.; Saltiel, S. M.; Sarkisyan, D.; Varzhapetyan, T.; Bloch, D.; Ducloy, M.
2007-07-01
Saturation effects affecting absorption and fluorescence spectra of an atomic vapor confined in an extremely thin cell (cell thickness L<1?m ) are investigated experimentally and theoretically. The study is performed on the D2 line (?=852nm) of Cs and concentrates on the two situations L=?/2 and L=? , the most contrasted ones with respect to the length dependence of the coherent Dicke narrowing. For L=?/2 , the Dicke-narrowed absorption profile simply broadens and saturates in amplitude when increasing the light intensity, while for L=? , sub-Doppler dips of reduced absorption at the line-center appear on the broad absorption profile. For a fluorescence detection at L=? , saturation induces narrow dips, but only for hyperfine components undergoing a population loss through optical pumping. These experimental results are interpreted with the help of the various existing models and are compared with numerical calculations based upon a two-level modeling that considers both a closed and an open system.
17. Atmospheric pressure laser-induced acoustic desorption chemical ionization mass spectrometry for analysis of saturated hydrocarbons.
PubMed
Nyadong, Leonard; Quinn, John P; Hsu, Chang S; Hendrickson, Christopher L; Rodgers, Ryan P; Marshall, Alan G
2012-08-21
We present atmospheric pressure laser-induced acoustic desorption chemical ionization (AP/LIAD-CI) with O(2) carrier/reagent gas as a powerful new approach for the analysis of saturated hydrocarbon mixtures. Nonthermal sample vaporization with subsequent chemical ionization generates abundant ion signals for straight-chain, branched, and cycloalkanes with minimal or no fragmentation. [M - H](+) is the dominant species for straight-chain and branched alkanes. For cycloalkanes, M(+) species dominate the mass spectrum at lower capillary temperature (<100 C) and [M - H](+) at higher temperature (>200 C). The mass spectrum for a straight-chain alkane mixture (C(21)-C(40)) shows comparable ionization efficiency for all components. AP/LIAD-CI produces molecular weight distributions similar to those for gel permeation chromatography for polyethylene polymers, Polywax 500 and Polywax 655. Coupling of the technique to Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) for the analysis of complex hydrocarbon mixtures provides unparalleled mass resolution and accuracy to facilitate unambiguous elemental composition assignments, e.g., 1754 peaks (rms error = 175 ppb) corresponding to a paraffin series (C(12)-C(49), double-bond equivalents, DBE = 0) and higher DBE series corresponding to cycloparaffins containing one to eight rings. Isoabundance-contoured plots of DBE versus carbon number highlight steranes (DBE = 4) of carbon number C(27)-C(30) and hopanes of C(29)-C(35) (DBE = 5), with sterane-to-hopane ratio in good agreement with field ionization (FI) mass spectrometry analysis, but performed at atmospheric pressure. The overall speciation of nonpolar, aliphatic hydrocarbon base oil species offers a promising diagnostic probe to characterize crude oil and its products. PMID:22881221
18. Generation of high concentration aerosols from low vapor pressure compounds
SciTech Connect
Blank, T.L.; Velasquez, D.J.; Bechtel, C.L.; Roloff, M.V.
1987-10-01
A generation system has been developed and used to produce exposure atmospheres containing respirable aerosols at high concentration (up to 5 mg of test compound per liter in air) from high boiling point, low vapor pressure compounds. Nine compounds were evaluated to demonstrate the effectiveness of the generation system. In each test at least 84% of the particles were in the respirable range (particle size 10 ..mu..m or less) with a mass median aerodynamic diameter of less than 3.2 ..mu..m. The system is easy to operate, reliable, versatile, provides reproducible results and is relatively inexpensive to construct.
19. 46 CFR 39.2013 - High and low vapor pressure protection for tankships-T/ALL.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 1 2013-10-01 2013-10-01 false High and low vapor pressure protection for tankships-T... CONTROL SYSTEMS Equipment and Installation § 39.2013 High and low vapor pressure protection for tankships... transfer is controlled; and (b) Has a high-pressure and a low-pressure alarm that— (1) Gives an audible...
20. 46 CFR 39.2013 - High and low vapor pressure protection for tankships-T/ALL.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 1 2014-10-01 2014-10-01 false High and low vapor pressure protection for tankships-T... CONTROL SYSTEMS Equipment and Installation § 39.2013 High and low vapor pressure protection for tankships... transfer is controlled; and (b) Has a high-pressure and a low-pressure alarm that— (1) Gives an audible...
1. 40 CFR 63.165 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2013 CFR
2013-07-01
... Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure... 40 Protection of Environment 10 2013-07-01 2013-07-01 false Standards: Pressure relief devices in gas/vapor service. 63.165 Section 63.165 Protection of Environment ENVIRONMENTAL PROTECTION...
2. 40 CFR 60.482-4a - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2014 CFR
2014-07-01
... Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure... 40 Protection of Environment 7 2014-07-01 2014-07-01 false Standards: Pressure relief devices in gas/vapor service. 60.482-4a Section 60.482-4a Protection of Environment ENVIRONMENTAL...
3. 40 CFR 60.482-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2011 CFR
2011-07-01
..., 2006 § 60.482-4 Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in gas/vapor service shall be operated with no detectable emissions... 40 Protection of Environment 6 2011-07-01 2011-07-01 false Standards: Pressure relief devices...
4. 40 CFR 63.165 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2010 CFR
2010-07-01
... Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure... 40 Protection of Environment 9 2010-07-01 2010-07-01 false Standards: Pressure relief devices in gas/vapor service. 63.165 Section 63.165 Protection of Environment ENVIRONMENTAL PROTECTION...
5. 40 CFR 265.1054 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2010 CFR
2010-07-01
...: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Standards: Pressure relief devices in gas/vapor service. 265.1054 Section 265.1054 Protection of Environment ENVIRONMENTAL PROTECTION...
6. 40 CFR 265.1054 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2011 CFR
2011-07-01
...: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Standards: Pressure relief devices in gas/vapor service. 265.1054 Section 265.1054 Protection of Environment ENVIRONMENTAL PROTECTION...
7. 40 CFR 60.482-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2013 CFR
2013-07-01
..., 2006 § 60.482-4 Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in gas/vapor service shall be operated with no detectable emissions... 40 Protection of Environment 7 2013-07-01 2013-07-01 false Standards: Pressure relief devices...
8. 40 CFR 60.482-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2014 CFR
2014-07-01
..., 2006 § 60.482-4 Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in gas/vapor service shall be operated with no detectable emissions... 40 Protection of Environment 7 2014-07-01 2014-07-01 false Standards: Pressure relief devices...
9. 40 CFR 60.482-4a - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2013 CFR
2013-07-01
... Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure... 40 Protection of Environment 7 2013-07-01 2013-07-01 false Standards: Pressure relief devices in gas/vapor service. 60.482-4a Section 60.482-4a Protection of Environment ENVIRONMENTAL...
10. 40 CFR 63.165 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2014 CFR
2014-07-01
... Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure... 40 Protection of Environment 10 2014-07-01 2014-07-01 false Standards: Pressure relief devices in gas/vapor service. 63.165 Section 63.165 Protection of Environment ENVIRONMENTAL PROTECTION...
11. 40 CFR 63.165 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2011 CFR
2011-07-01
... Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure... 40 Protection of Environment 9 2011-07-01 2011-07-01 false Standards: Pressure relief devices in gas/vapor service. 63.165 Section 63.165 Protection of Environment ENVIRONMENTAL PROTECTION...
12. 40 CFR 60.482-4a - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2010 CFR
2010-07-01
... Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure... 40 Protection of Environment 6 2010-07-01 2010-07-01 false Standards: Pressure relief devices in gas/vapor service. 60.482-4a Section 60.482-4a Protection of Environment ENVIRONMENTAL...
13. 40 CFR 60.482-4a - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2012 CFR
2012-07-01
... Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure... 40 Protection of Environment 7 2012-07-01 2012-07-01 false Standards: Pressure relief devices in gas/vapor service. 60.482-4a Section 60.482-4a Protection of Environment ENVIRONMENTAL...
14. 40 CFR 60.482-4a - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2011 CFR
2011-07-01
... Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure... 40 Protection of Environment 6 2011-07-01 2011-07-01 false Standards: Pressure relief devices in gas/vapor service. 60.482-4a Section 60.482-4a Protection of Environment ENVIRONMENTAL...
15. 40 CFR 265.1054 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2012 CFR
2012-07-01
...: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief... 40 Protection of Environment 27 2012-07-01 2012-07-01 false Standards: Pressure relief devices in gas/vapor service. 265.1054 Section 265.1054 Protection of Environment ENVIRONMENTAL PROTECTION...
16. 40 CFR 60.482-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2010 CFR
2010-07-01
..., 2006 § 60.482-4 Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in gas/vapor service shall be operated with no detectable emissions... 40 Protection of Environment 6 2010-07-01 2010-07-01 false Standards: Pressure relief devices...
17. 40 CFR 60.482-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2012 CFR
2012-07-01
..., 2006 § 60.482-4 Standards: Pressure relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in gas/vapor service shall be operated with no detectable emissions... 40 Protection of Environment 7 2012-07-01 2012-07-01 false Standards: Pressure relief devices...
18. Influence of vapor pressure on vapor-particle partitioning of trace organic pollutants
SciTech Connect
Foreman, W.T.
1986-01-01
Particle (P) and vapor (V) phase polycyclic aromatic hydrocarbons (PAH) at the Savannah River Plant were collected using a filter-polyurethane foam (PUF) plug hi-vol sampler. PUF was retentive for gaseous 3-ring PAH when air volumes not exceeding 600 m/sup 3/ were sampled on warm days. PAH breakthrough on PUF was governed by the liquid-phase vapor pressure (p/sub L//sup 0/) rather than the solid phase (p/sub S//sup 0/). The apparent VP partitioning of PAH, as estimated by (A(TSP)F) where A and F are the adsorbent- and filter-retained SOC concentrations and TSP is the total suspended particle concentration also correlated well with p/sub L//sup 0/. An apparatus was designed to equilibrate urban air particulate matter on a filter with controlled vapor concentrations of semivolatile organic compounds (SOC) at 20/sup 0/C under simulated air sampling conditions. VP for organochlorine pesticides and 3-4 ring PAH were estimated from laboratory measurements of A(TSP)F. Measured A(TSP)F correlated well with (p/sub L//sup 0/) of the SOC tested, but not with p/sub S//sup 0/. Comparisons of field and laboratory A(TSP)F were made and implications of p/sup 0/-dependent partitioning to the atmospheric chemistry of SOC are discussed
19. Effect of cationic surfactants on organic liquid-water capillary pressure-saturation relationships
Demond, A. H.; Desai, F. N.; Hayes, K. F.
1994-02-01
Many solutes, either naturally occurring or introduced, are surface active and sorb preferentially at the interfaces of subsurface systems. In multiphase systems, the sorption of surfactants affects the capillary pressure-saturation relationships, fundamental constitutive relationships in the modeling of multiphase flow. In this study, the impact of surfactant sorption on capillary pressure relationships for organic liquid-waters systems was demonstrated by qualitatively correlating measurements of sorption and zeta potential, with interfacial tension and contact angle and, in turn, quantitatively relating these measurements to changes in capillary pressure-saturation relationships for o-xylene-water-quartz systems containing a cationic surfactant, cetyltrimethylammonium bromide (CTAB). The results show that the sorption of CTAB causes the naturally hydrophilic system to become hydrophobic, as evidenced by a change in the contact angle from about 10-15 to 155 or 180, depending on the pH. This change in hydrophilicity is reflected in the zeta potential of the system which goes from negative to positive as the aqueous phase CTAB concentration increases. The spontaneous imbibition capillary pressure-saturation relationship is more sensitive to the sorption of CTAB than the drainage relationship. To predict the observed changes in both capillary pressure-saturation relationships, a modified form of Leverett's function was used where roughness and curvature corrections were incorporated into the intrinsic contact angle to give an operational contact angle. A comparison of the measured and predicted capillary pressure-saturation relationships showed reasonable agreement.
20. Effect of cationic surfactants on organic liquid-water capillary pressure-saturation relationships
SciTech Connect
Demond, A.H.; Hayes, K.F. ); Desai, F.N. )
1994-02-01
Many solutes, either naturally occurring or introduced, are surface active and sorb preferentially at the interfaces of subsurface systems. In multiphase systems, the sorption of surfactants affects the capillary pressure-saturation relationships, fundamental constitutive relationships in the modeling of multiphase flow. In this study, the impact of surfactant sorption on capillary pressure relationships for organic liquid-waters systems was demonstrated by qualitatively correlating measurements of sorption and zeta potential, with interfacial tension and contact angle and, in turn, quantitatively relating these measurements to changes in capillary pressure-saturation relationships for o-xylene-water-quartz systems containing a cationic surfactant, cetyltrimethylammonium bromide (CTAB). The results show that the sorption of CTAB causes the naturally hydrophilic system to become hydrophobic, as evidenced by a change in the contact angle from about 10[degrees]-15[degrees] to 155[degrees] or 180[degrees], depending on the pH. This change in hydrophilicity is reflected in the zeta potential of the system which goes from negative to positive as the aqueous phase CTAB concentration increases. The spontaneous imbibition capillary pressure-saturation relationship is more sensitive to the sorption of CTAB than the drainage relationship. To predict the observed changes in both capillary pressure-saturation relationships, a modified form of Leverett's function was used where roughness and curvature corrections were incorporated into the intrinsic contact angle to give an operational contact angle. A comparison of the measured and predicted capillary pressure-saturation relationships showed reasonable agreement. 33 refs., 8 figs., 3 tabs.
1. Laboratory measurements of the microwave opacity and vapor pressure of sulfuric acid vapor under simulated conditions for the middle atmosphere of Venus
NASA Technical Reports Server (NTRS)
Steffes, P. G.
1985-01-01
Microwave absorption measurements at wavelengths of 13.4 and 3.6 cm were made in gaseous H2SO4 in a CO2 atmosphere under simulated conditions for the Venus middle atmosphere. The results suggest that abundances of gaseous H2SO4 on the order of 15-30 ppm could account for the absorption observed by radio occultation measurements at these wavelengths. They also imply that such abundances would correspond to saturation vapor pressure existing at or above the 46-48-km range, which correlates with the observed cloud base.
2. Precision ozone calibration system based on vapor pressures of ozone
NASA Technical Reports Server (NTRS)
Mauersberger, K.; Hanson, D.; Morton, J.
1987-01-01
A precision ozone calibration system for stratospheric research has been developed and evaluated. Vapor pressures above solid ozone are mixed with a carrier gas (N2) to produce stratospheric ozone mixing ratios at total pressures of 1 to cover 20 torr. The uncertainty in the ozone mixing ratios is approximately + or - 1.5 percent, the stability of ozone is + or - 0.3 percent. Experiments to be calibrated may sample the gas mixture over a wide range of flow rates; the maximum throughput of gas with corrections of less than 1 percent to ozone is about 200 torr 1/min. A mass spectrometer system continuously monitors the purity and stability of the N2-O3 gas mixture.
3. Analysis of the saturation phenomena of the neutralization rate of positively charged 218Po in water vapor.
PubMed
Tan, Yanliang; Xiao, Detao; Shan, Jian; Zhou, Qingzhi; Qu, Jingnian
2014-09-01
Generally, 88% of the freshly generated 218Po ions decayed from 222Rn are positively charged. These positive ions become neutralized by recombination with negative ions, and the main source of the negative ions is the OH- ions formed by radiolysis of water vapor. However, the neutralization rate of positively charged 218Po versus the square root of the concentration of H2O will be a constant when the concentration of H2O is sufficiently high. Since the electron affinity of the hydroxyl radical formed by water vapor is high, the authors propose that the hydroxyl radical can grab an electron to become OH-. Because the average period of collision with other positively charged ions and the average life of the OH- are much longer than those of the electron, the average concentration of negative ions will grow when the water vapor concentration increases. The authors obtained a model to describe the growth of OH- ions. From this model, it was found that the maximum value of the OH- ion concentration is limited by the square root of the radon concentration. If the radon concentration is invariant, the OH- ion concentration should be approximately a constant when the water vapor concentration is higher than a certain value. The phenomenon that the neutralization rate of positively charged 218Po versus the square root of the water vapor concentration will be saturated when the water vapor concentration is sufficiently high can be explained by this mechanism. This mechanism can be used also to explain the phenomenon that the detection efficiency of a radon monitor based on the electrostatic collection method seems to be constant when the water vapor concentration is high. PMID:25068963
4. New Nickel Vapor Pressure Measurements: Possible Implications for Nebular Condensates
NASA Technical Reports Server (NTRS)
Johnson, N. M.; Meibom, A.; Ferguson, F. T.; Nuth, J. A., III
2004-01-01
Temperatures high enough to vaporize even refractory solids existed in the midplane of the solar nebula during its earliest evolutionary stages and played an important role in the processing of materials that went into the formation of the inner planets and asteroids. A variety of such high-T materials have been identified in primitive chondritic meteorites. These include chemically zoned FeNi metal grains that are generally believed to have formed directly by gas-solid condensation from a gas of approximately solar composition. These FeNi particles provide important information about the times scales of formation and physical transport mechanisms in the nebula, as well as formation temperature, pressure and gas chemistry. Currently, however, the interpretation of the chemical signatures in these FeNi particles rests on less than perfect information about the condensation sequence of siderophile elements. For example much, if not all, of the thermodynamic data for the vapor pressures of moderately refractory metals , such as Fe, Ni and Co, do not cover the desired temperature range. As a result, quite large extrapolations are needed. These extrapolations can be complex and uncertain due to factors such as oxygen fugacity or the presence of hydrogen gas.
5. 46 CFR 153.372 - Gauges and vapor return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia).
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 5 2012-10-01 2012-10-01 false Gauges and vapor return for cargo vapor pressures... COMPRESSED GAS HAZARDOUS MATERIALS Design and Equipment Cargo Venting Systems § 153.372 Gauges and vapor return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia). When table 1 references...
6. 46 CFR 153.372 - Gauges and vapor return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia).
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 5 2010-10-01 2010-10-01 false Gauges and vapor return for cargo vapor pressures... COMPRESSED GAS HAZARDOUS MATERIALS Design and Equipment Cargo Venting Systems § 153.372 Gauges and vapor return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia). When table 1 references...
7. Temperature/pressure and water vapor sounding with microwave spectroscopy
NASA Technical Reports Server (NTRS)
Muhleman, D. O.; Janssen, M. A.; Clancy, R. T.; Gulkis, S.; Mccleese, D. J.; Zurek, R.; Haberle, R. M.; Frerking, M.
1992-01-01
Two intense microwave spectra lines exist in the martian atmosphere that allow unique sounding capabilities: water vapor at 183 GHz and the (2-1) rotational line of CO at 230 GHz. Microwave spectra line sounding is a well-developed technique for the Earth's atmosphere for sounding from above from spacecraft and airplanes, and from below from fixed surface sites. Two simple instruments for temperature sounding on Mars (the CO line) and water vapor measurements are described. The surface sounder proposed for the MESUR sites is designed to study the boundary layer water vapor distribution and the temperature/pressure profiles with vertical resolution of 0.25 km up to 1 km with reduced resolution above approaching a scale height. The water channel will be sensitive to a few tenths of a micrometer of water and the temperature profile will be retrieved to an accuracy between 1 and 2 K. The latter is routinely done on the Earth using oxygen lines near 60 GHz. The measurements are done with a single-channel heterodyne receiver looking into a 10-cm mirror that is canned through a range of elevation angles plus a target load. The frequency of the receiver is sweep across the water and CO lines generating the two spectra at about 1-hr intervals throughout the mission. The mass and power for the proposed instrument are 2 kg and 5-8 W continuously. The measurements are completely immune to the atmospheric dust and ice particle loads. It was felt that these measurements are the ultimate ones to properly study the martian boundary layer from the surface to a few kilometers. Sounding from above requires an orbiting spacecraft with multichannel microwave spectrometers such as the instrument proposed for MO by a subset of the authors, a putative MESUR orbiter, and a proposed Discovery mission called MOES. Such an instrument can be built with less than 10 kg and use less than 15 W. The obvious advantage of this approach is that the entire atmosphere can be sounded for temperature and water vapor in a few hours with somewhat better than a scale height resolution. If a bigger mirror is used (greater than 30 cm) limb sounding geometry can be employed and half scale height resolution achieved to altitudes up to at least 60 km. Again, the measurements are immune to dust and ice loads. Water vapor sensitivity of 0.1 micrometer can be achieved (even with a nadir instrument) and temperature profiles retrieved to an accuracy of better than 2 K from the surface to about 60 km. Winds can be measured from the doppler shifts of CO lines in the limb sounding mode.
8. Effects of heterogeneities on capillary pressure-saturation-relative permeability relationships.
PubMed
2002-06-01
In theories of multiphase flow through porous media, capillary pressure-saturation and relative permeability-saturation curves are assumed to be intrinsic properties of the medium. Moreover, relative permeability is assumed to be a scalar property. However, numerous theoretical and experimental works have shown that these basic assumptions may not be valid. For example, relative permeability is known to be affected by the flow velocity (or pressure gradient) at which the measurements are carried out. In this article, it is suggested that the nonuniqueness of capillary pressure-relative permeability-saturation relationships is due to the presence of microheterogeneities within a laboratory sample. In order to investigate this hypothesis, a large number of "numerical experiments" are carried out. A numerical multiphase flow model is used to simulate the procedures that are commonly used in the laboratory for the measurement of capillary pressure and relative permeability curves. The dimensions of the simulation domain are similar to those of a typical laboratory sample (a few centimeters in each direction). Various combinations of boundary conditions and soil heterogeneity are simulated and average capillary pressure, saturation, and relative permeability for the "soil sample" are obtained. It is found that the irreducible water saturation is a function of the capillary number; the smaller the capillary number, the larger the irreducible water saturation. Both drainage and imbibition capillary pressure curves are found to be strongly affected by heterogeneities and boundary conditions. Relative permeability is also found to be affected by the boundary conditions; this is especially true about the nonaqueous phase permeability. Our results reveal that there is much need for laboratory experiments aimed at investigating the interplay of boundary conditions and microheterogeneities and their effect on capillary pressure and relative permeability. PMID:12102317
9. Elastic properties, annealing, and vapor pressure of neon and argon films
Metcalf, Thomas Harker
In order to study the elastic properties and vapor pressure of disordered solids, neon and argon films were quench-condensed onto a silicon double paddle oscillator held at temperatures far below the melting points of the gases. The bare oscillator has an extremely small mechanical damping and a narrow frequency resonance, and by measuring changes to the resonant frequency of a film-laden paddle at various temperatures, very sensitive measurements of the evaporation and stiffening of the film can be made. When films are annealed at temperatures above that at which they were deposited, the oscillator frequency is observed to increase. At the lower annealing temperatures (below 20% of the triple point), this increase is dominated by stiffening of the film, and at higher temperatures, evaporation dominates. Through measurements of the evaporation rate, the vapor pressure of both neon and argon were measured to a few x10-13 torr. This technique has extended the range over which there are such vapor pressure measurements by several orders of magnitude. The stiffening observed during the annealing is irreversible; cooling a film after annealing will not reverse a stiffness increase. At the highest annealing temperatures, the stiffening of the film reaches a saturation. The temperature dependence of the stiffening has been characterized. From the cumulative stiffness increases of each film, we can determine that the freshly deposited films were extremely soft, with shear moduli as low as 30% of that of the corresponding bulk solid. The internal friction of the films is also seen to increase sharply with increasing temperature, following an Arrhenius law. Thinner films are found to be softer and have higher internal frictions than thicker films. This thickness dependence indicates that the films are nonuniform along their growth direction, with the stiffening and elastic loss confined to a small layer of each film. Several explanations and possibilities for film structure are discussed.
10. Vapor pressures of HNO/sub 3//H/sub 2/O solutions at low temperatures
SciTech Connect
Hanson, D.; Mauersberger, K.
1988-10-20
Vapor pressures of liquid, supercooled, and frozen HNO/sub 3//H/sub 2/O mixtures of various concentrations have been measured over a wide range of temperatures and pressures. The vapor pressures as well as impurities were analyzed by a mass spectrometer system. Measurements made on liquid and supercooled mixtures were fit according to the Clausius-Clapeyron equation. Different concentrations showed the expected variability of HNO/sub 3/ and H/sub 2/O vapors as a function of temperature. Vapor pressures of partially frozen mixtures followed a freezing envelope leading to quadruple (eutectic) points. Completely frozen bulk mixtures resulted in the coexistence of two solid phases and vapor. Vapor pressures were measured over both the trihydrate and solid solutions of HNO/sub 3/ in ice and over the trihydrate and monohydrate. The H/sub 2/O and HNO/sub 3/ pressures were found to be uniquely determined for each of these solid mixtures.
11. The Observed Relationship Between Water Vapor and Ozone in the Tropical Tropopause Saturation Layer and the Influence of Meridional Transport
NASA Technical Reports Server (NTRS)
Selkirk, Henry B.; Schoeberl, M. R.; Olsen, M. A.; Douglass, A. R.
2011-01-01
We examine balloonsonde observations of water vapor and ozone from three Ticosonde campaigns over San Jose, Costa Rica [10 N, 84 W] during northern summer and a fourth during northern winter. The data from the summer campaigns show that the uppermost portion of the tropical tropopause layer between 360 and 380 K, which we term the tropopause saturation layer or TSL, is characterized by water vapor mixing ratios from proximately 3 to 15 ppmv and ozone from approximately 50 ppbv to 250 ppbv. In contrast, the atmospheric water vapor tape recorder at 380 K and above displays a more restricted 4-7 ppmv range in water vapor mixing ratio. From this perspective, most of the parcels in the TSL fall into two classes - those that need only additional radiative heating to rise into the tape recorder and those requiring some combination of additional dehydration and mixing with drier air. A substantial fraction of the latter class have ozone mixing ratios greater than 150 ppbv, and with water vapor greater than 7 ppmv this air may well have been transported into the tropics from the middle latitudes in conjunction with high-amplitude equatorial waves. We examine this possibility with both trajectory analysis and transport diagnostics based on HIRDLS ozone data. We apply the same approach to study the winter season. Here a very different regime obtains as the ozone-water vapor scatter diagram of the sonde data shows the stratosphere and troposphere to be clearly demarcated with little evidence of mixing in of middle latitude air parcels.
12. 40 CFR 61.242-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2011 CFR
2011-07-01
... devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in gas... 40 Protection of Environment 8 2011-07-01 2011-07-01 false Standards: Pressure relief devices in gas/vapor service. 61.242-4 Section 61.242-4 Protection of Environment ENVIRONMENTAL PROTECTION...
13. 40 CFR 61.242-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2014 CFR
2014-07-01
... devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in gas... 40 Protection of Environment 9 2014-07-01 2014-07-01 false Standards: Pressure relief devices in gas/vapor service. 61.242-4 Section 61.242-4 Protection of Environment ENVIRONMENTAL PROTECTION...
14. 40 CFR 61.242-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2012 CFR
2012-07-01
... devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in gas... 40 Protection of Environment 9 2012-07-01 2012-07-01 false Standards: Pressure relief devices in gas/vapor service. 61.242-4 Section 61.242-4 Protection of Environment ENVIRONMENTAL PROTECTION...
15. 40 CFR 63.1011 - Pressure relief devices in gas and vapor service standards.
Code of Federal Regulations, 2011 CFR
2011-07-01
... Pressure relief devices in gas and vapor service standards. (a) Compliance schedule. The owner or operator... section, each pressure relief device in gas or vapor service shall be operated with an instrument reading... 40 Protection of Environment 10 2011-07-01 2011-07-01 false Pressure relief devices in gas...
16. 40 CFR 264.1054 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2011 CFR
2011-07-01
... relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Standards: Pressure relief devices in gas/vapor service. 264.1054 Section 264.1054 Protection of Environment ENVIRONMENTAL PROTECTION...
17. 40 CFR 264.1054 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2012 CFR
2012-07-01
... relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in... 40 Protection of Environment 27 2012-07-01 2012-07-01 false Standards: Pressure relief devices in gas/vapor service. 264.1054 Section 264.1054 Protection of Environment ENVIRONMENTAL PROTECTION...
18. 40 CFR 63.1011 - Pressure relief devices in gas and vapor service standards.
Code of Federal Regulations, 2014 CFR
2014-07-01
... Pressure relief devices in gas and vapor service standards. (a) Compliance schedule. The owner or operator... section, each pressure relief device in gas or vapor service shall be operated with an instrument reading... 40 Protection of Environment 11 2014-07-01 2014-07-01 false Pressure relief devices in gas...
19. 40 CFR 264.1054 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2010 CFR
2010-07-01
... relief devices in gas/vapor service. (a) Except during pressure releases, each pressure relief device in... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Standards: Pressure relief devices in gas/vapor service. 264.1054 Section 264.1054 Protection of Environment ENVIRONMENTAL PROTECTION...
20. 40 CFR 63.1030 - Pressure relief devices in gas and vapor service standards.
Code of Federal Regulations, 2011 CFR
2011-07-01
... § 63.1030 Pressure relief devices in gas and vapor service standards. (a) Compliance schedule. The... section, each pressure relief device in gas and vapor service shall be operated with an instrument reading... 40 Protection of Environment 10 2011-07-01 2011-07-01 false Pressure relief devices in gas...
1. 40 CFR 63.1030 - Pressure relief devices in gas and vapor service standards.
Code of Federal Regulations, 2014 CFR
2014-07-01
... § 63.1030 Pressure relief devices in gas and vapor service standards. (a) Compliance schedule. The... section, each pressure relief device in gas and vapor service shall be operated with an instrument reading... 40 Protection of Environment 11 2014-07-01 2014-07-01 false Pressure relief devices in gas...
2. 40 CFR 63.1030 - Pressure relief devices in gas and vapor service standards.
Code of Federal Regulations, 2013 CFR
2013-07-01
... § 63.1030 Pressure relief devices in gas and vapor service standards. (a) Compliance schedule. The... section, each pressure relief device in gas and vapor service shall be operated with an instrument reading... 40 Protection of Environment 11 2013-07-01 2013-07-01 false Pressure relief devices in gas...
3. 40 CFR 63.1011 - Pressure relief devices in gas and vapor service standards.
Code of Federal Regulations, 2010 CFR
2010-07-01
... Pressure relief devices in gas and vapor service standards. (a) Compliance schedule. The owner or operator... section, each pressure relief device in gas or vapor service shall be operated with an instrument reading... 40 Protection of Environment 10 2010-07-01 2010-07-01 false Pressure relief devices in gas...
4. 40 CFR 63.1011 - Pressure relief devices in gas and vapor service standards.
Code of Federal Regulations, 2013 CFR
2013-07-01
... Pressure relief devices in gas and vapor service standards. (a) Compliance schedule. The owner or operator... section, each pressure relief device in gas or vapor service shall be operated with an instrument reading... 40 Protection of Environment 11 2013-07-01 2013-07-01 false Pressure relief devices in gas...
5. 40 CFR 63.1030 - Pressure relief devices in gas and vapor service standards.
Code of Federal Regulations, 2010 CFR
2010-07-01
... § 63.1030 Pressure relief devices in gas and vapor service standards. (a) Compliance schedule. The... section, each pressure relief device in gas and vapor service shall be operated with an instrument reading... 40 Protection of Environment 10 2010-07-01 2010-07-01 false Pressure relief devices in gas...
6. Capillary pressure characteristics necessary for simulating DNAPL infiltration, redistribution, and immobilization in saturated porous media
Gerhard, J. I.; Kueper, B. H.
2003-08-01
This study presents a capillary-pressure saturation (PC-S) constitutive model that incorporates the capillary phenomena necessary for simulating the spatial distribution of nonwetting fluid migrating in a saturated porous medium. To develop a model validation data set, a sequence of dense, nonaqueous phase liquid (DNAPL) pools were emplaced, under alternating drainage and imbibition conditions, in a one-dimensional, 1 m tall, saturated sand pack. A light transmission/image analysis system successfully distinguished between connected-phase and residual nonwetting fluid in the apparatus, thereby permitting the accurate measurement of DNAPL pool heights. These heights are found to depend on the nonzero capillary pressure across the fluid-fluid interface at the top of the pool. The terminal pressure is demonstrated to be the minimum sustainable capillary pressure in connected-phase nonwetting fluid experiencing imbibition, below which residual is formed. Additional bench-scale experiments demonstrate that a nonwetting phase pool will penetrate an underlying capillary barrier when the entry pressure is exceeded and that the resulting infiltration will terminate when the capillary pressure at the barrier reduces to the terminal pressure. At the macroscopic scale the terminal pressure corresponds to the extinction saturation (i.e., zero nonwetting phase flow) at the inflection point on the imbibition PC-S curve. A ratio of terminal to entry pressure of approximately 0.6 is found to apply at both bench and macroscopic scales and to be independent of porous media and fluid properties. The developed PC-S constitutive model, which extends the Brooks-Corey function to incorporate the terminal pressure, successfully predicted the behavior observed in the laboratory experiments. Constitutive models that do not incorporate both an entry and a terminal pressure, such as those based upon the standard van Genuchten function, are demonstrated to be unable to predict the observed equilibrium DNAPL pool heights in homogeneous media or above capillary barriers.
7. Revision of Primary Standards Laboratory's methods to calculate water vapor pressures. [ENHANC, RH, RHTAB
SciTech Connect
Odom, M.K.
1986-04-01
Accurate water vapor pressure values are important for humidity calibrations in the Primary Standards Laboratory. Updated and enhanced vapor pressure equations are given. Enhancement takes the presence of air into account. Computer programs that use the updated and enhanced vapor pressure equations are discussed. Included are descriptions of these programs, sample inputs and outputs, structural relationships between main programs, subroutines, and functions, and complete listings of these program elements. 4 refs. 3 tabs. (DWL)
8. Molecular weight of aquatic fulvic acids by vapor pressure osmometry
USGS Publications Warehouse
Aiken, G.R.; Malcolm, R.L.
1987-01-01
The molecular weights of aquatic fulvic acids extracted from five rivers were determined by vapor pressure osmometry with water and tetrahydrofuran as solvents. The values obtained ranged from 500 to 950 dallons, indicating that the molecular weights of aquatic fulvic acids are not as great as has been suggested in some other molecular weight studies. The samples were shown to be relatively monodisperse from radii of gyration measurements determined by small angle x-ray scattering. THF affords greater precision and accuracy than H2O in VPO measurements, and was found to be a suitable solvent for the determination of molecular weight of aquatic fulvic acid because it obviates the dissociation problem. An inverse correlation was observed with these samples between the concentration of Ca++ and Mg++ in the river water and the radii of gyration and molecular weights of the corresponding fulvic acid samples. ?? 1987.
9. The vapor pressures of solid and liquid ozone
NASA Technical Reports Server (NTRS)
1986-01-01
Vapor pressures of solid and liquid ozone have been measured over a temperature range 87 to below 66 K. The experiment was performed under flow conditions, and the gas was analyzed by a precision mass spectrometer system. In the range of solid ozone two forms, supercooled and crystalline ozone, were found. A least-square fit of the data for crystalline ozone resulted in the equation log P(torr) = A + B/T, where A = 10.460 and B = -1021.6. The estimated uncertainty of the data is + or - 1.0 percent. A triple-point temperature of 79.6 + or - 0.3 K was found where supercooled and crystalline ozone data intersect.
10. Measurement of equilibrium elemental vapor pressures using x-ray induced fluorescense.
SciTech Connect
Curry, J. J; Henins, A.; Estupinan, E. G.; Lapatovich, W. P.; Shastri, S. D.
2011-04-29
X-ray induced fluorescence is demonstrated as a novel and fast method for measuring vapor pressures at high temperatures and high pressures. As such, it is an excellent complement to the effusion method, which is limited to lower pressures. High-energy synchrotron radiation was used to measure the total densities of Dy in the equilibrium vapor over condensed DyI{sub 3} and Tm in the equilibrium vapor over condensed TmI{sub 3}. Corresponding vapor pressures were determined with measured vapor cell temperatures across a range of vapor pressures of nearly three orders of magnitude, from less than 10{sup 2} Pa to more than 10{sup 4} Pa. Individual data points were obtained in time periods ranging from 10 to 30 s each.
11. Comparison of average and point capillary pressure-saturation functions determined by steady-state centrifugation
SciTech Connect
Cropper, Clark; Perfect, Edmund; van den Berg, Dr. Elmer; Mayes, Melanie
2010-01-01
The capillary pressure-saturation function can be determined from centrifuge drainage experiments. In soil physics, the data resulting from such experiments are usually analyzed by the 'averaging method.' In this approach, average relative saturation, , is expressed as a function of average capillary pressure, <{psi}>, i.e., (<{psi}>). In contrast, the capillary pressure-saturation function at a physical point, i.e., S({psi}), has been extracted from similar experiments in petrophysics using the 'integral method.' The purpose of this study was to introduce the integral method applied to centrifuge experiments to a soil physics audience and to compare S({psi}) and (<{psi}>) functions, as parameterized by the Brooks-Corey and van Genuchten equations, for 18 samples drawn from a range of porous media (i.e., Berea sandstone, glass beads, and Hanford sediments). Steady-state centrifuge experiments were performed on preconsolidated samples with a URC-628 Ultra-Rock Core centrifuge. The angular velocity and outflow data sets were then analyzed using both the averaging and integral methods. The results show that the averaging method smoothes out the drainage process, yielding less steep capillary pressure-saturation functions relative to the corresponding point-based curves. Maximum deviations in saturation between the two methods ranged from 0.08 to 0.28 and generally occurred at low suctions. These discrepancies can lead to inaccurate predictions of other hydraulic properties such as the relative permeability function. Therefore, we strongly recommend use of the integral method instead of the averaging method when determining the capillary pressure-saturation function by steady-state centrifugation. This method can be successfully implemented using either the van Genuchten or Brooks-Corey functions, although the latter provides a more physically precise description of air entry at a physical point.
12. Arterial blood oxygen saturation during blood pressure cuff-induced hypoperfusion
Kyriacou, P. A.; Shafqat, K.; Pal, S. K.
2007-10-01
Pulse oximetry has been one of the most significant technological advances in clinical monitoring in the last two decades. Pulse oximetry is a non-invasive photometric technique that provides information about the arterial blood oxygen saturation (SpO2) and heart rate, and has widespread clinical applications. When peripheral perfusion is poor, as in states of hypovolaemia, hypothermia and vasoconstriction, oxygenation readings become unreliable or cease. The problem arises because conventional pulse oximetry sensors must be attached to the most peripheral parts of the body, such as finger, ear or toe, where pulsatile flow is most easily compromised. Pulse oximeters estimate arterial oxygen saturation by shining light at two different wavelengths, red and infrared, through vascular tissue. In this method the ac pulsatile photoplethysmographic (PPG) signal associated with cardiac contraction is assumed to be attributable solely to the arterial blood component. The amplitudes of the red and infrared ac PPG signals are sensitive to changes in arterial oxygen saturation because of differences in the light absorption of oxygenated and deoxygenated haemoglobin at these two wavelengths. From the ratios of these amplitudes, and the corresponding dc photoplethysmographic components, arterial blood oxygen saturation (SpO2) is estimated. Hence, the technique of pulse oximetry relies on the presence of adequate peripheral arterial pulsations, which are detected as photoplethysmographic (PPG) signals. The aim of this study was to investigate the effect of pressure cuff-induced hypoperfusion on photoplethysmographic signals and arterial blood oxygen saturation using a custom made finger blood oxygen saturation PPG/SpO2 sensor and a commercial finger pulse oximeter. Blood oxygen saturation values from the custom oxygen saturation sensor and a commercial finger oxygen saturation sensor were recorded from 14 healthy volunteers at various induced brachial pressures. Both pulse oximeters showed gradual decrease of saturations during induced hypoperfusion which demonstrate the direct relation between blood volumes (PPG amplitudes), arterial vessel stenosis and blood oxygen saturation. The custom made pulse oximeter was found to be more sensitive to SpO2 changes than the commercial pulse oximeter especially at high occluding pressures.
13. Effect of interfacial forces on two-phase capillary pressuresaturation relationships
Demond, Avery H.; Roberts, Paul V.
1991-03-01
Quantitative descriptions of two-phase flow in the subsurface require knowledge of the capillary pressure-saturation relationships. The effect of interfacial forces on the drainage capillary pressure-saturation relationship for organic liquid-water systems is usually expressed by the ratio of the liquid-liquid interfacial tensions as given by Leverett's (1941) function. To assess the appropriateness of this approach for primary drainage of organic liquid-water systems typical of hazardous waste sites and to evaluate its extendability to spontaneous imbibition, measurements were made of these relationships for various immiscible liquid systems in unconsolidated sand. The results showed increasing deviations with decreasing interfacial forces between the measured values and those predicted by a ratio of interfacial tensions. To improve the predictive capability of Leverett's function, forms including the intrinsic contact angle and roughness were examined. Scaling of the capillary pressure relationships was best achieved by including a correction for both interface curvature and roughness. These corrections became significant for drainage for contact angles larger than 35-55, and for imbibition for contact angles larger than 15-25. None of the forms of Leverett's function examined predicted the increased residual saturation with decreasing interfacial forces observed in this study. Consequently, their ability to scale the measured data was predicated on posing the saturation of the wetting phase in terms of the variable effective saturation.
14. Construction and performance of an ultrahigh vacuum-compatible high temperature vapor dosing system for low vapor pressure compounds
Thompson, L.; Lee, J.-G.; Maksymovych, P.; Ahner, J.; Yates, J. T., Jr.
2003-03-01
A gas dosing system for the quantitative deposition of low vapor pressure compounds onto surfaces in an ultrahigh vacuum system is reported. The dosing system is maintained at elevated temperature to achieve sufficiently high gas pressure for rapid transfer to the surface. Dosing is achieved through a heated calibrated leak valve which connects the high temperature source system to an internal tubular doser. The leak valve and the internal doser head are heated to a higher temperature than the source system to prevent condensation of the compound. The quantitative behavior of this doser is demonstrated for two low vapor pressure compounds.
15. Long shear fractures in CO/sub 2/ lines controlled by regulating saturation, arrest pressures
SciTech Connect
Maxey, W.A.
1986-08-01
Long shear fractures in liquid CO/sub 2/ pipelines can be controlled by lowering the saturation pressure of the liquid or raising the arrest pressure of the line pipe, or doing both. This is the major conclusion of ductile fracture propagation tests conducted by Battelle Laboratories, Columbus, Ohio. The saturation pressure is reduced by lowering the operating temperature of the pipeline and by removing impurities with lower critical temperatures than CO/sub 2/. The arrest pressure of the pipeline can be elevated by increasing the wall thickness, by increasing the wall thickness, by increasing the material toughness, by decreasing the pipe diameter, by increasing the material's yield strength, or some combination thereof. The Battelle tests further suggested the precracked drop-weight-tear test (DWTT) impact energy as an improved measure of material toughness.
16. Impact of sample geometry on the measurement of pressure-saturation curves: Experiments and simulations
Moura, M.; Fiorentino, E.-A.; Mly, K. J.; Schfer, G.; Toussaint, R.
2015-11-01
In this paper, we study the influence of sample geometry on the measurement of pressure-saturation relationships, by analyzing the drainage of a two-phase flow from a quasi-2-D random porous medium. The medium is transparent, which allows for the direct visualization of the invasion pattern during flow, and is initially saturated with a viscous liquid (a dyed glycerol-water mix). As the pressure in the liquid is gradually reduced, air penetrates from an open inlet, displacing the liquid which leaves the system from an outlet on the opposite side. Pressure measurements and images of the flow are recorded and the pressure-saturation relationship is computed. We show that this relationship depends on the system size and aspect ratio. The effects of the system's boundaries on this relationship are measured experimentally and compared with simulations produced using an invasion percolation algorithm. The pressure build up at the beginning and end of the invasion process are particularly affected by the boundaries of the system whereas at the central part of the model (when the air front progresses far from these boundaries), the invasion happens at a statistically constant capillary pressure. These observations have led us to propose a much simplified pressure-saturation relationship, valid for systems that are large enough such that the invasion is not influenced by boundary effects. The properties of this relationship depend on the capillary pressure thresholds distribution, sample dimensions, and average pore connectivity and its applications may be of particular interest for simulations of two-phase flow in large porous media.
17. Pressure and fluid saturation prediction in a multicomponent reservoir, using combined seismic and electromagnetic imaging
SciTech Connect
Hoversten, G.M.; Gritto, Roland; Washbourne, John; Daley, Tom
2002-06-10
This paper presents a method for combining seismic and electromagnetic measurements to predict changes in water saturation, pressure, and CO{sub 2} gas/oil ratio in a reservoir undergoing CO{sub 2} flood. Crosswell seismic and electromagnetic data sets taken before and during CO{sub 2} flooding of an oil reservoir are inverted to produce crosswell images of the change in compressional velocity, shear velocity, and electrical conductivity during a CO{sub 2} injection pilot study. A rock properties model is developed using measured log porosity, fluid saturations, pressure, temperature, bulk density, sonic velocity, and electrical conductivity. The parameters of the rock properties model are found by an L1-norm simplex minimization of predicted and observed differences in compressional velocity and density. A separate minimization, using Archie's law, provides parameters for modeling the relations between water saturation, porosity, and the electrical conductivity. The rock-properties model is used to generate relationships between changes in geophysical parameters and changes in reservoir parameters. Electrical conductivity changes are directly mapped to changes in water saturation; estimated changes in water saturation are used along with the observed changes in shear wave velocity to predict changes in reservoir pressure. The estimation of the spatial extent and amount of CO{sub 2} relies on first removing the effects of the water saturation and pressure changes from the observed compressional velocity changes, producing a residual compressional velocity change. This velocity change is then interpreted in terms of increases in the CO{sub 2}/oil ratio. Resulting images of the CO{sub 2}/oil ratio show CO{sub 2}-rich zones that are well correlated to the location of injection perforations, with the size of these zones also correlating to the amount of injected CO{sub 2}. The images produced by this process are better correlated to the location and amount of injected CO{sub 2} than are any of the individual images of change in geophysical parameters.
18. MODEL FOR HYSTERETIC CONSTITUTIVE RELATIONS GOVERNING MULTIPHASE FLOW. 1. SATURATION-PRESSURE RELATIONS
EPA Science Inventory
In these companion papers, a general theoretical model is presented for the description of functional relationships between relative permeability k, fluid saturation S, and pressure P in two- or three-phase (e.g., air-water or air-oil-water) porous media systems subject to arbitr...
19. MEASUREMENT AND PREDICTION OF SATURATION-PRESSURE RELATIONSHIPS IN THREE-PHASE POROUS MEDIA SYSTEMS
EPA Science Inventory
Scaled multiphase versions of the Brooks-Corey and van Genuchten retention functions were used to describe saturation-capillary pressure curves measured in air-water, air-organic liquid and organic liquid-water systems in a sandy porous medium for four organic liquids during mono...
20. Low pressure differential discharge characteristics of saturated liquids passing through orifices
SciTech Connect
Rohloff, T.J.; Catton, I.
1996-09-01
An experimental investigation has been performed to determine the effect of variation in the length-to-diameter ratios on the discharge characteristics of saturated liquids passing through square edge orifices subjected to low pressure differentials. Experiments were performed to confirm reported results for sharp edge orifices and for round edge orifices with appreciable ratios of inlet corner radius to orifice diameter.
1. Feasibility of hydroxyl concentration measurements by laser-saturated fluorescence in high-pressure flames
SciTech Connect
Carter, C.D.; Salmon, J.T.; King, G.B.; Leaurendau, N.M.
1987-11-01
A feasibility study has been performed on the application of laser-saturated fluorescence (LSF) to the measurement of OH concentration in high-pressure flames. Using a numerial model for the collisional dynamics of the OH molecule under nonuniform laser excitation, we have investigated the effect of pressure on the balanced cross-rate model and determined the sensitivity of the depopulation of the laser-coupled levels to the ratio of rate coefficients describing (1) electronic quenching of the vibrational levels for which v''>0 and (2) vibrational relaxation from v''>0 to v'' = 0. At sufficiently high pressures in near-saturated conditions, the total population of the laser-coupled levels reaches an asymptotic value, which is insensitive to the degree of saturation. When the ratio of electronic quenching is vibrational relaxation is small and the rate coefficients for rotational transfer in the ground and excited electronic states are nearly the same, the balanced cross-rate model remains a good approximation for all pressures. When the above ratio is large, depopulation of the laser-coupled levels becomes significant at high pressures, and thus the balanced cross-rate model no longer holds. In these conditions, however, knowledge of the asymptotic value achieved by the laser-coupled levels could be used to correct the balanced cross-rate model and thus allow LSF measurements at sufficiently high pressures.
2. Total sulfur dioxide emissions and pre-eruption vapor-saturated magma at Mount St. Helens, 1980-88
SciTech Connect
Gerlach, T.M.; McGee, K.A.
1994-12-15
SO{sub 2} from explosive volcanism can cause significant climatic and atmospheric impacts, but the source of the sulfur is controversial. TOMS, COSPEC, and ash leachate data for Mount St. Helens from the time of the climactic eruption on 18 May 1980 to the final stages of non-explosive degassing in 1988 give a total SO{sub 2} emission of 2 Mt. COSPEC data show a sharp drop in emission rate that was apparently controlled by a decreasing rate of magma supply. A total SO{sub 2} emission of only 0.08 Mt is estimated from melt inclusion data and the conventional assumption that the main sulfur source was pre-eruption melt; commonly invoked sources of {open_quotes}excess sulfur{close_quotes} (anhydrite decomposition, basaltic magma, and degassing of non-erupted magma) are unlikely in this case. Thus melt inclusions may significantly underestimate SO{sub 2} emissions and impacts of explosive volcanism on climate and the atmosphere. Measured CO{sub 2} emissions, together with the H{sub 2}O content of melt inclusions and experimental solubility data, indicate the Mount St. Helens dacite was vapor-saturated at depth prior to ascent and suggest that a vapor phase was the main source of sulfur for the 2-Mt of SO{sub 2}. A vapor source is consistent with experimental studies on the Mount St. Helens dacite and removes the need for a much debated shallow magma body. 23 refs., 3 figs.
3. Chemically enhanced mixed region vapor stripping of TCE-contaminated saturated peat and silty clay soils
SciTech Connect
West, O.R.; Cameron, P.A.; Lucero, A.J.; Koran, L.J. Jr.
1996-01-01
The objective of this study was to conduct further testing of MRVS, chemically enhanced with calcium oxide conditioning, on field- contaminated soils collected from beneath the NASA Michoud Rinsewater Impoundment. In this study, residual soil VOC levels as a function of vapor stripping time were measured to quantify VOC removal rates. Physical and chemical soil parameters expected to affect MRVS efficiency were measures. The effects of varying the calcium oxide loadings as well as varying the vapor stripping flow rates on VOC removal were also evaluated. The results of this study will be used to determine whether acceptable removals can be achieved within reasonable treatment times, remediation costs being directly proportional to the latter. The purpose of this report is to document the experimental results of this study, as well as to address issues that were raised after completion of the previous Michoud treatability work.
4. Temperature and saturation dependence in the vapor sensing of butterfly wing scales.
PubMed
Kertsz, K; Piszter, G; Jakab, E; Blint, Zs; Vrtesy, Z; Bir, L P
2014-06-01
The sensing of gasses/vapors in the ambient air is the focus of attention due to the need to monitor our everyday environment. Photonic crystals are sensing materials of the future because of their strong light-manipulating properties. Natural photonic structures are well-suited materials for testing detection principles because they are significantly cheaper than artificial photonic structures and are available in larger sizes. Additionally, natural photonic structures may provide new ideas for developing novel artificial photonic nanoarchitectures with improved properties. In the present paper, we discuss the effects arising from the sensor temperature and the vapor concentration in air during measurements with a photonic crystal-type optical gas sensor. Our results shed light on the sources of discrepancy between simulated and experimental sensing behaviors of photonic crystal-type structures. Through capillary condensation, the vapors will condensate to a liquid state inside the nanocavities. Due to the temperature and radius of curvature dependence of capillary condensation, the measured signals are affected by the sensor temperature as well as by the presence of a nanocavity size distribution. The sensing materials used are natural photonic nanoarchitectures present in the wing scales of blue butterflies. PMID:24863219
5. Method and apparatus to measure vapor pressure in a flow system
DOEpatents
Grossman, M.W.; Biblarz, O.
1991-10-15
The present invention is directed to a method for determining, by a condensation method, the vapor pressure of a material with a known vapor pressure versus temperature characteristic, in a flow system particularly in a mercury isotope enrichment process. 2 figures.
6. 40 CFR 65.111 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2013 CFR
2013-07-01
...: Pressure relief devices in gas/vapor service. (a) Compliance schedule. The owner or operator shall comply... 40 Protection of Environment 16 2013-07-01 2013-07-01 false Standards: Pressure relief devices in gas/vapor service. 65.111 Section 65.111 Protection of Environment ENVIRONMENTAL PROTECTION...
7. 40 CFR 65.111 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2012 CFR
2012-07-01
...: Pressure relief devices in gas/vapor service. (a) Compliance schedule. The owner or operator shall comply... 40 Protection of Environment 16 2012-07-01 2012-07-01 false Standards: Pressure relief devices in gas/vapor service. 65.111 Section 65.111 Protection of Environment ENVIRONMENTAL PROTECTION...
8. 40 CFR 65.111 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2011 CFR
2011-07-01
...: Pressure relief devices in gas/vapor service. (a) Compliance schedule. The owner or operator shall comply... 40 Protection of Environment 15 2011-07-01 2011-07-01 false Standards: Pressure relief devices in gas/vapor service. 65.111 Section 65.111 Protection of Environment ENVIRONMENTAL PROTECTION...
9. Analysis of crude oil vapor pressures at the U.S. Strategic Petroleum Reserve.
SciTech Connect
Rudeen, David Keith; Lord, David L.
2005-08-01
Crude oil storage caverns at the U.S. Strategic Petroleum Reserve (SPR) are solution-mined from subsurface salt domes along the U.S. Gulf Coast. While these salt domes exhibit many attractive characteristics for large-volume, long-term storage of oil such as low cost for construction, low permeability for effective fluids containment, and secure location deep underground, they also present unique technical challenges for maintaining oil quality within delivery standards. The vapor pressures of the crude oils stored at SPR tend to increase with storage time due to the combined effects of geothermal heating and gas intrusion from the surrounding salt. This presents a problem for oil delivery offsite because high vapor-pressure oil may lead to excessive atmospheric emissions of hydrocarbon gases that present explosion hazards, health hazards, and handling problems at atmospheric pressure. Recognizing this potential hazard, the U.S. Department of Energy, owner and operator of the SPR, implemented a crude oil vapor pressure monitoring program that collects vapor pressure data for all the storage caverns. From these data, DOE evaluates the rate of change in vapor pressures of its oils in the SPR. Moreover, DOE implemented a vapor pressure mitigation program in which the oils are degassed periodically and will be cooled immediately prior to delivery in order to reduce the vapor pressure to safe handling levels. The work described in this report evaluates the entire database since its origin in 1993, and determines the current levels of vapor pressure around the SPR, as well as the rate of change for purposes of optimizing both the mitigation program and meeting safe delivery standards. Generally, the rate of vapor pressure increase appears to be lower in this analysis than reported in the past and, problematic gas intrusion seems to be limited to just a few caverns. This being said, much of the current SPR inventory exceeds vapor pressure delivery guidelines and must be degassed and cooled in order to meet current delivery standards.
10. 46 CFR 153.372 - Gauges and vapor return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia).
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 5 2011-10-01 2011-10-01 false Gauges and vapor return for cargo vapor pressures... COMPRESSED GAS HAZARDOUS MATERIALS Design and Equipment Cargo Venting Systems 153.372 Gauges and vapor... section, the containment system must have a: (a) Tank pressure gauge at the point where cargo flow...
11. 46 CFR 153.372 - Gauges and vapor return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia).
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 5 2014-10-01 2014-10-01 false Gauges and vapor return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia). 153.372 Section 153.372 Shipping COAST GUARD, DEPARTMENT OF HOMELAND... return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia). When table 1 references...
12. 46 CFR 153.372 - Gauges and vapor return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia).
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 5 2013-10-01 2013-10-01 false Gauges and vapor return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia). 153.372 Section 153.372 Shipping COAST GUARD, DEPARTMENT OF HOMELAND... return for cargo vapor pressures exceeding 100 kPa (approx. 14.7 psia). When table 1 references...
13. 46 CFR 39.20-13 - High and low vapor pressure protection for tankships-T/ALL.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false High and low vapor pressure protection for tankships-T... VAPOR CONTROL SYSTEMS Design and Equipment § 39.20-13 High and low vapor pressure protection for... vessel where the cargo transfer is controlled; and (b) Has a high pressure and a low pressure alarm...
14. 46 CFR 39.20-13 - High and low vapor pressure protection for tankships-T/ALL.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 1 2011-10-01 2011-10-01 false High and low vapor pressure protection for tankships-T... VAPOR CONTROL SYSTEMS Design and Equipment § 39.20-13 High and low vapor pressure protection for... vessel where the cargo transfer is controlled; and (b) Has a high pressure and a low pressure alarm...
15. 46 CFR 39.20-13 - High and low vapor pressure protection for tankships-T/ALL.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 1 2012-10-01 2012-10-01 false High and low vapor pressure protection for tankships-T... VAPOR CONTROL SYSTEMS Design and Equipment § 39.20-13 High and low vapor pressure protection for... vessel where the cargo transfer is controlled; and (b) Has a high pressure and a low pressure alarm...
16. Correlation of chemical evaporation rate with vapor pressure.
PubMed
Mackay, Donald; van Wesenbeeck, Ian
2014-09-01
A new one-parameter correlation is developed for the evaporation rate (ER) of chemicals as a function of molar mass (M) and vapor pressure (P) that is simpler than existing correlations. It applies only to liquid surfaces that are unaffected by the underlying solid substrate as occurs in the standard ASTM evaporation rate test and to quiescent liquid pools. The relationship has a sounder theoretical basis than previous correlations because ER is correctly correlated with PM rather than P alone. The inclusion of M increases the slope of previous log ER versus log P regressions to a value close to 1.0 and yields a simpler one-parameter correlation, namely, ER (?g m(-1) h(-1)) = 1464P (Pa) M (g mol(-1)). Applications are discussed for the screening level assessment and ranking of chemicals for evaporation rate, such as pesticides, fumigants, and hydrocarbon carrier fluids used in pesticide formulations, liquid consumer products used indoors, and accidental spills of liquids. The mechanistic significance of the single parameter as a mass-transfer coefficient or velocity is discussed. PMID:25105222
17. Binding Energy, Vapor Pressure and Melting Point of Semiconductor Nanoparticles
SciTech Connect
H. H. Farrell; C. D. Van Siclen
2007-07-01
Current models for the cohesive energy of nanoparticles generally predict a linear dependence on the inverse particle diameter for spherical clusters, or, equivalently, on the inverse of the cube root of the number of atoms in the cluster. Although this is generally true for metals, we find that for the group IV semiconductors, C, Si and Ge, this linear dependence does not hold. Instead, using first principles, density functional theory calculations to calculate the binding energy of these materials, we find a quadratic dependence on the inverse of the particle size. Similar results have also been obtained for the metallic group IV elements Sn and Pb. This is in direct contradiction to current assumptions. Further, as a consequence of this quadratic behavior, the vapor pressure of semiconductor nanoparticles rises more slowly with decreasing size than would be expected. In addition, the melting point of these nanoparticles will experience less suppression than experienced by metal nanoparticles with comparable bulk binding energies. This non-linearity also affects sintering or Ostwald ripening behavior of these nanoparticles as well as other physical properties that depend on the nanoparticle binding energy. The reason for this variation in size dependence involves the covalent nature of the bonding in semiconductors, and even in the poor metals. Therefore, it is expected that this result will hold for compound semiconductors as well as the elemental semiconductors.
18. A new ozone standard - The vapor pressure of ozone at liquid argon temperatures
NASA Technical Reports Server (NTRS)
Mauersberger, K.; Hanson, D.; Morton, J.
1985-01-01
The vapor pressure of ozone has been measured at liquid argon temperatures. At the normal boiling point of argon (-185.9 C) an ozone pressure of 0.0405 torr was obtained with an accuracy of + or - 1.5 percent. Increases and decreases in liquid argon temperatures raised and lowered the ozone vapor pressure, respectively. During the vapor pressure measurements the purity of ozone was monitored with a mass spectrometer. The proposed ozone standard will considerably improve the calibration of experiments for atmospheric research, the determination of absorption cross sections and other laboratory ozone studies.
19. Oxygen saturation changes in the optic nerve head during acute intraocular pressure elevation in monkeys
Khoobehi, Bahram; Kawano, Hiroyuki; Ning, Jinfeng; Burgoyne, Claude F.; Rice, David A.; Khan, Fareeha; Thompson, Hilary W.; Beach, James M.
2009-02-01
Background and Objective: To evaluate the effect of an acute elevated intraocular pressure (IOP) on oxygen saturation of structures of the optic nerve head. Study Design/Materials and Methods: In the cynomolgus monkey eye, IOP was set to 10 mm Hg, and then raised to 30, 45, and 55 mm Hg. The ONH and overlying vessels were imaged using a fundus camera attached to a hyperspectral imaging system (HSI) at 10 and 30 minutes after IOP elevation. Results: Raising IOP from 10 to 30 mm Hg did not significantly (P < 0.0001) change saturation in vessels or ONH tissue structures but at 55 mm Hg, all structures showed significant reduction. Conclusions: Quantitative assay of the blood oxygen saturation in structures on the surface and overlying the optic nerve head is possible using hyperspectral imaging techniques.
20. Vapor pressures and heats of vaporization of primary coal tars. Quarterly technical progress report, July 1--September 30, 1995
SciTech Connect
Suuberg, E.M.
1995-12-31
There is significant current interest in general area of coal pyrolysis, particularly because of the central role of pyrolysis in all thermally driven coal conversion processes-gasification, combustion, liquefaction, mild gasification, or thermal beneficiation. There remain several key data needs in these application areas. Among them is a need for more reliable correlation for prediction of vapor pressure of heavy, primary coal tars. The vapor pressure correlations that exist at present for coal tars are very crude and they are not considered reliable to even an order of magnitude when applied to tars. The present project seeks to address this important gap in the near term by direct measurement of vapor pressures of coal tar fractions, by application of well-established techniques and modifications thereof. The principal objectives of the program are to: (1) obtain data on the vapor pressures and heats of vaporization of tars from a range of ranks of coal, (2) develop correlations based on a minimum set of conveniently measurable characteristics of the tars, (3) develop equipment that would allow performing such measurements in a reliable, straightforward fashion. A significant amount of time has been devoted during this quarter to extending the work on measurements of vapor pressures of tars. For this purpose, cellulose tar and cellulose tar related compounds have been selected as model systems. Cellulose tar has a much narrower distribution of molecular weight than does coal tar, and it is much more homogeneous. Thus it is better to develop the methods to be used for coal tars on this simpler model system first.
1. Sound Propagation in Saturated Gas-Vapor-Droplet Suspensions Considering the Effect of Transpiration on Droplet Evaporation
NASA Technical Reports Server (NTRS)
Kandula, Max
2012-01-01
The Sound attenuation and dispersion in saturated gas-vapor-droplet mixtures with evaporation has been investigated theoretically. The theory is based on an extension of the work of Davidson (1975) to accommodate the effects of transpiration on the linear particle relaxation processes of mass, momentum and energy transfer. It is shown that the inclusion of transpiration in the presence of mass transfer improves the agreement between the theory and the experimental data of Cole and Dobbins (1971) for sound attenuation in air-water fogs at low droplet mass concentrations. The results suggest that transpiration has an appreciable effect on both sound absorption and dispersion for both low and high droplet mass concentrations.
2. An Inexpensive Microscale Method for Measuring Vapor Pressure, Associated Thermodynamic Variables, and Molecular Weight
Demuro, Jason C.; Margarian, Hovanes; Mkhikian, Artavan; No, Kwang Hi; Peterson, Andrew R.
1999-08-01
Existing methods for measuring vapor pressure are too expensive or not quantitative enough for chemistry classes in secondary schools. Our method measures the vapor pressure inside a bubble trapped in a graduated microtube made from a disposable 1-mL glass pipet. Vapor pressures of water, methanol, and ethanol are measured over temperature ranges of 4-90 C. The enthalpy and entropy of vaporization and boiling points, calculated using the Clausius-Clapeyron equation, agree well with published values. The vapor pressures of aqueous solutions of ethanol and methanol plotted against mole fractions of water give positive deviations from Raoult's law, but concentrations were identified from which molecular weights of the alcohols could be calculated. These molecular weights are not significantly different from published values. Sources of error in the method are analyzed. A procedure for use in secondary schools is outlined.
3. U.S. Strategic Petroleum Reserve Vapor Pressure Committee 2009 annual report.
SciTech Connect
Allen, Ray; Eldredge, Lisa; DeLuca, Charles; Mihalik, Patrick; Maldonado, Julio; Lord, David L.; Rudeen, David Keith; Berndsen, Gerard
2010-05-01
This report comprises an annual summary of activities under the U.S. Strategic Petroleum Reserve (SPR) Vapor Pressure Committee in FY2009. The committee provides guidance to senior project management on the issues of crude oil vapor pressure monitoring nd mitigation. The principal objectives of the vapor pressure program are, in the event of an SPR drawdown, to minimize the impact on the environment and assure worker safety and public health from crude oil vapor emissions. The annual report reviews key program areas ncluding monitoring program status, mitigation program status, new developments in measurements and modeling, and path forward including specific recommendations on cavern sampling for the next year. The contents of this report were first presented to SPR senior anagement in December 2009, in a deliverable from the vapor pressure committee. The current SAND report is an adaptation for the Sandia technical audience.
4. Pluto's atmosphere - Models based on refraction, inversion, and vapor-pressure equilibrium
NASA Technical Reports Server (NTRS)
Eshleman, Von R.
1989-01-01
Viking spacecraft radio-occultation measurements indicate that, irrespective of substantial differences, the polar ice cap regions on Mars have inversions similar to those of Pluto, and may also share vapor pressure equilibrium characteristics at the surface. This temperature-inversion phenomenon occurs in a near-surface boundary layer; surface pressure-temperature may correspond to the vapor-pressure equilibrium with CH4 ice, or the temperature may be slightly higher to match the value derived from IRAS data.
5. PHOTOLYSIS OF ARYL KETONES WITH VARYING VAPOR PRESSURE ON SOIL
EPA Science Inventory
The photolysis of a series of aryl ketones on air-dried soil surfaces was examined to establish whether vapor transport has an effect on the rate and extent of photolysis. f vapor transport were significant on light-exposed soils, then differences in the observed photolysis rate ...
6. A Transformed Pressure Head-Based Approach to Solve Richards' Equation for Variably Saturated Soils
Pan, Lehua; Wierenga, Peter J.
1995-04-01
This paper presents a new approach to solve Richards' equation. It introduces a nonlinear transformed pressure, Pt, as the dependent variable with the modified Picard method. The new approach was compared to, and contrasted with, two efficient existing methods: the ϕ-based transformation method (Kirkland et al., 1992), and the h-based modified Picard method (Celia et al., 1990). A total of 12 different one-dimensional cases were considered (saturated, unsaturated, layered and uniform soil profiles, with pressure and flux type boundary conditions). The results show that the new method offers excellent CPU efficiency and, unlike the h-based method, is numerically robust for all cases of variably saturated, heterogeneous media, and first or second type boundary conditions. The method does not require difficult numerical coding, and its CPU efficiency is not affected by complicated heterogeneous and hysteretic media. The Pt transformation is easy to incorporate into existing h-based codes.
7. A new theoretical method for calculating temperature and water vapor saturation ratio in an expansion cloud chamber
Moteki, Nobuhiro; Kondo, Yutaka
2013-06-01
The expansion cloud chamber is a widely used apparatus for investigating the dynamics of condensational growth of aerosols and clouds. Theoretical calculations of temperature T and water vapor saturation ratio S are necessary for quantitative interpretations of experimental data obtained from the expansion cloud chamber. In this paper, we revisit the thermodynamics associated with the underlying assumptions for calculating the time-dependent temperature T(t) and saturation ratio S(t) in an expansion chamber as a function of experimentally observable parameters. We introduce an intuitive and robust method, the virtual path (VP) method, by which changes in the thermodynamic state of a moist air parcel containing cloud droplets are schematically represented on a thermodynamic diagram. The validity of the VP method is confirmed by comparisons with the differential equation (DE) method, which is a numerical simulation of real physical processes according to the time evolution equations involving T and S. In contrast to the conventional DE method, the governing equations of the VP method do not involve time t, an irrelevant parameter in the framework of classical thermodynamics. The VP method is advantageous compared to the DE method because the former is applicable to the raw experimental data acquired with a finite time resolution, allowing a robust calculation of the T and S values and the errors that are only caused by the measurement errors of the input data.
8. Relating oxygen partial pressure, saturation and content: the haemoglobinoxygen dissociation curve
PubMed Central
Rudenski, Aram; Gibson, John; Howard, Luke; ODriscoll, Ronan
2015-01-01
Key Points In clinical practice, the level of arterial oxygenation can be measured either directly by blood gas sampling to measure partial pressure (PaO2) and percentage saturation (SaO2) or indirectly by pulse oximetry (SpO2). This review addresses the strengths and weaknesses of each of these tests and gives advice on their clinical use. The haemoglobinoxygen dissociation curve describing the relationship between oxygen partial pressure and saturation can be modelled mathematically and routinely obtained clinical data support the accuracy of a historical equation used to describe this relationship. Educational Aims To understand how oxygen is delivered to the tissues. To understand the relationships between oxygen saturation, partial pressure, content and tissue delivery. The clinical relevance of the haemoglobinoxygen dissociation curve will be reviewed and we will show how a mathematical model of the curve, derived in the 1960s from limited laboratory data, accurately describes the relationship between oxygen saturation and partial pressure in a large number of routinely obtained clinical samples. To understand the role of pulse oximetry in clinical practice. To understand the differences between arterial, capillary and venous blood gas samples and the role of their measurement in clinical practice. The delivery of oxygen by arterial blood to the tissues of the body has a number of critical determinants including blood oxygen concentration (content), saturation (SO2) and partial pressure, haemoglobin concentration and cardiac output, including its distribution. The haemoglobinoxygen dissociation curve, a graphical representation of the relationship between oxygen saturation and oxygen partial pressure helps us to understand some of the principles underpinning this process. Historically this curve was derived from very limited data based on blood samples from small numbers of healthy subjects which were manipulated in vitro and ultimately determined by equations such as those described by Severinghaus in 1979. In a study of 3524 clinical specimens, we found that this equation estimated the SO2 in blood from patients with normal pH and SO2 >70% with remarkable accuracy and, to our knowledge, this is the first large-scale validation of this equation using clinical samples. Oxygen saturation by pulse oximetry (SpO2) is nowadays the standard clinical method for assessing arterial oxygen saturation, providing a convenient, pain-free means of continuously assessing oxygenation, provided the interpreting clinician is aware of important limitations. The use of pulse oximetry reduces the need for arterial blood gas analysis (SaO2) as many patients who are not at risk of hypercapnic respiratory failure or metabolic acidosis and have acceptable SpO2 do not necessarily require blood gas analysis. While arterial sampling remains the gold-standard method of assessing ventilation and oxygenation, in those patients in whom blood gas analysis is indicated, arterialised capillary samples also have a valuable role in patient care. The clinical role of venous blood gases however remains less well defined. PMID:26632351
9. Uni-axial wave propagation and pore pressure generation in fluid saturated sands exhibiting irreversible compaction
Morland, L. W.; Staroszczyk, R.
1998-09-01
The propagation of a plane load-unload pulse through a compacting sand is analysed and illustrated for both dry sand and liquid saturated sand in undrained conditions. A major feature is the interaction between the initial loading wave and the faster following unloading wave. Free draining and undrained conditions exhibit distinct qualitative and quantitative results, and the pore liquid pressure generation is a significant physical feature. Illustrations show the effects of different applied surface pulse shapes.
10. Prediction of two-phase capillary pressure-saturation relationships in fractional wettability systems.
PubMed
O'Carroll, Denis M; Abriola, Linda M; Polityka, Catherine A; Bradford, Scott A; Demond, Avery H
2005-05-01
Capillary pressure/saturation data are often difficult and time consuming to measure, particularly for non-water-wetting porous media. Few capillary pressure/saturation predictive models, however, have been developed or verified for the range of wettability conditions that may be encountered in the natural subsurface. This work presents a new two-phase capillary pressure/saturation model for application to the prediction of primary drainage and imbibition relations in fractional wettability media. This new model is based upon an extension of Leverett scaling theory. Analysis of a series of DNAPL/water experiments, conducted for a number of water/intermediate and water/organic fractional wettability systems, reveals that previous models fail to predict observed behavior. The new Leverett-Cassie model, however, is demonstrated to provide good representations of these data, as well as those from two earlier fractional wettability studies. The Leverett-Cassie model holds promise for field application, based upon its foundation in fundamental scaling principles, its requirement for relatively few and physically based input parameters, and its applicability to a broad range of wetting conditions. PMID:15854719
11. Relation of blood pressure to reported intake of salt, saturated fats, and alcohol in healthy middle-aged population.
PubMed Central
Salonen, J T; Tuomilehto, J; Tanskanen, A
1983-01-01
The association of blood pressure with reported intake of salt, saturated fats, and alcohol was studied in a sample of 8479 subjects based on a cross sectional survey in a population aged 30 to 64 years. A consistent association was found between the mean arterial pressure and the intake of alcohol (p less than 0.001) and saturated fats (p less than 0.01). There was also a weak association between blood pressure and dietary salt intake, but this association was mostly explained by the correlation of salt intake with alcohol and saturated fats. The observed relationships support the hypothesis that blood pressure is influenced by diet. PMID:6875442
12. New expressions to describe solution nonideal osmotic pressure, freezing point depression, and vapor pressure.
PubMed
Fullerton, G D; Zimmerman, R J; Cantu, C; Cameron, I L
1992-12-01
New empirical expressions for osmotic pressure, freezing point depression, and vapor pressure are proposed based on the concepts of volume occupancy and (or) hydration force. These expressions are in general inverse relationships in comparison to the standard ideal expressions for the same properties. The slopes of the new equations are determined by the molecular weight of the solute and known constants. The accuracy and precision of the molecular weights calculated from the slope are identical and approximately 1% for the experiments reported here. The nonideality of all three colligative expressions is described by a dimensionless constant called the solute-solvent interaction parameter I. The results on sucrose have the same I = 0.26 for all three solution properties. The nonideality parameter I increased from 0.26 on sucrose to 1.7 on hemoglobin to successfully describe the well-known nonideal response of macromolecules. PMID:1299270
13. Elasticity of water-saturated rocks as a function of temperature and pressure.
NASA Technical Reports Server (NTRS)
Takeuchi, S.; Simmons, G.
1973-01-01
Compressional and shear wave velocities of water-saturated rocks were measured as a function of both pressure and temperature near the melting point of ice to confining pressure of 2 kb. The pore pressure was kept at about 1 bar before the water froze. The presence of a liquid phase (rather than ice) in microcracks of about 0.3% porosity affected the compressional wave velocity by about 5% and the shear wave velocity by about 10%. The calculated effective bulk modulus of the rocks changes rapidly over a narrow range of temperature near the melting point of ice, but the effective shear modulus changes gradually over a wider range of temperature. This phenomenon, termed elastic anomaly, is attributed to the existence of liquid on the boundary between rock and ice due to local stresses and anomalous melting of ice under pressure.
14. Dynamic testing of concrete under high confined pressure. Influence of saturation ratio and aggregate size
Forquin, P.; Piotrowska, E.; Gary, G.
2015-09-01
Concrete structures can be exposed to intense pressure loadings such as projectile-impact or detonation near a concrete structural element. To investigate the mechanical behaviour of concrete under high confining pressure, dynamic quasi-oedometric compression tests have been performed with a large diameter (80 mm) Split Hopkinson Pressure Bar apparatus. The concrete sample is placed within a steel confining ring and compressed along its axial direction. Hydrostatic pressures as high as 800 MPa and axial strain of about - 10% are reached during the tests. In the present work, experiments have been conducted on two types of concrete: MB50 microconcrete with a maximum grain size of 2 mm and R30A7 ordinary concrete of maximum grain size about 8 mm. Both concretes are tested in dry or saturated conditions. According to these dynamic experiments it is noted that grain size has a small influence whereas water content has a strong effect on the confined behaviour of concrete.
15. Critical flow in small nozzles for saturated and subcooled water at high pressure. [PWR
SciTech Connect
Lin, J.C.; Gruen, G.E.; Quapp, W.J.
1980-01-01
Critical flow rate measurements of 4 mm and 16 mm nozzles have been performed with saturated and subcooled water at high pressure. The steady state and transient critical flow tests were conducted by discharging the fluid from a pressurized vessel through a blowdown leg. The fluid stagnation conditions upstream of the nozzle were measured by a gamma densitometer, thermocouple, and pressure transducer. The pressure and temperature of the tests range from 4.5 MPa to 15.0 MPa and from 530 K to 560 K, respectively. The results show that the flow upstream of the nozzle is stratified. The discharge mass flux obtained by this experiment is in good agreement with General Electric (GE) critical flow test data and Henry-Fauske and Burnell critical flow model predictions using a multiplier of 1.0 +- 0.3.
16. Saturated fluorescence measurements of the hydroxyl radical in laminar high-pressure flames
NASA Technical Reports Server (NTRS)
Carter, Campbell D.; King, Galen B.; Laurendeau, Normand M.
1990-01-01
The efficacy of laser saturated fluorescence (LSF) for OH concentration measurements in high pressure flames was studied theoretically and experimentally. Using a numerical model describing the interaction of hydroxyl with nonuniform laser excitation, the effect of pressure on the validity of the balanced cross-rate model was studied along with the sensitivity of the depopulation of the laser-coupled levels to the ratio of rate coefficients describing: (1) electronic quenching to (sup 2) Sigma (+) (v double prime greater than 0), and (2) vibrational relaxation from v double prime greater than 0 to v double prime = 0. At sufficiently high pressures and near-saturated conditions, the total population of the laser-coupled levels reaches an asymptotic value, which is insensitive to the degree of saturation. When the ratio of electronic quenching to vibrational relaxation is small and the rate of coefficients for rotational transfer in the ground and excited electronic states are nearly the same, the balanced cross-rate model remains a good approximation for all pressures. When the above ratio is large, depopulation of the laser-coupled levels becomes significant at high pressures, and thus the balanced cross-rate model no longer holds. Under these conditions, however, knowledge of the depletion of the laser-coupled levels can be used to correct the model. A combustion facility for operation up to 20 atm was developed to allow LSF measurements of OH in high pressure flames. Using this facility, partial saturation in laminar high pressure (less than or equal to 12.3 atm) C2H6/O2/N2 flames was achieved. To evaluate the limits of the balanced cross-rate model, absorption and calibrated LSF measurements at 3.1 and 6.1 atm were compared. The fluorescence voltages were calibrated with absorption measurements in an atmospheric flame and corrected for their finite sensitivity to quenching with: (1) estimated quenching rate coefficients, and (2) an in situ measurement from a technique employing two fluorescence detection geometries.
17. The influence of surfactant sorption on capillary pressure-saturation relationships
SciTech Connect
Desai, F.N.; Demond, A.H.; Hayes, K.F.
1991-12-31
The capillary pressure-saturation relationship, a fundamental relationship in the description of multiphase flow, depends on the interfacial properties of the system. Sorption of a cationic surfactant such as cetyltrimethylammonium bromide (CTAB) at the various interfaces of a system changes interfacial properties such as electrophoretic mobility, interfacial tensions, and contact angle. The objective of this paper is to examine the effect of the changes in these interfacial properties on the capillary pressure-saturation relationships for the air-water-silica system. The results presented here show that as the sorption of CTAB increases, the naturally negatively-charged silica surface becomes positively charged. This change in charge is reflected in the contact angle which passes through a maximum when the electrophoretic mobility is close to zero. The spontaneous imbibition capillary pressure relationship is more sensitive to changes in interfacial properties than the drainage relationship. In the air-water-silica system studied here, no imbibition is observed at the maximum contact angle. The surface tension and contact angle can be used to predict both the drainage and imbibition relationships of the air-water-silica-CTAB systems from that of the air-water-silica system. The prediction is accomplished through scaling using the value of surface tension and the operational contact angle, which can be obtained from the intrinsic angle through the incorporation of corrections for roughness and interfacial curvature. A comparison of the measured and calculated capillary pressure relationships shows that it is possible to predict the effect of surfactant sorption on both drainage and imbibition capillary pressure-saturation relationships for the system studied.
18. The influence of surfactant sorption on capillary pressure-saturation relationships
SciTech Connect
Desai, F.N.; Demond, A.H.; Hayes, K.F.
1991-01-01
The capillary pressure-saturation relationship, a fundamental relationship in the description of multiphase flow, depends on the interfacial properties of the system. Sorption of a cationic surfactant such as cetyltrimethylammonium bromide (CTAB) at the various interfaces of a system changes interfacial properties such as electrophoretic mobility, interfacial tensions, and contact angle. The objective of this paper is to examine the effect of the changes in these interfacial properties on the capillary pressure-saturation relationships for the air-water-silica system. The results presented here show that as the sorption of CTAB increases, the naturally negatively-charged silica surface becomes positively charged. This change in charge is reflected in the contact angle which passes through a maximum when the electrophoretic mobility is close to zero. The spontaneous imbibition capillary pressure relationship is more sensitive to changes in interfacial properties than the drainage relationship. In the air-water-silica system studied here, no imbibition is observed at the maximum contact angle. The surface tension and contact angle can be used to predict both the drainage and imbibition relationships of the air-water-silica-CTAB systems from that of the air-water-silica system. The prediction is accomplished through scaling using the value of surface tension and the operational contact angle, which can be obtained from the intrinsic angle through the incorporation of corrections for roughness and interfacial curvature. A comparison of the measured and calculated capillary pressure relationships shows that it is possible to predict the effect of surfactant sorption on both drainage and imbibition capillary pressure-saturation relationships for the system studied.
19. Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar
NASA Technical Reports Server (NTRS)
Jacobsen, Richard T.; Stewart, Richard B.
1973-01-01
Tables of thermodynamic properties of nitrogen are presented for the liquid and vapor phases for temperatures from the freezing line to 2000K and pressures to 10,000 bar. The tables include values of density, internal energy, enthalpy, entropy, isochoric heat capacity, isobaric heat capacity velocity of sound, the isotherm derivative, and the isochor derivative. The thermodynamic property tables are based on an equation of state, P=P (p,T), which accurately represents liquid and gaseous nitrogen for the range of pressures and temperatures covered by the tables. Comparisons of property values calculated from the equation of state with measured values for P-p-T, heat capacity, enthalpy, latent heat, and velocity of sound are included to illustrate the agreement between the experimental data and the tables of properties presented here. The coefficients of the equation of state were determined by a weighted least squares fit to selected P-p-T data and, simultaneously, to isochoric heat capacity data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and the saturated vapor. The vapor pressure equation, melting curve equation, and an equation to represent the ideal gas heat capacity are also presented. Estimates of the accuracy of the equation of state, the vapor pressure equation, and the ideal gas heat capacity equation are given. The equation of state, derivatives of the equation, and the integral functions for calculating derived thermodynamic properties are included.
20. Accurate determination of the vapor pressure of potassium using optical absorption
NASA Technical Reports Server (NTRS)
1983-01-01
The vapor pressure of potassium has been measured in absorption using a CW tunable laser and calibrated against the accurate radiative lifetime of the 4s-4p doublet of potassium. An accurate value of 20,850 + or - 30 cal/mol for the heat of vaporization (from the liquid phase) at the melting point was determined.
1. Vapor Pressure of Hexamethylene Triperoxide Diamine (HMTD) Estimated Using Secondary Electrospray Ionization Mass Spectrometry.
PubMed
Aernecke, Matthew J; Mendum, Ted; Geurtsen, Geoff; Ostrinskaya, Alla; Kunz, Roderick R
2015-11-25
A rapid method for vapor pressure measurement was developed and used to derive the vapor pressure curve of the thermally labile peroxide-based explosive hexamethylene triperoxide diamine (HMTD) over the temperature range from 28 to 80 C. This method uses a controlled flow of vapor from a solid-phase HMTD source that is presented to an ambient-pressure-ionization mass spectrometer equipped with a secondary-electrospray-ionization (SESI) source. The subpart-per-trillion sensitivity of this system enables direct detection of HMTD vapor through an intact [M + H](+) ion in real time at temperatures near 20 C. By calibrating this method using vapor sources of cocaine and heroin, which have known pressure-temperature (P-T) curves, the temperature dependence of HMTD vapor was determined, and a Clausius-Clapeyron plot of ln[P (Pa)] vs 1/[T (K)] yielded a straight line with the expression ln[P (Pa)] = {(-11091 356) 1/[T (K)]} + 25 1 (error limits are the standard error of the regression analysis). From this equation, the sublimation enthalpy of HMTD was estimated to be 92 3 kJ/mol, which compares well with the theoretical estimate of 95 kJ/mol, and the vapor pressure at 20 C was estimated to be ?60 parts per trillion by volume, which is within a factor of 2 of previous theoretical estimates. Thus, this method provides not only the first direct experimental determination of HMTD vapor pressure but also a rapid, near-real-time capability to quantitatively measure low-vapor-pressure compounds, which will be useful for aiding in the development of training aids for bomb-sniffing canines. PMID:26505487
2. MEASUREMENT OF PARTIAL VAPOR PRESSURE OF AMMONIA OVER ACID AMMONIUM SULFATE SOLUTIONS BY AN INTEGRAL METHOD
EPA Science Inventory
We present a simple, integral, passive method for measuring partial vapor pressure. ntegral methods are useful tools when dealing with very low concentrations because collection over extended periods increases the analytical sensitivity. assive methods have the advantage of not i...
3. Determination of Vapor Pressure-Temperature Relationships of Current Use Pesticides and Transformation Products
Technology Transfer Automated Retrieval System (TEKTRAN)
Sub-cooled liquid vapor pressures of current use organochlorine and organophosphate pesticides (chlorothalonil, chlorpyrifos methyl, diazinon, fipronil) and selected transformation products (chlorpyrifos oxon, heptachlor epoxide, oxychlordane, 3,5,6-trichloro-2-pyridinol) were determined at multiple...
4. The Oxidation Rate of SiC in High Pressure Water Vapor Environments
NASA Technical Reports Server (NTRS)
Opila, Elizabeth J.; Robinson, R. Craig
1999-01-01
CVD SiC and sintered alpha-SiC samples were exposed at 1316 C in a high pressure burner rig at total pressures of 5.7, 15, and 25 atm for times up to 100h. Variations in sample emittance for the first nine hours of exposure were used to determine the thickness of the silica scale as a function of time. After accounting for volatility of silica in water vapor, the parabolic rate constants for Sic in water vapor pressures of 0.7, 1.8 and 3.1 atm were determined. The dependence of the parabolic rate constant on the water vapor pressure yielded a power law exponent of one. Silica growth on Sic is therefore limited by transport of molecular water vapor through the silica scale.
5. Sulfide saturation of basalt and andesite melts at high pressures and temperatures
NASA Technical Reports Server (NTRS)
Wendlandt, R. F.
1982-01-01
When the sulfur content of an Fe-bearing magma exceeds the saturation limit for the bulk composition, an immiscible iron sulfide melt fraction separates. For an understanding of the geochemistry of sulfur-bearing magmatic systems, more information is needed regarding the solubility of metal sulfide in silicate melt at its source and the solubility changes as a function of changing intensive and extensive variables. In the present investigation, the sulfur saturation surface is determined for the pressure range from 12.5 to 30 kbar and the temperature range from 1300 to 1460 C for three silicate melt compositions representing a range of SiO2 and FeO compositions.
6. Liquid-vapor equilibrium under elevated pressures in the systems formed by pentanes with sulfur compounds
SciTech Connect
Shakirzyanov, R.G.; Telyakov, E.S.; Serafimov, L.A.
1982-10-20
The possibility of removing sulfur compounds from the pentane fraction was studied. Experimental data obtained on liquid-vapor equilibrium in the system formed by pentanes with sulfur compounds under elevated pressures is presented. Vapor-liquid equilibrium was studied with the aid of a modified Swietoslawski apparatus made of stainless steel. Experimental data on phase equilibria of binary mixtures in the system studied are presented. The compositions and boiling points of binary azeotropes at the pressures studied are also presented.
7. Determination of vapor pressures for nonpolar and semipolar organic compounds from gas chromatographic retention data
USGS Publications Warehouse
Hinckley, D.A.; Bidleman, T.F.; Foreman, W.T.; Tuschall, J.R.
1990-01-01
Vapor pressures for nonpolar and moderately polar organochlorine, pyrethroid, and organophosphate insecticides, phthalate esters, and organophosphate flame retardants were determined by capillary gas chromatography (GC). Organochlorines and polycyclic aromatic hydrocarbons with known liquid-phase vapor pressures (P??L) (standard compounds) were chromatographed along with two reference compounds n-C20 (elcosane) and p,p???-DDT on a 1.0-m-long poly(dimethylsiloxane) bonded-phase (BP-1) column to determine their vapor pressures by GC (P??GC). A plot of log P??L vs log P??GC for standard compounds was made to establish a correlation between measured and literature values, and this correlation was then used to compute P??L of test compounds from their measured P??GC. P??L of seven major components of technical chlordane, endosulfan and its metabolites, ??-hexachlorocyclohexane, mirex, and two components of technical toxaphene were determined by GC. This method provides vapor pressures within a factor of 2 of average literature values for nonpolar compounds, similar to reported interlaboratory precisions of vapor pressure determinations. GC tends to overestimate vapor pressures of moderately polar compounds. ?? 1990 American Chemical Society.
8. Melting Processes at the Base of the Mantle Wedge: Melt Compositions and Melting Reactions for the First Melts of Vapor-Saturated Lherzolite
Grove, T. L.; Till, C. B.
2014-12-01
Vapor-saturated melting experiments have been performed at pressures near the base of the mantle wedge (3.2 GPa). The starting composition is a metasomatized lherzolite containing 3 wt. % H2O. Near-solidus melts and coexisting mineral phases have been characterized in experiments that span 925 to 1100 oC with melt % varying from 6 to 9 wt. %. Olivine, orthopyroxene, clinopyroxene and garnet coexist with melt over the entire interval and rutile is also present at < 1000 oC. Melt is andesitic in composition and varies from 60 wt. % SiO2 at 950 oC to 52 wt. % at 1075 oC. The Al2O3 contents of the melt are 13 to 14 wt. %, and CaO contents range from 1 and 4 wt. %. Melting is peritectic with orthopyroxene + liquid produced by melting of garnet + olivine + high-Ca pyroxene. In addition to quenched melt, we observe a quenched silicate component that is rhyolitic (>72 % SiO2) that we interpret as a precipitate from the coexisting supercritical H2O-rich vapor. Extrapolation of the measured compositional variation toward the solidus suggests that the first melt may be very SiO2 rich (i.e., granitic). We suggest that these granitic melts are the first melts of the mantle near the slab-wedge interface. As these SiO2-rich melts ascend into shallower, hotter overlying mantle, they continue to interact with the surrounding mantle and evolve in composition. These first melts may elucidate the geochemical and physical processes that accompany the beginnings of H2O flux melting.
9. Loudness discomfort level for speech: comparison of two instructional sets for saturation sound pressure level selection.
PubMed
Beattie, R C; Svihovec, D A; Carmen, R E; Kunkel, H A
1980-01-01
This study was undertaken to compare the speech loudness discomfort levels (LDL's) with two instructional sets which have been proposed for saturation sound pressure level selection of hearing aids. The phraseology recommended by McCandless and by Berger was presented to normal-hearing and hearing-impaired listeners. The normal-hearing subjects obtained mean LDL's of 94.6 and 111.9 dB SPL for these respective instructions, which was statistically significant. The hearing-impaired listeners also showed LDL's with Berger's instructions (114.7 dB SPL) to be significantly higher than with McCandless' instructional set (109.3 dB SPL). Consequently, this investigation suggests that these two instructional sets may lead to substantially different saturation sound pressure levels. Further studies are needed to determine the most appropriate phraseology for LDL measurement, including the assessment of speech intelligibility at various saturation sound pressure levels. Another instructional set was constructed which (1) includes an explanation to patients of the purpose and importance of the test, (2) requests listeners to indicate the upper level they are "willing" to listen as opposed to the level they are "able" to listen, (3) instructs patients to search thoroughly around their LDL before making a final judgment, and (4) contains a statement that the LDL should be made with the understanding that the speech could be listened to for a period of time. Whatever instructions are used, clinicians are advised to interpret their LDL's very cautiously until validational studies are available. PMID:7409356
10. Ice nucleation of Snomax® particles below water vapor saturation: immersion freezing in concentrated solution droplets
Wex, Heike; Kanji, Zamin A.; Boose, Yvonne; Beyer, Alexander; Henning, Silvia; Augustin-Bauditz, Stefanie
2015-04-01
Heterogeneous ice nucleation has received an increasing amount of interest in the past years, as it initiates the ice phase in mixed phase clouds (MPCs) and, to some extent, also in cirrus clouds. The presence of ice influences cloud radiative properties and, for mixed phase clouds, also the formation of precipitation. Immersion freezing is thought to be the most important mechanism through which ice formation could take place in MPCs. Here, we examine the ice nucleation activity of biological ice nucleating particles (INP) derived from bacteria, namely, particles generated from Snomax® suspensions, both above and below water vapor saturation. During a measurement campaign in Leipzig, ice nucleation measurements were conducted with PINC (Portable Ice Nucleus Counter, Chou et al., 2011) and LACIS (Leipzig Aerosol Cloud Interaction Simulator, see e.g. Wex et al., 2014a). Immersion freezing measurements from PINC and LACIS were in agreement in the temperature regime for which both instruments operate reliably. Here, we will show that measurements done below water vapour saturation and above the deliquescence relative humidity of the Snomax® particles follow what would be expected for immersion freezing in concentrated solutions, similar to what was suggested for coated kaolinite particles in Wex et al. (2014b). Additionally, some measurements reported in the literature that were done in the water vapour sub-saturated regime will be evaluated based on the assumption made above, showing that at least some of the ice nucleation which previously was ascribed to deposition ice nucleation rather follows the behavior of immersion freezing in concentrated solutions. Literature: Chou, C., O. Stetzer, E. Weingartner, Z. Juranyi, Z. A. Kanji, and U. Lohmann (2011), Ice nuclei properties within a Saharan dust event at the Jungfraujoch in the Swiss Alps, Atmos. Chem. Phys., 11(10), 4725-4738, doi:10.5194/acp-11-4725-2011. Wex, H. et al. (2014a) Intercomparing different devices for the investigation of ice nucleating particles using Snomax as test substance, Atmos. Chem. Phys. Discuss. (accepted for ACP), 14, 22321-22384, 2014. Wex, H., P. J. DeMott, Y. Tobo, S. Hartmann, M. Rösch, T. Clauss, L. Tomsche, D. Niedermeier, and F. Stratmann (2014b), Kaolinite particles as ice nuclei: learning from the use of different kaolinite samples and different coatings, Atmos. Chem. Phys., 14, doi:10.5194/acp-14-5529-2014.
11. Measurements of Capillary Pressure-Saturation Relationships for Silica Sands Using Light Transmission Visualization and a Rapid Pseudo Static Methods
EPA Science Inventory
Measurement of water saturation in porous media is essential for many types of studies including subsurface water flow, subsurface colloids transport and contaminant remediation to name a few. Water saturation (S) in porous media is dependent on the capillary pressure (Pc) which,...
12. Pore pressure diffusion and the hydrologic response of nearly saturated, thin landslide deposits of rainfall
SciTech Connect
Haneberg, W.C. )
1991-11-01
Previous workers have correlated slope failures during rainstorms with rainfall intensity, rainfall duration, and seasonal antecedent rainfall. This note shows how such relationships can be interpreted using a periodic steady-state solution to the well-known linear pressure diffusion equation. Normalization of the governing equation yields a characteristic response time that is a function of soil thickness, saturated hydraulic conductivity, and pre-storm effective porosity, and which is analogous to the travel time of a piston wetting front. The effects of storm frequency and magnitude are also successfully quantified using dimensionless attenuation factors and lag times.
13. The Dynamics of Vapor Bubbles in Acoustic Pressure Fields
NASA Technical Reports Server (NTRS)
Hao, Y.; Prosperetti, A.
1999-01-01
In spite of a superficial similarity with gas bubbles, the intimate coupling between dynamical and thermal processes confers to oscillating vapor bubbles some unique characteristics. This paper examines numerically the validity of some asymptotic-theory predictions such as the existence of two resonant radii and a limit size for a given sound amplitude and frequency. It is found that a small vapor bubble in a sound field of sufficient amplitude grows quickly through resonance and continues to grow thereafter at a very slow rate, seemingly indefinitely. Resonance phenomena therefore play a role for a few cycles at most, and reaching a limit size-if one exists at all-is found to require far more than several tens of thousands of cycles. It is also found that some small bubbles may grow or collapse depending on the phase of the sound field. The model accounts in detail for the thermo-fluid-mechanic processes in the vapor. In the second part of the paper, an approximate formulation valid for bubbles small with respect to the thermal penetration length in the vapor is derived and its accuracy examined, The present findings have implications for acoustically enhanced boiling heat transfer and other special applications such as boiling in microgravity.
14. Pore Network Modeling of Capillary Pressure -- Saturation Relations Through Retention Cells and Equilibrium Fluid Distributions in Long Columns
Glantz, R.; Hilpert, M.
2009-12-01
Standard methods for experimentally determining capillary pressure -- saturation relations of a porous medium use retention cells: a small cell filled with the porous medium is connected to two pressure reservoirs for the two given fluids. Then, the saturation is recorded as the pressure difference is changed. Conversely, one can infer capillary pressure -- saturation relations by analyzing equilibrium fluid distributions in long vertical columns. Capillary pressure -- saturation relations measured in retention cells differ from those inferred from equilibrium fluid distributions in long columns: at the point where the nonwetting phase starts invading the porous medium, retention cell curves are much smoother than long-column curves, which possess a close to angular shoulder. The objectives of our contribution are to (1) use a pore-network model to simulate long-column experiments and thus capillary pressure-saturation relations, (2) compare simulation results to actual measurements in a glass bead and a sand column, and (3) shed additional light onto the adequacy of both retention cell and long-column experiments for the determination of capillary pressure -- saturation relations.
15. Temperature and water vapor pressure effects on the friction coefficient of hydrogenated diamondlike carbon films.
SciTech Connect
Dickrell, P. L.; Sawyer, W. G.; Eryilmaz, O. L.; Erdemir, A.; Energy Technology; Univ. of Florida
2009-07-01
Microtribological measurements of a hydrogenated diamondlike carbon film in controlled gaseous environments show that water vapor plays a significant role in the friction coefficient. These experiments reveal an initial high friction transient behavior that does not reoccur even after extended periods of exposure to low partial pressures of H{sub 2}O and O{sub 2}. Experiments varying both water vapor pressure and sample temperature show trends of a decreasing friction coefficient as a function of both the decreasing water vapor pressure and the increasing substrate temperature. Theses trends are examined with regard to first order gas-surface interactions. Model fits give activation energies on the order of 40 kJ/mol, which is consistent with water vapor desorption.
16. The effect of temperature on capillary pressure-saturation relationships for air-water and perchloroethylene-water systems
She, Hugh Y.; Sleep, Brent E.
1998-10-01
The temperature dependence of capillary pressure-saturation relationships was measured for air-water and perchloroethylene-water systems in silica sand. Changes in capillary pressures, irreducible water phase saturations, and residual nonwetting saturations with temperature were determined. Relationships for temperature dependence of contact angle and interfacial tension were incorporated into the van Genuchten [1980] model and fitted to the data. Capillary pressures at constant degrees of saturation decreased as temperature increased. Hysteresis decreased, irreducible water saturations increased, and residual nonwetting saturations decreased as temperature increased. The magnitude of the change in capillary pressures could not be explained by the temperature dependence of wetting-nonwetting interfacial tensions alone. Derived parameters for the temperature dependence of the contact angle predicted an increase of contact angle of roughly 45-50 for air-water and perchloroethylene systems with a temperature increase from 20 to 80C, while literature studies suggest that contact angles should decrease with increasing temperature. It was concluded that the parametric relationship for temperature effects incorporated into the van Genuchten [1980] model fit the data well, but other effects in addition to changes in interfacial tension and contact angle played a role in the temperature dependence of capillary pressure-saturation relationships.
17. EVAPORISATION: a new vapor pressure model taking into account neighbour effects
Compernolle, Steven; Ceulemans, Karl; Muller, Jean-Francois
2010-05-01
Secondary organic aerosol (SOA) is a complex mixture of water and organic molecules. The vapor pressure of an organic molecule is one of the most important properties regulating its partitioning to the particulate phase, but as it is unknown for most- typically polyfunctional- organic molecules in Biogenic SOA it has to be estimated by a vapor pressure model fitted to experimental data. While a lot of vapor pressure data is generally available for hydrocarbons and monofunctional compounds, much less data are available for bifunctional compounds. For compounds with more functional groups, data is sparse and relatively inaccurate. We have developed a vapor pressure model, EVAPORISATION (Estimation of VApor Pressure of ORganics, Including effects Such As The Interaction of Neighbours), starting from the group-contribution principle: each functional group gives a contribution to the logarithm of the vapor pressure. On top of that, second order effects -chemically rationalized- are added due to carbon skeleton, nonadditivity of functional groups and -for neighbouring functional groups- intramolecular interactions . These effects can be very significant: eg. when two carbonyl groups are neighbouring, the vapor pressure is about 1 order of magnitude higher than when they are nonneighbouring. Due to the lack of data, some of these effects must be estimated by analogy. The method is compared to several other vapor pressure estimation techniques, such as SIMPOL (Pankow et al. 2008), SPARC (Hilal et al. 2003), and the methods of Myrdal and Yalkowsky (1997), Capouet and Muller (2006), Nannoolal et al. (2008), Moller et al. (2008). We extended some of these methods as they are not able to treat hydroperoxides, peracids, peroxy acyl nitrates. With our model BOREAM, outlined in a previous publication (Capouet et al. 2008), several smog chamber experiments are simulated, and the impact of vapor pressure method choice is elucidated. It turns out that the choice of the vapor pressure method can have a major impact on aerosol yield, considerably larger than the choice of activity coefficient model (Compernolle et al. 2009). M. Capouet and J.-F. Muller, Atm. Chem. Phys. 6, 1455-1467 (2006) M. Capouet, J.-F. Muller, K. Ceulemans, S. Compernolle, L. Vereecken and J. Peeters, J. Geophys. Res. 113, D02308 (2008) S. Compernolle, K. Ceulemans and J. Muller, Atm. Chem. Phys. 9, 1325-1388 (2009) S.H. Hilal, S.W. Karickhoff and L.A. Carreira , QSAR Comb. Sci. 22, 565-574 (2003) P.B. Myrdal and S.H. Yalkowsky, Ind. Eng. Chem. Res. 36, 2494-2499 (1997) Y. Nannoolal, J. Rarey and D. Ramjugernath, Fluid Phase Eq. 269, 117-133 (2008) B. Moller, J. Rarey and D. Ramjugernath, J. Mol. Liq. 143, 52-63 (2008)
18. Integrated Rig for the Production of Boron Nitride Nanotubes via the Pressurized Vapor-Condenser Method
NASA Technical Reports Server (NTRS)
Smith, Michael W. (Inventor); Jordan, Kevin C. (Inventor)
2014-01-01
An integrated production apparatus for production of boron nitride nanotubes via the pressure vapor-condenser method. The apparatus comprises: a pressurized reaction chamber containing a continuously fed boron containing target having a boron target tip, a source of pressurized nitrogen and a moving belt condenser apparatus; a hutch chamber proximate the pressurized reaction chamber containing a target feed system and a laser beam and optics.
19. Integrated rig for the production of boron nitride nanotubes via the pressurized vapor-condenser method
DOEpatents
Smith, Michael W; Jordan, Kevin C
2014-03-25
An integrated production apparatus for production of boron nitride nanotubes via the pressure vapor-condenser method. The apparatus comprises: a pressurized reaction chamber containing a continuously fed boron containing target having a boron target tip, a source of pressurized nitrogen and a moving belt condenser apparatus; a hutch chamber proximate the pressurized reaction chamber containing a target feed system and a laser beam and optics.
20. Saturation meter
DOEpatents
Gregurech, S.
1984-08-01
A saturation meter for use in a pressurized water reactor plant comprising a differential pressure transducer having a first and second pressure sensing means and an alarm. The alarm is connected to the transducer and is preset to activate at a level of saturation prior to the formation of a steam void in the reactor vessel.
1. Laboratory measurement of capillary pressure-saturation relationships in a rock fracture
Reitsma, Stanley; Kueper, Bernard H.
1994-04-01
A laboratory technique has been developed to measure the hysteretic relationship between capillary pressure and fluid saturation for a rough-walled rock fracture under different states of normal stress. The technique incorporates a loading system and a uniquely designed capillary barrier to the nonwetting phase which allows for fracture closure and provides excellent hydraulic connection of the wetting phase in the fracture with external pressure control. The method is applied to a single, rough-walled fracture in limestone using oil and water as the nonwetting and wetting phase, respectively. The measured capillary pressure curves were found to be well represented by a Brooks-Corey porous media capillary pressure function. A distinct entry pressure, giving rise to initial nonwetting phase invasion, was observed in each test. It was found that the inferred aperture distributions became less skewed with increased normal load. These aperture distributions were inferred using one of three conceptual models presented for nonwetting phase invasion of a rough-walled fracture under conditions of main drainage.
2. 40 CFR 65.111 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 15 2010-07-01 2010-07-01 false Standards: Pressure relief devices in... (CONTINUED) AIR PROGRAMS (CONTINUED) CONSOLIDATED FEDERAL AIR RULE Equipment Leaks 65.111 Standards: Pressure relief devices in gas/vapor service. (a) Compliance schedule. The owner or operator shall...
3. 40 CFR 65.111 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 16 2014-07-01 2014-07-01 false Standards: Pressure relief devices in... (CONTINUED) AIR PROGRAMS (CONTINUED) CONSOLIDATED FEDERAL AIR RULE Equipment Leaks 65.111 Standards: Pressure relief devices in gas/vapor service. (a) Compliance schedule. The owner or operator shall...
4. Assessment of the Accuracy of Pharmacy Students Compounded Solutions Using Vapor Pressure Osmometry
PubMed Central
McPherson, Timothy B.
2013-01-01
Objective. To assess the effectiveness of using a vapor pressure osmometer to measure the accuracy of pharmacy students compounding skills. Design. Students calculated the theoretical osmotic pressure (mmol/kg) of a solution as a pre-laboratory exercise, compared their calculations with actual values, and then attempted to determine the cause of any errors found. Assessment. After the introduction of the vapor pressure osmometer, the first-time pass rate for solution compounding has varied from 85% to 100%. Approximately 85% of students surveyed reported that the instrument was valuable as a teaching tool because it objectively assessed their work and provided immediate formative assessment. Conclusions. This simple technique of measuring compounding accuracy using a vapor pressure osmometer allowed students to see the importance of quality control and assessment in practice for both pharmacists and technicians. PMID:23610476
5. Vapor pressure and void size effects on failure of a constrained ductile film
Guo, T. F.; Cheng, L.
2003-06-01
To achieve certain properties, semiconductor adhesives and molding compounds are made by blending filler particles with polymer matrix. Moisture collects at filler particle/polymer matrix interfaces and within voids of the composite. At reflow temperatures, the moisture vaporizes. The rapidly expanding vapor creates high internal pressure on pre-existing voids and particle/matrix interfaces. The simultaneous action of thermal stresses and internal vapor pressure drives both pre-existing and newly nucleated voids to grow and coalesce causing material failure. Particularly susceptible are polymeric films and adhesives joining elastic substrates, e.g. Ag filled epoxy. Several competing failure mechanisms are studied including: near-tip void growth and coalescence with the crack; extensive void growth and formation of an extended damaged zone emanating from the crack; and rapid void growth at highly stressed sites at large distances ahead of the crack, leading to multiple damaged zones. This competition is driven by the interplay between stress elevation induced by constrained plastic flow and stress relaxation due to vapor pressure assisted void growth. A model problem of a ductile film bonded between two elastic substrates, with a centerline crack, is studied. The computational study employs a Gurson porous material model incorporating vapor pressure effects. The formation of multiple damaged zones is favored when the film contains small voids or dilute second-phase particle distribution. The presence of large voids or high vapor pressure favor the growth of a self-similar damage zone emanating from the crack. High vapor pressure accelerates film cracking that can cause device failures.
6. Application of quantitative structure-property relationship analysis to estimate the vapor pressure of pesticides.
PubMed
Goodarzi, Mohammad; Dos Santos Coelho, Leandro; Honarparvar, Bahareh; Ortiz, Erlinda V; Duchowicz, Pablo R
2016-06-01
The application of molecular descriptors in describing Quantitative Structure Property Relationships (QSPR) for the estimation of vapor pressure (VP) of pesticides is of ongoing interest. In this study, QSPR models were developed using multiple linear regression (MLR) methods to predict the vapor pressure values of 162 pesticides. Several feature selection methods, namely the replacement method (RM), genetic algorithms (GA), stepwise regression (SR) and forward selection (FS), were used to select the most relevant molecular descriptors from a pool of variables. The optimum subset of molecular descriptors was used to build a QSPR model to estimate the vapor pressures of the selected pesticides. The Replacement Method improved the predictive ability of vapor pressures and was more reliable for the feature selection of these selected pesticides. The results provided satisfactory MLR models that had a satisfactory predictive ability, and will be important for predicting vapor pressure values for compounds with unknown values. This study may open new opportunities for designing and developing new pesticide. PMID:26890190
7. Vapor pressures of substituted polycarboxylic acids are much lower than previously reported
Huisman, A. J.; Krieger, U. K.; Zuend, A.; Marcolli, C.; Peter, T.
2013-07-01
The partitioning of compounds between the aerosol and gas phase is a primary focus in the study of the formation and fate of secondary organic aerosol. We present measurements of the vapor pressure of 2-methylmalonic (isosuccinic) acid, 2-hydroxymalonic (tartronic) acid, 2-methylglutaric acid, 3-hydroxy-3-carboxy-glutaric (citric) acid and DL-2,3-dihydroxysuccinic (DL-tartaric) acid, which were obtained from the evaporation rate of supersaturated liquid particles levitated in an electrodynamic balance. Our measurements indicate that the pure component liquid vapor pressures at 298.15 K for tartronic, citric and tartaric acids are much lower than the same quantity that was derived from solid state measurements in the only other room temperature measurement of these materials (made by Booth et al., 2010). This strongly suggests that empirical correction terms in a recent vapor pressure estimation model to account for the inexplicably high vapor pressures of these and similar compounds should be revisited, and that due caution should be used when the estimated vapor pressures of these and similar compounds are used as inputs for other studies.
8. Vapor pressures of substituted polycarboxylic acids are much lower than previously reported
Huisman, A. J.; Krieger, U. K.; Zuend, A.; Marcolli, C.; Peter, T.
2013-01-01
The partitioning of compounds between the aerosol and gas phase is a primary focus in the study of the formation and fate of secondary organic aerosol. We present measurements of the vapor pressure of 2-Methylmalonic (isosuccinic) acid, 2-Hydroxymalonic (tartronic) acid, 2-Methylglutaric acid, 3-Hydroxy-3-carboxy-glutaric (citric) acid and 2,3-Dihydroxysuccinic (tartaric) acid which were obtained from the evaporation rate of supersaturated liquid particles levitated in an electrodynamic balance. Our measurements indicate that the pure component liquid vapor pressures at 298.15 K for tartronic, citric and tartaric acids are much lower than the same quantity which was derived from solid state measurements in the only other room temperature measurement of these materials (made by Booth et al., 2010). This strongly suggests that empirical correction terms in vapor pressure estimation models to account for the inexplicably high vapor pressures of these and similar compounds should be revisited, and that due caution should be used when the estimated vapor pressures of these and similar compounds are used as inputs for other studies.
9. Vapor pressure of heptane from the triple point to the critical point
SciTech Connect
Weber, L.A.
2000-04-01
The author has used a metal ebulliometer to make measurements of the vapor pressures of heptane. Measurements spanned the temperature range from 335 K to 503 K, and measured pressures ranged from 30 kPa to 1,597 kPa. The sample purity was determined by chromatographic analysis, and the measured pressures were adjusted for the presence of the impurities found. The adjusted results were found to be in good agreement with the best available data from the literature, and a reliable vapor pressure curve could be established for temperatures up to the critical point (540.13 K). The author has also used thermodynamic calculations and published thermal data to extend the vapor pressures down to the triple point (182.603 K). He estimates that the vapor pressure curve has an uncertainty of 0.2% to 0.3% in the vicinity of the triple point, decreasing to 0.03% to 0.05% in the range 300 K to 400 K, and increasing to about 0.1% at 500 K. The calculated critical pressure was found to be (2,739.7 {+-} 2.5(1{sigma})) kPa.
10. Effects of vapor pressure on thermodynamic equilibrium in multiphase flow for thermochemical hydrogen production
Pope, K.; Naterer, G. F.; Wang, Z. L.
2013-12-01
This paper examines the effects of H2O vapor pressure on the equilibrium conditions of a CuCl2 hydrolysis reactor in the thermochemical Cu-Cl cycle of hydrogen production. A new predictive model is developed to determine the minimum steam requirement in the reactor based on the chemical equilibrium condition, reactor pressure and fraction of gaseous reactant. Experimental data, at three separate vapour pressures of steam, compared well with the new predictive formulation.
11. Pressure-coupled vaporization and combustion responses of liquid-fuel droplets in high-pressure environments
NASA Technical Reports Server (NTRS)
Yang, Vigor; Shuen, J. S.; Hsiao, C. C.
1991-01-01
The dynamic responses of liquid-fuel droplet vaporization and combustion to ambient pressure oscillations are examined. The analysis is based on the complete sets of conservation equations for both gas and liquid phases, and accommodates detailed treatments of finite-rate chemical kinetics and variable properties. With a full account of thermodynamic phase equilibrium at the droplet surface, the model enables a systematic examination of the effects of ambient flow conditions on the droplet behavior. The responses of hydrocarbon fuel droplets in both sub- and super-critical environments are investigated. Results indicate that the droplet gasification and burning mechanisms depend greatly on the ambient pressure. In particular, a rapid enlargement of the vaporization and combustion responses occurs when the droplet surface reaches its critical point, mainly due to the strong variations of latent heat of vaporization and thermophysical properties at the critical state.
12. 40 CFR 63.7944 - How do I determine the maximum HAP vapor pressure of my remediation material?
Code of Federal Regulations, 2010 CFR
2010-07-01
... pressure of the remediation material: (i) Method 25E in 40 CFR part 60 appendix A; (ii) Methods described... vapor pressure of my remediation material? 63.7944 Section 63.7944 Protection of Environment... Pollutants: Site Remediation Performance Tests § 63.7944 How do I determine the maximum HAP vapor pressure...
13. 40 CFR 63.7944 - How do I determine the maximum HAP vapor pressure of my remediation material?
Code of Federal Regulations, 2011 CFR
2011-07-01
... pressure of the remediation material: (i) Method 25E in 40 CFR part 60 appendix A; (ii) Methods described... vapor pressure of my remediation material? 63.7944 Section 63.7944 Protection of Environment... Pollutants: Site Remediation Performance Tests § 63.7944 How do I determine the maximum HAP vapor pressure...
14. 40 CFR 63.7944 - How do I determine the maximum HAP vapor pressure of my remediation material?
Code of Federal Regulations, 2014 CFR
2014-07-01
... pressure of the remediation material: (i) Method 25E in 40 CFR part 60 appendix A; (ii) Methods described... vapor pressure of my remediation material? 63.7944 Section 63.7944 Protection of Environment... Pollutants: Site Remediation Performance Tests § 63.7944 How do I determine the maximum HAP vapor pressure...
15. Damping Effect of an Unsaturated-Saturated System on Tempospatial Variations of Pressure Head and Specific Flux
Yang, C.; Zhang, Y. K.; Liang, X.
2014-12-01
Damping effect of an unsaturated-saturated system on tempospatialvariations of pressurehead and specificflux was investigated. The variance and covariance of both pressure head and specific flux in such a system due to a white noise infiltration were obtained by solving the moment equations of water flow in the system and verified with Monte Carlo simulations. It was found that both the pressure head and specific flux in this case are temporally non-stationary. The variance is zero at early time due to a deterministic initial condition used, then increases with time, and approaches anasymptotic limit at late time.Both pressure head and specific flux arealso non-stationary in space since the variance decreases from source to sink. The unsaturated-saturated systembehavesasa noise filterand it damps both the pressure head and specific flux, i.e., reduces their variations and enhances their correlation. The effect is stronger in upper unsaturated zone than in lower unsaturated zone and saturated zone. As a noise filter, the unsaturated-saturated system is mainly a low pass filter, filtering out the high frequency components in the time series of hydrological variables. The damping effect is much stronger in the saturated zone than in the saturated zone.
16. A simple grand canonical approach to compute the vapor pressure of bulk and finite size systems
SciTech Connect
Factorovich, Matías H.; Scherlis, Damián A.
2014-02-14
In this article we introduce a simple grand canonical screening (GCS) approach to accurately compute vapor pressures from molecular dynamics or Monte Carlo simulations. This procedure entails a screening of chemical potentials using a conventional grand canonical scheme, and therefore it is straightforward to implement for any kind of interface. The scheme is validated against data obtained from Gibbs ensemble simulations for water and argon. Then, it is applied to obtain the vapor pressure of the coarse-grained mW water model, and it is shown that the computed value is in excellent accord with the one formally deduced using statistical thermodynamics arguments. Finally, this methodology is used to calculate the vapor pressure of a water nanodroplet of 94 molecules. Interestingly, the result is in perfect agreement with the one predicted by the Kelvin equation for a homogeneous droplet of that size.
17. Preconcentrator with high volume chiller for high vapor pressure particle detection
DOEpatents
2013-10-22
Apparatus and method for collecting particles of both high and low vapor pressure target materials entrained in a large volume sample gas stream. Large volume active cooling provides a cold air supply which is mixed with the sample gas stream to reduce the vapor pressure of the particles. In embodiments, a chiller cools air from ambient conditions to 0-15.degree. C. with the volumetric flow rate of the cold air supply being at least equal to the volumetric flow rate of the sample gas stream. In further embodiments an adsorption media is heated in at least two stages, a first of which is below a threshold temperature at which decomposition products of the high vapor pressure particle are generated.
18. Spectral properties of molecular iodine in absorption cells filled to specified saturation pressure.
PubMed
Hrabina, Jan; Šarbort, Martin; Acef, Ouali; Burck, Frédéric Du; Chiodo, Nicola; Holá, Miroslava; Číp, Ondřej; Lazar, Josef
2014-11-01
We present the results of measurement and evaluation of spectral properties of iodine absorption cells filled at certain saturation pressure. A set of cells made of borosilicate glass instead of common fused silica was tested for their spectral properties in greater detail with special care for the long-term development of the absorption media purity. The results were compared with standard fused silica cells and the high quality of iodine was verified. A measurement method based on an approach relying on measurement of linewidth of the hyperfine transitions is proposed as a novel technique for iodine cell absorption media purity evaluation. A potential application in laser metrology of length is also discussed. PMID:25402909
19. Synthetic fluid inclusions. V. Solubility relations in the system NaCl-KCl-H sub 2 O under vapor-saturated conditions
SciTech Connect
Sterner, S.M.; Hall, D.L.; Bodnar, R.J. )
1988-05-01
Vapor-saturated solubility relationships in the system NaCl-KCl-H{sub 2}O have been determined by experimentally synthesizing fluid inclusions in quartz in the presence of known brine compositions and then measuring the dissolution temperatures of halite and/or sylvite daughter crystals within the inclusions using a microscope equipped with a heating stage. These data, along with other literature values have been used in a stepwise multiple regression routine to generate a series of equations describing vapor-saturated solubility relations within the halite, sylvite and hydrohalite stability fields. These equations, together with a recently published equation for the ice stability field have been used to construct the complete vapor-saturated solubility surface in the NaCl-KCl-H{sub 2}O ternary system. The diagram may be used in the interpretation of microthermometric data to determine the compositions of fluid inclusions approximated by the NaCl-KCl-H{sub 2}O system. Solubility data obtained from synthetic fluid inclusions are in good agreement with recently published data for the KCl-H{sub 2}O and NaCl-H{sub 2}O binary systems but are at variance with some earlier works.
20. Experimental Investigation of the Effect of Pressure and Fluid Saturation on Carbonate Rocks
Scotellaro, C.; Vanorio, T.; Mavko, G.
2006-12-01
Gassmann's model is commonly used to predict how changes in pore fluids affect in-situ seismic velocities. Although Gassmann's model is generally successful in medium to high porosity sandstones, its appropriateness for quantifying fluid effects in carbonate rocks is questioned in literature. Questions rice from the model assumptions which, very likely oversimplify the complex rock-fluid interaction in carbonates. Critical issues include 1) rock-fluid chemical interaction (e.g. dissolution), violating Gassmann's purely mechanical model, and 2) substantial pore fabric heterogeneity, potentially violating Gassmann's assumption of good fluid mobility in a well-connected pore space. We present the preliminary results of measurements showing the variation of Vp and Vs as a function of pressure and fluid saturation. Theoretical velocities predicted by Gassmann's equation are also shown for comparison. Different saturating fluids, an inert gas (Helium) and degassed, distilled water are used to create experimental conditions that vary one fluid interaction at a time. The goal is to identify the conditions (i.e. fluid type, pressure, pore shape distribution) under which the assumptions of Gassman's theory may apply to carbonates and evaluate which conditions appear to be responsible for the failure of the seismic property prediction. Carbonate samples (porosity range from 5% to 50%) from Gravina di Puglia (Bari, Italy), and Monte Sant'Angelo and Peschici (Foggia, Italy) have been classified based on mineralogy, pore type and connectivity. From each sample, 2 core plugs have been extracted and used for measurements. Dissolution (i.e., changes to the rock framework) is expected to be different for different pore fluids. Hence, seismic fluid substitution in carbonates is likely more than a purely mechanical problem.
1. VAPOR PRESSURE ISOTOPE EFFECTS IN THE MEASUREMENT OF ENVIRONMENTAL TRITIUM SAMPLES.
SciTech Connect
Kuhne, W.
2012-12-03
Standard procedures for the measurement of tritium in water samples often require distillation of an appropriate sample aliquot. This distillation process may result in a fractionation of tritiated water and regular light water due to the vapor pressure isotope effect, introducing either a bias or an additional contribution to the total tritium measurement uncertainty. The magnitude of the vapor pressure isotope effect is characterized as functions of the amount of water distilled from the sample aliquot and the heat settings for the distillation process. The tritium concentration in the distillate is higher than the tritium concentration in the sample early in the distillation process, it then sharply decreases due to the vapor pressure isotope effect and becomes lower than the tritium concentration in the sample, until the high tritium concentration retained in the boiling flask is evaporated at the end of the process. At that time, the tritium concentration in the distillate again overestimates the sample tritium concentration. The vapor pressure isotope effect is more pronounced the slower the evaporation and distillation process is conducted; a lower heat setting during the evaporation of the sample results in a larger bias in the tritium measurement. The experimental setup used and the fact that the current study allowed for an investigation of the relative change in vapor pressure isotope effect in the course of the distillation process distinguish it from and extend previously published measurements. The separation factor as a quantitative measure of the vapor pressure isotope effect is found to assume values of 1.034 {+-} 0.033, 1.052 {+-} 0.025, and 1.066 {+-} 0.037, depending on the vigor of the boiling process during distillation of the sample. A lower heat setting in the experimental setup, and therefore a less vigorous boiling process, results in a larger value for the separation factor. For a tritium measurement in water samples, this implies that the tritium concentration could be underestimated by 3 - 6%.
2. Theoretical and experimental studies on freezing point depression and vapor pressure deficit as methods to measure osmotic pressure of aqueous polyethylene glycol and bovine serum albumin solutions.
PubMed
Kiyosawa, Keitaro
2003-05-01
For survival in adverse environments where there is drought, high salt concentration or low temperature, some plants seem to be able to synthesize biochemical compounds, including proteins, in response to changes in water activity or osmotic pressure. Measurement of the water activity or osmotic pressure of simple aqueous solutions has been based on freezing point depression or vapor pressure deficit. Measurement of the osmotic pressure of plants under water stress has been mainly based on vapor pressure deficit. However, differences have been noted for osmotic pressure values of aqueous polyethylene glycol (PEG) solutions measured by freezing point depression and vapor pressure deficit. For this paper, the physicochemical basis of freezing point depression and vapor pressure deficit were first examined theoretically and then, the osmotic pressure of aqueous ethylene glycol and of PEG solutions were measured by both freezing point depression and vapor pressure deficit in comparison with other aqueous solutions such as NaCl, KCl, CaCl(2), glucose, sucrose, raffinose, and bovine serum albumin (BSA) solutions. The results showed that: (1) freezing point depression and vapor pressure deficit share theoretically the same physicochemical basis; (2) theoretically, they are proportional to the molal concentration of the aqueous solutions to be measured; (3) in practice, the osmotic pressure levels of aqueous NaCl, KCl, CaCl(2), glucose, sucrose, and raffinose solutions increase in proportion to their molal concentrations and there is little inconsistency between those measured by freezing point depression and vapor pressure deficit; (4) the osmotic pressure levels of aqueous ethylene glycol and PEG solutions measured by freezing point depression differed from the values measured by vapor pressure deficit; (5) the osmotic pressure of aqueous BSA solution measured by freezing point depression differed slightly from that measured by vapor pressure deficit. PMID:12834836
3. Non-invasive Positive Pressure Ventilation during Sleep at 3800m: relationship to Acute Mountain Sickness and sleeping oxyhemoglobin saturation
PubMed Central
Johnson, PL; Popa, DA; Prisk, GK; Sullivan, CE; Edwards, N
2014-01-01
Background and objectives Ascent to high altitude results in hypobaric hypoxia and some individuals will develop Acute Mountain Sickness, which has been shown to be associated with low oxyhemoglobin saturation during sleep. Previous research has shown that positive end-expiratory pressure by use of expiratory valves in a face mask while awake, results in a reduction in AMS symptoms and higher oxyhemoglobin saturation. We aimed to test whether pressure ventilation during sleep would prevent AMS by keeping oxyhaemoglobin higher during sleep. Methods We compared sleeping oxyhemoglobin saturation and the incidence and severity of Acute Mountain Sickness in seven subjects sleeping for two consecutive nights at 3800m above sea level using either non-invasive positive pressure ventilation that delivered positive inspiratory and expiratory airway pressure via a face mask, or sleeping without assisted ventilation. The presence and severity of Acute Mountain Sickness was assessed by administration of the Lake Louise questionnaire. Results We found significant increases in the mean and minimum sleeping oxyhemoglobin saturation and decreases in AMS symptoms in subjects who used positive pressure ventilation during sleep. Mean and minimum sleeping SaO2 was lower in subjects who developed AMS after the night spent without positive pressure ventilation. Conclusion The use of positive pressure ventilation during sleep at 3800m significantly increased the sleeping oxygen saturation; we suggest that the marked reduction in symptoms of AMS is due to this higher sleeping SaO2. We agree with the findings from previous studies that the development of AMS is associated with a lower sleeping oxygen saturation. PMID:20051046
4. Communication: Dynamical and structural analyses of solid hydrogen under vapor pressure.
PubMed
Hyeon-Deuk, Kim; Ando, Koji
2015-11-01
Nuclear quantum effects play a dominant role in determining the phase diagram of H2. With a recently developed quantum molecular dynamics simulation method, we examine dynamical and structural characters of solid H2 under vapor pressure, demonstrating the difference from liquid and high-pressure solid H2. While stable hexagonal close-packed lattice structures are reproduced with reasonable lattice phonon frequencies, the most stable adjacent configuration exhibits a zigzag structure, in contrast with the T-shape liquid configuration. The periodic angular distributions of H2 molecules indicate that molecules are not a completely free rotor in the vapor-pressure solid reflecting asymmetric potentials from surrounding molecules on adjacent lattice sites. Discrete jumps of librational and H-H vibrational frequencies as well as H-H bond length caused by structural rearrangements under vapor pressure effectively discriminate the liquid and solid phases. The obtained dynamical and structural information of the vapor-pressure H2 solid will be useful in monitoring thermodynamic states of condensed hydrogens. PMID:26547150
5. Communication: Dynamical and structural analyses of solid hydrogen under vapor pressure
Hyeon-Deuk, Kim; Ando, Koji
2015-11-01
Nuclear quantum effects play a dominant role in determining the phase diagram of H2. With a recently developed quantum molecular dynamics simulation method, we examine dynamical and structural characters of solid H2 under vapor pressure, demonstrating the difference from liquid and high-pressure solid H2. While stable hexagonal close-packed lattice structures are reproduced with reasonable lattice phonon frequencies, the most stable adjacent configuration exhibits a zigzag structure, in contrast with the T-shape liquid configuration. The periodic angular distributions of H2 molecules indicate that molecules are not a completely free rotor in the vapor-pressure solid reflecting asymmetric potentials from surrounding molecules on adjacent lattice sites. Discrete jumps of librational and H-H vibrational frequencies as well as H-H bond length caused by structural rearrangements under vapor pressure effectively discriminate the liquid and solid phases. The obtained dynamical and structural information of the vapor-pressure H2 solid will be useful in monitoring thermodynamic states of condensed hydrogens.
PubMed
Alcaide, Mara; Stogios, Peter J; Lafraya, lvaro; Tchigvintsev, Anatoli; Flick, Robert; Bargiela, Rafael; Chernikova, Tatyana N; Reva, Oleg N; Hai, Tran; Leggewie, Christian C; Katzke, Nadine; La Cono, Violetta; Matesanz, Ruth; Jebbar, Mohamed; Jaeger, Karl-Erich; Yakimov, Michail M; Yakunin, Alexander F; Golyshin, Peter N; Golyshina, Olga V; Savchenko, Alexei; Ferrer, Manuel
2015-02-01
The present study provides a deeper view of protein functionality as a function of temperature, salt and pressure in deep-sea habitats. A set of eight different enzymes from five distinct deep-sea (3040-4908?m depth), moderately warm (14.0-16.5C) biotopes, characterized by a wide range of salinities (39-348 practical salinity units), were investigated for this purpose. An enzyme from a 'superficial' marine hydrothermal habitat (65C) was isolated and characterized for comparative purposes. We report here the first experimental evidence suggesting that in salt-saturated deep-sea habitats, the adaptation to high pressure is linked to high thermal resistance (P value?=?0.0036). Salinity might therefore increase the temperature window for enzyme activity, and possibly microbial growth, in deep-sea habitats. As an example, Lake Medee, the largest hypersaline deep-sea anoxic lake of the Eastern Mediterranean Sea, where the water temperature is never higher than 16C, was shown to contain halopiezophilic-like enzymes that are most active at 70C and with denaturing temperatures of 71.4C. The determination of the crystal structures of five proteins revealed unknown molecular mechanisms involved in protein adaptation to poly-extremes as well as distinct active site architectures and substrate preferences relative to other structurally characterized enzymes. PMID:25330254
7. Vapor pressures and heats of vaporization of primary coal tars. Quarterly technical progress report, April 1, 1996--June 30, 1996
SciTech Connect
Suuberg, E.M.; Oja, V.; Lilly, W.D.
1997-12-31
As the world continues to deplete its petroleum reserves, then heavy crude oil, coal liquids, and other heavy fossil fuels may be required to meet the world energy needs. Heavy fossil fuels contain molecules that are large and more aromatic and that contain more heteroatoms than those found in liquid crude oil. There is also significant current interest in general area of coal pyrolysis, particularly with respect to comprehensive models of this complicated phenomenon. This interest derives from central role of pyrolysis in all thermally driven coal conversion processes - gasification, combustion, liquefaction, mild gasification, or thermal beneficiation. There remain several key data needs in these application areas. Among them is a need for a more reliable correlation for prediction of the vapor pressures of heavy, primary coal tars. Such information is important in design of all coal conversion processes, in which the volatility of tarry products is of major concern. This paper presents work on the vapor pressures of coal tars using the continuous knudsen effusion technique.
8. Prediction of the liquid-vapor equilibrium pressure using the quasi-Gaussian entropy theory
Amadei, A.; Roccatano, D.; Apol, M. E. F.; Berendsen, H. J. C.; Di Nola, A.
1996-10-01
We derived a method to evaluate the liquid-vapor equilibrium pressure, with high accuracy over a large range of temperature, using the quasi-Gaussian entropy theory. The final expression that we obtain for the equilibrium pressure as a function of the temperature can be considered as a very accurate approximate solution of the Clausius-Clapeyron equation. The method was applied to water, methanol and mercury, and was compared to two usual approximations of the Clausius-Clapeyron equation.
9. VAPOR PRESSURE AND MELTING BEHAVIOR OF SULFURIC ACID-WATER SYSTEMS
EPA Science Inventory
An experimental apparatus was designed and constructed to use high vacuum and mass spectrometric techniques to determine total and partial vapor pressures above bulk liquid samples in the temperature range between -65C and 25C. Observations on the sulfuric acid-water system revea...
10. Molar Mass and Second Virial Coefficient of Polyethylene Glycol by Vapor Pressure Osmometry
ERIC Educational Resources Information Center
Schwinefus, Jeffrey J.; Checkal, Caleb; Saksa, Brian; Baka, Nadia; Modi, Kalpit; Rivera, Carlos
2015-01-01
In this laboratory experiment, students determine the number-average molar masses and second virial coefficients of polyethylene glycol (PEG) polymers ranging in molar mass from 200 to 1500 g mol[superscript -1] using vapor pressure osmometry (VPO). Students assess VPO in relation to accurate molar mass calculations of PEG polymers. Additionally,
11. Molar Mass and Second Virial Coefficient of Polyethylene Glycol by Vapor Pressure Osmometry
ERIC Educational Resources Information Center
Schwinefus, Jeffrey J.; Checkal, Caleb; Saksa, Brian; Baka, Nadia; Modi, Kalpit; Rivera, Carlos
2015-01-01
In this laboratory experiment, students determine the number-average molar masses and second virial coefficients of polyethylene glycol (PEG) polymers ranging in molar mass from 200 to 1500 g mol[superscript -1] using vapor pressure osmometry (VPO). Students assess VPO in relation to accurate molar mass calculations of PEG polymers. Additionally,…
12. Vapor Pressures and Thermodynamics of Oxygen-Containing Polycyclic Aromatic Hydrocarbons Measured Using Knudsen Effusion
PubMed Central
Goldfarb, Jillian L.
2013-01-01
Polycyclic aromatic hydrocarbons (PAHs) and their oxygenated derivatives (OPAHs) are ubiquitous environmental pollutants resulting from the incomplete combustion of coal and fossil fuels. Their vapor pressures are key thermodynamic data essential for modeling fate and transport within the environment. The present study involved nine PAHs containing oxygen heteroatoms, including aldehyde, carboxyl and nitro groups, specifically: 2-nitrofluorene; 9-fluorenecarboxylic acid; 2-fluorenecarboxaldehyde; 2-anthracenecarboxylic acid; 9-anthracenecarboxylic acid; 9-anthraldehyde; 1-nitropyrene; 1-pyrenecarboxaldehyde and 1-bromo-2-naphthoic acid. The vapor pressures of these compounds, with molecular weights ranging from 194 to 251 grams per mole, were measured using the isothermal Knudsen effusion technique in the temperature range of 329 to 421. The corresponding enthalpies of sublimation, calculated via the Clausius-Clapeyron equation, are compared to parent, non-oxygenated PAH compound data to determine the effect of the addition of these oxygen-containing heteroatoms. As expected, the addition of CHO,COOH, and NO2 groups onto these PAHs increases the enthalpy of sublimation and decreases the vapor pressure as compared to the parent PAH; the position of substitution also plays a significant role in determining the vapor pressure of these OPAHs. PMID:18220445
13. Vapor pressure deficit effects on leaf area expansion and transportation of soybean subjected to soil drying
Technology Transfer Automated Retrieval System (TEKTRAN)
Effects of leaf-to-air vapor pressure difference (VPD) and soil water deficit on transpiration rate (TR) of plants are well understood but their effects on plant leaf area expansion (PLAE) are less defined. Both PLAE and TR are unaffected by soil drying until the fraction transpirable soil water (FT...
14. Unusual effect of water vapor pressure on dehydration of dibasic calcium phosphate dihydrate.
PubMed
Kaushal, Aditya M; Vangala, Venu R; Suryanarayanan, Raj
2011-04-01
Dibasic calcium phosphate occurs as an anhydrate (DCPA; CaHPO?) and as a dihydrate (DCPD; CaHPO?2H?O). Our objective was to investigate the unusual behavior of these phases. Dibasic calcium phosphate dihydrate was dehydrated in a (i) differential scanning calorimeter (DSC) in different pan configurations; (ii) variable-temperature X-ray diffractometer (XRD) at atmospheric and under reduced pressure, and in sealed capillaries; and (iii) water vapor sorption analyzer at varying temperature and humidity conditions. Dehydration was complete by 210C in an open DSC pan and under atmospheric pressure in the XRD. Unlike "conventional" hydrates, the dehydration of DCPD was facilitated in the presence of water vapor. Variable-temperature XRD in a sealed capillary and DSC in a hermetic pan with pinhole caused complete dehydration by 100C and 140C, respectively. Under reduced pressure, conversion to the anhydrate was incomplete even at 300C. The increase in dehydration rate with increase in water vapor pressure has been explained by the Smith-Topley effect. Under "dry" conditions, a coating of poorly crystalline product is believed to form on the surface of particles and act as a barrier to further dehydration. However, in the presence of water vapor, recrystallization occurs, creating cracks and channels and facilitating continued dehydration. PMID:24081471
15. 40 CFR 265.1054 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Standards: Pressure relief devices in gas/vapor service. 265.1054 Section 265.1054 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES (CONTINUED) INTERIM STATUS STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND...
16. 40 CFR 264.1054 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Standards: Pressure relief devices in gas/vapor service. 264.1054 Section 264.1054 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES (CONTINUED) STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Air...
17. Quasi-static vapor pressure measurements on reactive systems in inert atmosphere box
NASA Technical Reports Server (NTRS)
Fischer, A. K.
1968-01-01
Apparatus makes vapor pressure measurements on air-sensitive systems in an inert atmosphere glove box. Once the apparatus is loaded with the sample and all connections made, all measuring operations may be performed outside the box. The apparatus is a single-tube adaptation of the double-tube quasi-static technique.
18. 40 CFR 63.165 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 10 2012-07-01 2012-07-01 false Standards: Pressure relief devices in gas/vapor service. 63.165 Section 63.165 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS (CONTINUED) NATIONAL EMISSION STANDARDS FOR HAZARDOUS AIR POLLUTANTS FOR SOURCE CATEGORIES National Emission Standards...
19. 40 CFR 61.242-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 9 2013-07-01 2013-07-01 false Standards: Pressure relief devices in gas/vapor service. 61.242-4 Section 61.242-4 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS (CONTINUED) NATIONAL EMISSION STANDARDS FOR HAZARDOUS AIR POLLUTANTS National Emission Standard for Equipment Leaks...
20. Transient-pressure analysis in geothermal steam reservoirs with an immobile vaporizing liquid phase
USGS Publications Warehouse
Moench, A.F.; Atkinson, P.G.
1978-01-01
A finite-difference model for the radial horizontal flow of steam through a porous medium is used to evaluate transient-pressure behavior in the presence of an immobile vaporizing or condensing liquid phase. Graphs of pressure drawdown and buildup in terms of dimensionless pressure and time are obtained for a well discharging steam at a constant mass flow rate for a specified time. The assumptions are made that the steam is in local thermal equilibrium with the reservoir rocks, that temperature changes are due only to phase change, and that effects of vapor-pressure lowering are negligible. Computations show that when a vaporizing liquid phase is present the pressure drawdown exhibits behavior similar to that observed in noncondensable gas reservoirs, but delayed in time. A theoretical analysis allows for the computation of this delay and demonstrates that it is independent of flow geometry. The response that occurs upon pressure buildup is markedly different from that in a noncondensable gas system. This result may provide a diagnostic tool for establishing the existence of phase-change phenomena within a reservoir. ?? 1979.
1. The relationship between gas hydrate saturation and P-wave velocity of pressure cores obtained in the Eastern Nankai Trough
Konno, Y.; Yoneda, J.; Jin, Y.; Kida, M.; Suzuki, K.; Nakatsuka, Y.; Fujii, T.; Nagao, J.
2014-12-01
P-wave velocity is an important parameter to estimate gas hydrate saturation in sediments. In this study, the relationship between gas hydrate saturation and P-wave velocity have been analyzed using natural hydrate-bearing-sediments obtained in the Eastern Nankai Trough, Japan. The sediment samples were collected by the Hybrid Pressure Coring System developed by Japan Agency for Marine-Earth Science and Technology during June-July 2012, aboard the deep sea drilling vessel CHIKYU. P-wave velocity was measured on board by the Pressure Core Analysis and Transfer System developed by Geotek Ltd. The samples were maintained at a near in-situ pressure condition during coring and measurement. After the measurement, the samples were stored core storage chambers and transported to MHRC under pressure. The samples were manipulated and cut by the Pressure-core Non-destructive Analysis Tools or PNATs developed by MHRC. The cutting sections were determined on the basis of P-wave velocity and visual observations through an acrylic window equipped in the PNATs. The cut samples were depressurized to measure gas volume for saturation calculations. It was found that P-wave velocity correlates well with hydrate saturation and can be reproduced by the hydrate frame component model. Using pressure cores and pressure core analysis technology, nondestructive and near in-situ correlation between gas hydrate saturation and P-wave velocity can be obtained. This study was supported by funding from the Research Consortium for Methane Hydrate Resources in Japan (MH21 Research Consortium) planned by the Ministry of Economy, Trade and Industry (METI), Japan.
2. In Pursuit of Parental Arc Magmas: The effects of pressure on the composition of H2O-saturated peridotite melts
Till, C. B.; Grove, T. L.
2012-12-01
In the continued pursuit to understand the mantle origin of parental arc magmas, we investigate the nature and composition of quench products in a subset of the super-solidus H2O-saturated peridotite melting experiments of Till et al. (2012) and Grove et al. (2006). We examine a variety of filtering techniques for electron microprobe analyses of the quench products that utilize published mineral-fluid and mineral-melt partition coefficients. Our results suggest melts in equilibrium with olivine, orthopyroxene, clinopyroxene and spinel between 1-2 GPa are silica-saturated quartz tholeiites at melt fractions of 11-14%. We find both a low-alkali silica-undersaturated tholeiitic melt and a high-silica vapor-phase quench in equilibrium with a garnet peridotite assemblage at melt fractions of 10-20% from 3.2-4 GPa, suggesting that the peridotite-H2O system is below the second critical end point at these conditions. Between 860 and 1100C at 3.2 GPa, the H2O-saturated peridotite melting reaction consumes olivine, clinopyroxene and garnet to produce orthopyroxene and melt, while above 1100C olivine and orthopyroxene are consumed to produce melt. The isobaric melt production rates in these experiments are extremely low (dF/dT= 0.05-0.13%/C for 10-30% melt) and may represent a minimum in peridotite melt production rates, which occur when a melt is H2O-saturated. Our melt compositions are similar to those from the landmark experimental studies of Kushiro (1972) and Mysen (1973) who also analyzed the compositions of low degree mantle melts formed in the presence of excess H2O. Together the experimental observations suggest that low-extent melts of H2O-saturated peridotite are silica-saturated at lower pressures but become increasingly silica-undersaturated at higher pressures. Our experimental results also point to the likelihood of multiple inputs into the base of the mantle wedge when melting commences near 100 km depth beneath arcs. We discuss the composition of the hydrous silicate melt input into the mantle wedge relative to that of a coexisting solute-rich H2O fluid, as documented in this and previous experimental studies.
3. Surface tension, coexistence curve, and vapor pressure of binary liquid-gas mixtures
Do, V. T.; Straub, J.
1986-01-01
The objective of this paper is to present measurements of the vapor pressure, capillary coefficient, and refractive index of four binary mixtures, CO2-SF6, R14-SF6, SF6-R13B1, and SF6-R22, at liquid-vapor equilibrium at different average concentrations. The measuring temperature range covered the entire liquid-vapor region from the triple line up to the critical point. The capillary coefficient was determined by means of the capillary rise method; the refractive index, by measuring the angle of refraction of a light beam passing through a prism and the sample. In order to obtain the liquid-vapor densities of pure substances the Lorentz-Lorenz relation can be used. However, in applying this relation to calculate the liquid-vapor densities of a mixture, one may need the concentrations of both the liquid and the vapor phase, which are, for the most part, quite different from the average concentration of the mixture. Calculating the concentrations of both fluid phases with the aid of an equation of state and comparing with measurements, we could show that the molar refraction coefficient of the mixtures can be simply determined from the average concentration and the molar refraction coefficients of their pure components. The surface tension of the mixtures could then be calculated from the measured capillary coefficient and the refractive index with the aid of the Lorentz-Lorenz relation.
4. Advanced Computational Modeling of Vapor Deposition in a High-Pressure Reactor
NASA Technical Reports Server (NTRS)
Cardelino, Beatriz H.; Moore, Craig E.; McCall, Sonya D.; Cardelino, Carlos A.; Dietz, Nikolaus; Bachmann, Klaus
2004-01-01
In search of novel approaches to produce new materials for electro-optic technologies, advances have been achieved in the development of computer models for vapor deposition reactors in space. Numerical simulations are invaluable tools for costly and difficult processes, such as those experiments designed for high pressures and microgravity conditions. Indium nitride is a candidate compound for high-speed laser and photo diodes for optical communication system, as well as for semiconductor lasers operating into the blue and ultraviolet regions. But InN and other nitride compounds exhibit large thermal decomposition at its optimum growth temperature. In addition, epitaxy at lower temperatures and subatmospheric pressures incorporates indium droplets into the InN films. However, surface stabilization data indicate that InN could be grown at 900 K in high nitrogen pressures, and microgravity could provide laminar flow conditions. Numerical models for chemical vapor deposition have been developed, coupling complex chemical kinetics with fluid dynamic properties.
5. Advanced Computational Modeling of Vapor Deposition in a High-pressure Reactor
NASA Technical Reports Server (NTRS)
Cardelino, Beatriz H.; Moore, Craig E.; McCall, Sonya D.; Cardelino, Carlos A.; Dietz, Nikolaus; Bachmann, Klaus
2004-01-01
In search of novel approaches to produce new materials for electro-optic technologies, advances have been achieved in the development of computer models for vapor deposition reactors in space. Numerical simulations are invaluable tools for costly and difficult processes, such as those experiments designed for high pressures and microgravity conditions. Indium nitride is a candidate compound for high-speed laser and photo diodes for optical communication system, as well as for semiconductor lasers operating into the blue and ultraviolet regions. But InN and other nitride compounds exhibit large thermal decomposition at its optimum growth temperature. In addition, epitaxy at lower temperatures and subatmospheric pressures incorporates indium droplets into the InN films. However, surface stabilization data indicate that InN could be grown at 900 K in high nitrogen pressures, and microgravity could provide laminar flow conditions. Numerical models for chemical vapor deposition have been developed, coupling complex chemical kinetics with fluid dynamic properties.
6. The vapor pressures of supercooled NHO3/H2O solutions. [in polar stratospheric clouds
NASA Technical Reports Server (NTRS)
Hanson, David R.
1990-01-01
A procedure utilizing the Gibbs-Duhem relation is used to extrapolate vapor pressures of supercooled HNO3 mixtures to 190 K. Values of A and B from the equation logP = A - B/T are presented for solutions between 0.20 and 0.25 mole fraction HNO3. In the stratosphere, if sufficient HNO3 vapor is present because it has not come into equilibrium with the nitric acid trihydrate, supercooled nitric acid solutions could condense at temperatures up to 1.5 + or - 0.8 K above the ice point.
7. Vapor-modulated heat pipe for improved temperature control
NASA Technical Reports Server (NTRS)
Edwards, D. K.; Eninger, J. E.; Ludeke, E. E.
1978-01-01
Dryout induced by vapor throttling makes control of equipment temperature less dependent on variations in sink environment. Mechanism controls flow of vapor in heat pipe by using valve in return path to build difference in pressure and also difference in saturation temperature of the vapor. In steady state, valve closes just enough to produce partial dryout that achieves required temperature drop.
8. Measurements of blast waves from bursting frangible spheres pressurized with flash-evaporation vapor or liquid
NASA Technical Reports Server (NTRS)
Esparaza, E. D.; Baker, W. E.
1977-01-01
Incident overpressure data from frangible spheres pressurized with a flash-evaporating fluid in liquid and vapor form were obtained in laboratory experiments. Glass spheres under higher than ambient internal pressure of Freon-12 were purposely burst to obtain time histories of overpressure. Nondimensional peak pressures, arrival and duration times, and impulses are presented, and whenever possible plotted and compared with compiled data for Pentolite high-explosive. The data are generally quite repeatable and show differences from blast data produced by condensed high-explosives.
9. On the dynamics of fuel vapor pressure buildup in voided liquid-metal fast breeder reactor cores during transient heating
SciTech Connect
Rao, P.B.; Singh, O.P.
1986-11-01
An extension of previous work, the study examines the implications of the approximation that the fuel vapor and liquid temperatures remain equal during the transient. Modified mathematical formulations for calculating the transient fuel vapor temperatures separately are provided as well as the results of calculations of the dynamics of fuel vapor pressure buildup during transient heating in voided liquid-metal fast breeder reactor cooling channels by dispensing with the above approximation. The results with and without the approximation are compared with each other. The study indicates that, although the fuel vapor temperatures lag the liquid-fuel temperatures, the fuel vapor pressure buildup is relatively less sensitive to this lag. The use of the above approximation results in an overprediction of the transient vapor pressure by <10%.
10. Synthetic fluid inclusions. V. Solubility relations in the system NaCl-KCl-H 2O under vapor-saturated conditions
Sterner, S. Michael; Hall, Donald L.; Bodnar, Robert J.
1988-05-01
Vapor-saturated solubility relationships in the system NaCl-KCl-H 2O have been determined by experimentally synthesizing fluid inclusions in quartz in the presence of known brine compositions and then measuring the dissolution temperatures of halite and/or sylvite daughter crystals within the inclusions using a microscope equipped with a heating stage. These data, along with other literature values have been used in a stepwise multiple regression routine to generate a series of equations describing vapor-saturated solubility relations within the halite, sylvite and hydrohalite stability fields. These equations, together with a recently published equation for the ice stability field ( HALLet al., 1987), have been used to construct the complete vapor-saturated solubility surface in the NaCl-KCl-H 2O ternary system. The diagram may be used in the interpretation of microthermometric data to determine the compositions of fluid inclusions approximated by the NaCl-KCl-H 2O system. For the NaCl-H 2O binary system, the ternary halite field expression reduces to Wt.% NaCl = 26.242 + 0.4928 ? + 1.42 ?2 - 0.223 ?3 + 0.04129 ?4 + 0.006295 ?5- 0.001967 ?6 + 0.0001112 ?7 ( ? = T C/100, where 0.1 ? T C ?801 C) which describes halite solubilities along the three-phase halite + liquid + vapor (H + L + V) curve. Similarly, sylvite solubilities along the three-phase sylvite + liquid + vapor (S + L + V) curve are described by the equation Wt.% KC1 = 21.886 + 20.28 ? - 9.603 ?2 + 4.078 ?3 - 0.8724 ?4 + 0.09174 ?5 - 0.003776 ?6 ( ?= T C/100, where -10.7 ? T C ? 770 C). Solubility data obtained from synthetic fluid inclusions are in good agreement with recently published data for the KC1-H 2O and NaCl-H 2O binary systems but are at variance with some earlier works.
11. Observations on vapor pressure in SPR caverns : sources.
SciTech Connect
Munson, Darrell Eugene
2010-05-01
The oil of the Strategic Petroleum Reserve (SPR) represents a national response to any potential emergency or intentional restriction of crude oil supply to this country, and conforms to International Agreements to maintain such a reserve. As assurance this reserve oil will be available in a timely manner should a restriction in supply occur, the oil of the reserve must meet certain transportation criteria. The transportation criteria require that the oil does not evolve dangerous gas, either explosive or toxic, while in the process of transport to, or storage at, the destination facility. This requirement can be a challenge because the stored oil can acquire dissolved gases while in the SPR. There have been a series of reports analyzing in exceptional detail the reasons for the increases, or regains, in gas content; however, there remains some uncertainty in these explanations and an inability to predict why the regains occur. Where the regains are prohibitive and exceed the criteria, the oil must undergo degasification, where excess portions of the volatile gas are removed. There are only two known sources of gas regain, one is the salt dome formation itself which may contain gas inclusions from which gas can be released during oil processing or storage, and the second is increases of the gases release by the volatile components of the crude oil itself during storage, especially if the stored oil undergoes heating or is subject to biological generation processes. In this work, the earlier analyses are reexamined and significant alterations in conclusions are proposed. The alterations are based on how the fluid exchanges of brine and oil uptake gas released from domal salt during solutioning, and thereafter, during further exchanges of fluids. Transparency of the brine/oil interface and the transfer of gas across this interface remains an important unanswered question. The contribution from creep induced damage releasing gas from the salt surrounding the cavern is considered through computations using the Multimechanism Deformation Coupled Fracture (MDCF) model, suggesting a relative minor, but potentially significant, contribution to the regain process. Apparently, gains in gas content can be generated from the oil itself during storage because the salt dome has been heated by the geothermal gradient of the earth. The heated domal salt transfers heat to the oil stored in the caverns and thereby increases the gas released by the volatile components and raises the boiling point pressure of the oil. The process is essentially a variation on the fractionation of oil, where each of the discrete components of the oil have a discrete temperature range over which that component can be volatized and removed from the remaining components. The most volatile components are methane and ethane, the shortest chain hydrocarbons. Since this fractionation is a fundamental aspect of oil behavior, the volatile component can be removed by degassing, potentially prohibiting the evolution of gas at or below the temperature of the degas process. While this process is well understood, the ability to describe the results of degassing and subsequent regain is not. Trends are not well defined for original gas content, regain, and prescribed effects of degassing. As a result, prediction of cavern response is difficult. As a consequence of this current analysis, it is suggested that solutioning brine of the final fluid exchange of a just completed cavern, immediately prior to the first oil filling, should be analyzed for gas content using existing analysis techniques. This would add important information and clarification to the regain process. It is also proposed that the quantity of volatile components, such as methane, be determined before and after any degasification operation.
12. Benzene under high pressure: A story of molecular crystals transforming to saturated networks, with a possible intermediate metallic phase
SciTech Connect
Wen, Xiao-Dong; Hoffmann, Roald; Ashcroft, N. W.
2011-01-01
In a theoretical study, benzene is compressed up to 300 GPa. The transformations found between molecular phases generally match the experimental findings in the moderate pressure regime (<20 GPa): phase I (Pbca) is found to be stable up to 4 GPa, while phase II (P43212) is preferred in a narrow pressure range of 47 GPa. Phase III (P21/c) is at lowest enthalpy at higher pressures. Above 50 GPa, phase V (P21 at 0 GPa; P21/c at high pressure) comes into play, slightly more stable than phase III in the range of 5080 GP, but unstable to rearrangement to a saturated, four-coordinate (at C), one-dimensional polymer. Actually, throughout the entire pressure range, crystals of graphane possess lower enthalpy than molecular benzene structures; a simple thermochemical argument is given for why this is so. In several of the benzene phases there nevertheless are substantial barriers to rearranging the molecules to a saturated polymer, especially at low temperatures. Even at room temperature these barriers should allow one to study the effect of pressure on the metastable molecular phases. Molecular phase III (P21/c) is one such; it remains metastable to higher pressures up to ~200 GPa, at which point it too rearranges spontaneously to a saturated, tetracoordinate CH polymer. At 300 K the isomerization transition occurs at a lower pressure. Nevertheless, there may be a narrow region of pressure, between P = 180 and 200 GPa, where one could find a metallic, molecular benzene state. We explore several lower dimensional models for such a metallic benzene. We also probe the possible first steps in a localized, nucleated benzene polymerization by studying the dimerization of benzene molecules. Several new (C6H6)2 dimers are predicted.
13. Simultaneous measurement of capillary pressure, saturation, and effective permeability of immiscible liquids in porous media
Dane, J. H.; Hofstee, C.; Corey, A. T.
1998-12-01
In many studies involving a liquid and air, the effective permeability of the wetting phase (kw) is determined from the capillary pressure (Pc)-saturation (S) relation and a corresponding, measured kw value. The movement, and therefore the effective permeability, knw, of air in an air-liquid system is often ignored, especially by those who consider only the flow of water in soils. However, if a wetting and a nonwetting liquid coexist (two immiscible liquids), the effective permeability function of the nonwetting liquid must be determined as well. Rather than using some indirect method to determine the knw (Pc) or knw (S) relationship of the nonwetting liquid, we propose a direct measurement technique by using a permeameter which allows for steady state flow of the nonwetting liquid over a range of Pc and S values. During each steady state flow condition of the nonwetting liquid, Pc and S are constant and uniform throughout the permeameter, while the wetting liquid is at rest. The nonwetting liquid can either be a dense non-aqueous phase liquid (DNAPL) or a light non-aqueous phase liquid (LNAPL). The knw values are calculated as a function of Pc and S from the measured flow rates and the density difference between the wetting and nonwetting liquid. The proposed technique can be applied during drainage as well as imbibition. The S values are determined by recording the amount of water being displaced from the cell each time the Pc is changed. Results are discussed for the DNAPL perchloroethylene (PCE) and the LNAPL Soltrol.
14. Border control! Capillary pressure / saturation relationships in a diphasic flow in a random medium: Influence of the boundary conditions
Fiorentino, Eve-Agns; Toussaint, Renaud; Moura, Marcel; Jankov, Mihailo; Schfer, Gerhard; Jrgen Mly, Knut
2013-04-01
Solving problems involving biphasic flows in porous media, at a scale larger than the pore one, normally requires the use of relationships between pressure and saturation. These allow the closure of generalized Darcy flow models for two phases, commonly used in hydrology or large scale problems of diphasic flow in porous media. There are mathematical models which approximate experimental records with curve-fitting equations. The two most common models are the Brooks-Corey and van Genchten ones, they are used to complete a system of generalized Darcy equations. The purpose of the current study is the influence of the boundary conditions on the relationship between pressure and saturation. We perform numerical simulations of drainage experiments. Water is the wetting fluid and air is the non wetting fluid. The results highlight the fact that a filter which allows only water to flow at the exit face of the system modifies both the shape of the curve and the value of the residual saturation. The pressure of the models that are commonly used does not match with the pressure of real flows since there is no filter to cross, to flow from an elementary volume to another. Experiments performed in transparent Hele-Shaw cells exhibit the same features, showing the influence of the semi permeable boundary conditions on the pressure-saturation measures obtained. This effect corresponding to the formation of localized plugging clusters at the boundaries, is obtained in slow flow conditions, and is independent of any dynamic fingering, also known to affect such relations (1,2,3). Modeling flows in open media thus would require to use the central part of the curves pressure saturation where the effect of the boundaries is the least important, or to modify properly these relationships to extract the behavior unaffected by boundaries. References: (1) Two-phase flow: structure, upscaling, and consequences for macroscopic transport properties Renaud Toussaint ; Knut Jrgen Mly; Yves Mheust; Grunde Lvoll; Mihailo Jankov; Gerhard Schfer; Jean Schmittbuhl Vadose Zone Journal, 2012, 11 (3), pp. vzj2011.0123 (2) Lvoll, G., M. Jankov, K.J. Mly, R. Toussaint, J. Schmittbuhl, G. Schaefer and Y. Mheust, Influence of viscous fingering on dynamic saturation-pressure curves in porous media, Transport in Porous Media, 86, 1, 305-324, 2010 (3) Toussaint, R., G. Lvoll, Y. Mheust, K.J. Mly and J. Schmittbuhl, Influence of pore-scale disorder on viscous fingering during drainage, Europhys. Lett., 71, 583 (2005).
15. Preliminary Heat Capacity and Vapor Pressure Measurements of 2D 4He on ZYX Graphite
Nakamura, S.; Matsui, K.; Matsui, T.; Fukuyama, Hiroshi
2013-06-01
We report preliminary heat capacity and vapor pressure measurements of the first and second layers of 4He adsorbed on ZYX graphite. ZYX is known to have much better crystallinity than Grafoil, the most commonly-used exfoliated graphite substrate, such as a ten-times larger platelet size. This allows us to distinguish different phases in 2D 4He much more clearly and may provide qualitatively different insights into this system. We found a significantly asymmetric density-dependence of the heat-capacity peak associated with the sqrt{3}sqrt{3} phase formation comparing with that obtained with Grafoil. The 2nd-layer promotion density is determined as 11.80.3 nm-2 from the heat-capacity measurement of low density samples in the 2nd layer and vapor pressure measurement.
16. Temperature dependence of the vapor pressure and evaporation coefficient of supercooled water
Davies, James F.; Miles, Rachael E. H.; Haddrell, Allen E.; Reid, Jonathan P.
2014-09-01
We report measurements of the vapor pressure of water over the supercooled temperature range 248 to 273 K derived from evaporation kinetics measurements of single water droplets. Accurate measurements of the relative humidity of the surrounding gas phase are derived from comparative and sequential measurements of the evaporation kinetics of droplets containing sodium chloride. The temperature dependence of the vapor pressure of supercooled water is shown to conform closely to the parameterization provided by Murphy and Koop (2005) once the uncertainties in experimental and thermophysical parameters are accounted for by ensuring an accurate representation of evaporation rates at temperatures above 273 K. Further, from a sensitivity analysis of all of the data over the full temperature range from 248 to 293 K, we can conclude that the evaporation coefficient of water, and thus the mass accommodation coefficient, is greater than, or equal to, 0.5.
17. Initial Measurement of the Vapor Pressures of Simple Refractory Materials: Cu and Fe
NASA Technical Reports Server (NTRS)
Nuth, Joseph A., III; Ferguson, Frank T.; Johnson, Natasha; Martinez, Daniel
2003-01-01
It has become increasingly clear over the past decade that high temperature processes played important roles in the Primitive Solar Nebula. Unfortunately, basic data, such as the vapor pressures of iron or SiO have not been measured over the appropriate temperature range (near T approximately equal to 2000K), but must be extrapolated from lower temperature measurements often made more than 50 years ago. The extrapolation of the available data to higher temperatures can be quite complex and can depend on other factors such as the oxygen fugacity or the presence of hydrogen gas. Moreover, modern technology has made possible more accurate measurements of such quantities over a wider temperature range. We recently acquired a commercial Thermo-Cahn Thermogravimetric system capable of vacuum operation to 1700 C and measurement of mass change with microgram accuracy in a 100g sample or smaller. In this paper, we will report our progress in learning to make vapor pressure measurements using this system.
18. Water-vapor pressure in nests of the San Miguel Island Song Sparrow
USGS Publications Warehouse
Kern, Michael D.; Sogge, Mark K.; van Riper, Charles, III
1990-01-01
The water-vapor pressure (PN) in nests of the San Miguel Island race of Song Sparrows (Melospiza melodia micronyx) averaged 16 torr, but varied considerable between nests and within individual nests during successive days of incubation. Large daily fluctuations occurred throughout the incubation period and did not parallel concurrent changes in ambien vapor pressure (P1). Daily rates of water loss from nest eggs (MH2O) averaged 28 mg day-1, but also varied considerable within and between nests and did not correlate with changes in P1. MH2O increased 6-33% after the third day of incubation. PN was significantly higher and MH2O significantly lower in nests located in sheltered gullies than in nests from a windswept slope. These data suggest that Song Sparrows do not regulate PN to achieve hatching success.
19. Some possible filler alloys with low vapor pressures for refractory-metal brazing
NASA Technical Reports Server (NTRS)
Morris, J. F.
1973-01-01
A compilation of eutectics and melting-point minima for binary combinations of metals having vapor pressures below 10 to the minus 10th power torr at 1500 degrees K and .00005 torr at 2000 degree K is presented. These compositions and others near them on their phase diagrams are potential special brazing fillers for refractory metals. Some possible problems and advantages for fusion bonds of such mixtures are indicated. Evaluations of brazing fillers containing refractory metals are reported.
20. Synthesis of diamond nanowires using atmospheric-pressure chemical vapor deposition.
PubMed
Hsu, Chih-Hsun; Cloutier, Sylvain G; Palefsky, Steven; Xu, Jimmy
2010-09-01
We report diamond nanowires grown in an atmospheric pressure chemical vapor deposition process. These diamond nanowires are straight, thin and long, and uniform in diameter (60-90 nm) over tens of micrometers. Spectroscopic analysis, electron diffraction, and transmission electron microscopy provided confirmation that these nanowires are diamond with high crystallinity and high structural uniformity. They further revealed that these diamond nanowires are encased within multiwalled carbon nanotubes. PMID:20677795
1. Vapor Pressure and Evaporation Coefficient of Silicon Monoxide over a Mixture of Silicon and Silica
NASA Technical Reports Server (NTRS)
Ferguson, Frank T.; Nuth, Joseph A., III
2012-01-01
The evaporation coefficient and equilibrium vapor pressure of silicon monoxide over a mixture of silicon and vitreous silica have been studied over the temperature range (1433 to 1608) K. The evaporation coefficient for this temperature range was (0.007 plus or minus 0.002) and is approximately an order of magnitude lower than the evaporation coefficient over amorphous silicon monoxide powder and in general agreement with previous measurements of this quantity. The enthalpy of reaction at 298.15 K for this reaction was calculated via second and third law analyses as (355 plus or minus 25) kJ per mol and (363.6 plus or minus 4.1) kJ per mol respectively. In comparison with previous work with the evaporation of amorphous silicon monoxide powder as well as other experimental measurements of the vapor pressure of silicon monoxide gas over mixtures of silicon and silica, these systems all tend to give similar equilibrium vapor pressures when the evaporation coefficient is correctly taken into account. This provides further evidence that amorphous silicon monoxide is an intimate mixture of small domains of silicon and silica and not strictly a true compound.
2. Methods of Measuring Vapor Pressures of Lubricants With Their Additives Using TGA and/or Microbalances
NASA Technical Reports Server (NTRS)
Scialdone, John J.; Miller, Michael K.; Montoya, Alex F.
1996-01-01
The life of a space system may be critically dependent on the lubrication of some of its moving parts. The vapor pressure, the quantity of the available lubricant, the temperature and the exhaust venting conductance passage are important considerations in the selection and application of a lubricant. In addition, the oil additives employed to provide certain properties of low friction, surface tension, antioxidant and load bearing characteristics, are also very important and need to be known with regard to their amounts and vapor pressures. This paper reports on the measurements and analyses carried out to obtain those parameters for two often employed lubricants, the Apiezon(TM)-C and the Krytox(TM) AB. The measurements were made employing an electronic microbalance and a thermogravimetric analyzer (TGA) modified to operate in a vacuum. The results have been compared to other data on these oils when available. The identification of the mass fractions of the additives in the oil and their vapor pressures as a function of the temperature were carried out. These may be used to estimate the lubricant life given its quantity and the system vent exhaust conductance. It was found that the Apiezon(TM)-C has three main components with different rates of evaporation while the Krytox(TM) did not indicate any measurable additive.
3. Pressure drop in fully developed, duct flow of dispersed liquid-vapor mixture at zero gravity
NASA Technical Reports Server (NTRS)
Sridhar, K. R.; Chao, B. T.; Soo, S. L.
1990-01-01
The dynamics of steady, fully developed dispersed liquid-vapor flow in a straight duct at 0-g is simulated by flowing water containing n-butyl benzoate droplets. Water and benzoate are immiscible and have identical density at room temperature. The theoretical basis of the simulation is given. Experiments showed that, for a fixed combined flow rate of water and benzoate, the frictional pressure drop is unaffected by large changes in the volume fraction of benzoate drops and their size distribution. Measured power spectra of the static wall pressure fluctuations induced by the turbulent water-benzoate flow also revealed that their dynamics is essentially unaltered by the presence of the droplets. These experimental findings, together with the theoretical analysis, led to the conclusion that the pressure drop in fully developed, dispersed liquid-vapor flow in straight ducts of constant cross section at 0-g is identical to that due to liquid flowing alone at the same total volumetric flow rate of the liquid-vapor mixture and, therefore, can be readily determined.
4. In-Reactor Oxidation of Zircaloy-4 Under Low Water Vapor Pressures
SciTech Connect
Luscher, Walter G.; Senor, David J.; Clayton, Kevin; Longhurst, Glen
2015-01-01
Complementary in- and ex-reactor oxidation tests have been performed to evaluate the oxidation and hydrogen absorption performance of Zircaloy-4 (Zr-4) under relatively low partial pressures (300 and 1000 Pa) of water vapor at specified test temperatures (330° and 370°C). Data from these tests will be used to support fabrication of components intended for isotope-producing targets and provide information regarding the temperature and pressure dependence of oxidation and hydrogen absorption of Zr-4 over the specified range of test conditions. Comparisons between in- and ex- reactor test results were performed to evaluate the influence of irradiation.
5. In-reactor oxidation of zircaloy-4 under low water vapor pressures
SciTech Connect
Luscher, Walter G.; Senor, David J.; Clayton, Kevin K.; Longhurst, Glen R.
2015-01-01
Complementary in- and ex-reactor oxidation tests have been performed to evaluate the oxidation and hydrogen absorption performance of Zircaloy-4 (Zr-4) under relatively low partial pressures (300 and 1000 Pa) of water vapor at specified test temperatures (330 and 370 ºC). Data from these tests will be used to support the fabrication of components intended for isotope-producing targets and provide information regarding the temperature and pressure dependence of oxidation and hydrogen absorption of Zr- 4 over the specified range of test conditions. Comparisons between in- and ex-reactor test results were performed to evaluate the influence of irradiation.
6. Characterization of Gas-Hydrate Sediment: In Situ Evaluation of Hydrate Saturation in Pores of Pressured Sedimental Samples
Jin, Y.; Konno, Y.; Kida, M.; Nagao, J.
2014-12-01
Hydrate saturation of gas-hydrate bearing sediment is a key of gas production from natural gas-hydrate reservoir. Developable natural gas-hydrates by conventional gas/oil production apparatus almost exist in unconsolidated sedimental layer. Generally, hydrate saturations of sedimental samples are directly estimated by volume of gas generated from dissociation of gas hydrates in pore spaces, porosity data and volume of the sediments. Furthermore, hydrate saturation can be also assessed using velocity of P-wave through sedimental samples. Nevertheless, hydrate saturation would be changed by morphological variations (grain-coating, cementing and pore-filling model) of gas hydrates in pore spaces. Jin et al.[1,2] recently observed the O-H stretching bands of H2O molecules of methane hydrate in porous media using an attenuated total reflection IR (ATR-IR) spectra. They observed in situ hydrate formation/dissociation process in sandy samples (Tohoku Keisya number 8, grain size of ca. 110 ?m). In this presentation, we present IR spectroscopy approach to in situ evaluation of hydrate saturation of pressured gas-hydrate sediments. This work was supported by funding from the Research Consortium for Methane Hydrate Resources in Japan (MH21 Research Consortium) planned by the Ministry of Economy, Trade and Industry (METI), Japan. [1] Jin, Y.; Konno, Y.; Nagao, J. Energy Fules, 2012, 26, 2242-2247. [2] Jin, Y.; Oyama, H.; Nagao, J. Jpn. J. Appl. Phys. 2009, 48, No. 108001.
7. Measurements and Correlations of cis-1,3,3,3-Tetrafluoroprop-1-ene (R1234ze(Z)) Saturation Pressure
Fedele, Laura; Di Nicola, Giovanni; Brown, J. Steven; Bobbo, Sergio; Zilio, Claudio
2014-01-01
cis-1,3,3,3-Tetrafluoroprop-1-ene (R1234ze(Z)) is being investigated as a working fluid possessing a low global warming potential (GWP) for high-temperature heat pumping applications, organic Rankine cycles, and air-conditioning and refrigeration applications, and as a potential solvent, propellant, and foam blowing agent. Its GWP is less than one. The open literature contains a total of 79 vapor-pressure data from three sources and the critical state properties from a single source. The current paper provides 64 vapor-pressure data from two different laboratories over the temperature range from 238.13 K to 372.61 K. These data are regressed using Wagner and extended Antoine vapor-pressure correlations and then compared to the existing open literature data and correlations. The normal-boiling-point temperature and acentric factor for R1234ze(Z) are estimated to be 282.73 K and 0.3257, respectively.
8. Synthesis of Diamond-like Carbon Films by Nanopulse Plasma Chemical Vapor Deposition at Subatmospheric Pressure
Ohtake, Naoto; Saito, Takao; Kondo, Yoshimasa; Hosono, Shintaro; Nakamura, Yukinori; Imanishi, Yu-ichiro
2004-11-01
The deposition of diamond-like carbon (DLC) films at subatmospheric pressure has been achieved by the nanopulse plasma chemical vapor deposition (CVD) method. To realize this process, a high ion density and non-arcing plasma at subatmospheric pressure are required. A static induction (SI) thyristor with an inductive energy storage (IES) circuit was used. The DLC film was obtained under the conventional low-pressure process at 6 Pa, and the characteristics of the high electron temperature and the exponential relationship between pulse frequency and growth rate were observed. Deposition of the DLC film was also achieved at the subatmospheric pressure of 26.7 kPa (200 Torr) using this nanopulse plasma CVD method.
9. Determination of capillary pressure-saturation relation by pore-morphology-based and lattice-Boltzmann simulation
Schulz, V.; Toelke, J.; Vogel, H.; Krafzcyk, M.; Roth, K.
2002-12-01
In this study we present two different models for the determination of the capillary pressure-saturation relation in porous media. The first one is a pore-morphology-based model where we use methods from morphological image analysis to calculate the quasi-static primary drainage curve. Compared to previous publications in this field (Hilpert and Miller 2001), we extended the method to model trapped or irreducible wetting phase (WP). Additionally, we could optimize it in a way that the computing time is significantly reduced. The second method to determine the capillary pressure-saturation relation is a two-phase lattice-Boltzmann (LB) model. Using a recently developed model for multi-phase flow (Tlke et al. 2001) we simulated the drainage of the porous medium by several pressure steps starting at total saturation. As test systems, we used generated randomly sphere packages and x-ray images of a sintered borosilicate glass. Our simulations show that the capillary pressure-saturation curves from the both methods are very similar. However the morphological model is orders of magnitude faster than the LB simulation. But we point out that the good agreement strongly depends on the geometry of the investigated porous medium. Due to the model formulation, the pore-morphology-based simulation cannot be applied if the pore structure is strongly anisotropic (e. g. cracks). References: M. Hilpert and C. T. Miller: Pore-morphology-based simulations of drainage in totally wetting porous media, Advances in Water Resources, 24, p.243 (2001) J. Tlke, M. Krafczyk, M. Schulz, E. Rank: Lattice Boltzmann simulations of binary fluid flow through porous media, Phil. Trans. R. Soc. Lond. A, Vol 360, Nr. 1792, p.535 (2002)
10. Status of the CNRS-LCSR program on high pressure droplet vaporization and burning
NASA Technical Reports Server (NTRS)
Chauveau, Christian; Goekalp, Iskender
1993-01-01
Depending on the surrounding flow and thermodynamic conditions, a single droplet may experience several gasification regimes, ranging from the envelope flame regime to pure vaporization. In practical situations, such as rocket propulsion or diesel combustion, the size distribution of droplets is, at best, bimodal, so that the possibility exists for the simultaneous presence of various regimes. For example, very small droplets are transported by the gas phase with zero relative velocity. This picture validates then the spherical symmetry hypothesis applied to the droplet and to the diffusion flame enveloping it. On the other hand, for larger droplets, a relative velocity exists due to drag forces. The most important influence of forced convection on droplet burning is the possibility to extinguish globally the envelope flame, or to establish a flame stabilized in the wake region. The burning rates of these regimes differ strongly. The characteristic time of droplet gasification is also influenced by the surrounding pressure and temperature. A parametric investigation of single droplet burning regimes is then helpful in providing the necessary physical ideas for sub-grid models used in spray combustion numerical prediction codes. The CNRS-LCSR experimental program on droplet vaporization and burning deals with these various regimes: stagnant and convective monocomponent droplet burning convective mono and bicomponent droplet vaporization; high temperature convective mono and biocomponent droplet vaporization; burning regimes of hydrazine and hydroxyl-ammonium-nitrate based monopropellant droplets and the vaporization regimes of liquid oxygen droplets. Studies on interacting droplets and on liquid aluminum droplets will start in the near future. The influence of high pressure is a common feature of all these studies. This paper summarizes the status of the CNRS-LCSR program on the effects of high pressure on monocomponent single droplet burning and vaporization, and some recent results obtained under normal and reduced gravity conditions with suspended droplets are presented. In the work described here, parabolic flights of an aircraft is used to create a reduced gravity environment of the order of 10(exp -2) g.
11. Two-phase heat transfer and pressure drop of LNG during saturated flow boiling in a horizontal tube
Chen, Dongsheng; Shi, Yumei
2013-12-01
Two-phase heat transfer and pressure drop of LNG (liquefied natural gas) have been measured in a horizontal smooth tube with an inner diameter of 8 mm. The experiments were conducted at inlet pressures from 0.3 to 0.7 MPa with a heat flux of 8-36 kW m-2, and mass flux of 49.2-201.8 kg m-2 s-1. The effect of vapor quality, inlet pressure, heat flux and mass flux on the heat transfer characteristic are discussed. The comparisons of the experimental data with the predicted value by existing correlations are analyzed. Zou et al. (2010) correlation shows the best accuracy with 24.1% RMS deviation among them. Moreover four frictional pressure drop methods are also chosen to compare with the experimental database.
12. Disjoining pressure and capillarity in the constrained vapor bubble heat transfer system.
PubMed
Chatterjee, Arya; Plawsky, Joel L; Wayner, Peter C
2011-10-14
Using the disjoining pressure concept in a seminal paper, Derjaguin, Nerpin and Churaev demonstrated that isothermal liquid flow in a very thin film on the walls of a capillary tube enhances the rate of evaporation of moisture by several times. The objective of this review is to present the evolution of the use of Churaev's seminal research in the development of the Constrained Vapor Bubble (CVB) heat transfer system. In this non-isothermal "wickless heat pipe", liquid and vapor flow results from gradients in the intermolecular force field, which depend on the disjoining pressure, capillarity and temperature. A Kelvin-Clapeyron model allowed the use of the disjoining pressure to be expanded to describe non-isothermal heat, mass and momentum transport processes. The intermolecular force field described by the convenient disjoining pressure model is the boundary condition for "suction" and stability at the leading edge of the evaporating curved flow field. As demonstrated by the non-isothermal results, applications that depend on the characteristics of the evaporating meniscus are legion. PMID:21470588
13. Calculation of the vapor-saturated liquidus for the NaCl-CO2-H2O system
USGS Publications Warehouse
Barton, P.B.; I-Ming, C.
1993-01-01
The polybaric liquidus surface for the H2O-rich corner of the NaCl-CO2-H2O ternary is calculated, relying heavily on 1. (1) a Henry's law equation for CO2 in brines (modified from Drummond, 1981), 2. (2) the assumption that the contributions of dissolved NaCl and CO2 in lowering the activity of H2O are additive, and 3. (3) data on the CO2 clathrate solid solution (nominally CO2 ?? 7.3H2O, but ranging from 5.75 to 8 or 9 H2O) from Bozzo et al. (1975). The variation with composition of the activity of CO2??7.3H2O, or any other composition within the clathrate field, is small, thereby simplifying the calculations appreciably. Ternary invariant points are 1. (1) ternary eutectic at -21.5??C, with ice + clathrate + hydrohalite NaCl-??H2O + brine mNaCl = 5.15, mco2 = 0.22 + vapor Ptotal ??? Pco2 = 5.7 atm; 2. (2) peritectic at -9.6??C, with clathrate + hydrohalite + liquid CO2 + brine mNaCl = 5.18, mco2 = 0.55 + vapor (Ptotal ??? Pco2 = 26.47 atm); and 3. (3) peritectic slightly below +0.1 ??C, with halite + hydrohalite + liquid CO2 + brine (mNaCl ??? 5.5, mco2 ??? 0.64) + vapor (Ptotal ??? Pco2 ??? 34 atm). CO2 isobars have been contoured on the ternary liquidus and also on the 25??C isotherm. An important caveat regarding the application of this information to the interpretation of the freezing-thawing behavior of fluid inclusions is that metastable behavior is a common characteristic of the clathrate. ?? 1993.
14. Partial Pressures of In-Se from Optical Absorbance of the Vapor
NASA Technical Reports Server (NTRS)
Brebrick, R. F.; Su, Ching-Hua; Curreri, Peter A. (Technical Monitor)
2001-01-01
The optical absorbance of the vapor phase over various In-Se compositions between 33.3 and 61 atomic percent and 673 and 1418K has been measured and used to obtain the partial pressures of Se2(g) and In2Se(g). The results are in agreement with silica Bourdon gage measurements for compositions between 50 and 61 atomic percent but significantly higher than those from Knudsen cell and simultaneous Torsion-Knudsen cell measurements. The sequiselenide is found to sublime incongruently. Congruent vaporization occurs for the liquid above 1000 K between 50.08 and 56 at. percent Se. The Gibbs energy of formation of the liquid from its pure liquid elements between 1000 and 1300K is essentially independent of temperature and falls between -36 and -38 kJ per gram atomic weight for 50 and 56 percent Se at 1200 and 1300K.
15. High-pressure vapor-liquid equilibria in the propane-1-propanol system
SciTech Connect
Muehlbauer, A.L.; Raal, J.D. )
1993-04-01
High-pressure isothermal vapor liquid equilibrium data were measured for the propane-1-propanol system at 81.6, 105.2, and 120.1 C in a static equilibrium cell with liquid-phase sampling by a piston-driven sampling rod and homogenizing the sample with a static jet mixer. The vapor phase was sampled by releasing it into an evacuated manifold, and the gas chromatograph was calibrated with a new variable volumetric device. Satisfactory modeling was achieved with the combined method using the UNIQUAC equation with equations of sate: the group contribution EOS, Peng-Robinson EOS, or the two-parameter Virial EOS. Differences between the measured and calculated vapor-phase mole fractions, however, were significant for the lower pressure regions of the 81.6 and 120.1 C isotherms. UNIQUAC parameters, hitherto unavailable, with fairly strong temperature dependence in the 81.6 to 120.1 C range are proposed for the system. The covariance matrix indicated a significant correlation among the parameters. The classical mixing rule interaction parameters required for the original Peng-Robinson EOS in the combined method were obtained using the direct method and were temperature-independent for the isotherms for which the propane was supercritical. The possibility of propane/1-propanol immiscibility was theoretically examined according to the criteria of Baker et al. The plots of Gibbs energy of mixing vs. phase mole fractions did not indicate liquid-phase splitting, but the inferences are EOS-dependent and must await visual confirmation. The authors earlier vapor-phase thermodynamic consistency test indicated the data for all three data sets not to be inconsistent.
16. Highly ionized physical vapor deposition plasma source working at very low pressure
SciTech Connect
Stranak, V.; Herrendorf, A.-P.; Drache, S.; Hippler, R.; Cada, M.; Hubicka, Z.; Tichy, M.
2012-04-02
Highly ionized discharge for physical vapor deposition at very low pressure is presented in the paper. The discharge is generated by electron cyclotron wave resonance (ECWR) which assists with ignition of high power impulse magnetron sputtering (HiPIMS) discharge. The magnetron gun (with Ti target) was built into the single-turn coil RF electrode of the ECWR facility. ECWR assistance provides pre-ionization effect which allows significant reduction of pressure during HiPIMS operation down to p = 0.05 Pa; this is nearly more than an order of magnitude lower than at typical pressure ranges of HiPIMS discharges. We can confirm that nearly all sputtered particles are ionized (only Ti{sup +} and Ti{sup ++} peaks are observed in the mass scan spectra). This corresponds well with high plasma density n{sub e} {approx} 10{sup 18} m{sup -3}, measured during the HiPIMS pulse.
17. PARAMETER ESTIMATION OF TWO-FLUID CAPILLARY PRESSURE-SATURATION AND PERMEABILITY FUNCTIONS
EPA Science Inventory
Capillary pressure and permeability functions are crucial to the quantitative description of subsurface flow and transport. Earlier work has demonstrated the feasibility of using the inverse parameter estimation approach in determining these functions if both capillary pressure ...
18. Vapor pressures and heats of vaporization of primary coal tars. Quarterly technical progress report, 1 April 1993--30 June 1993
SciTech Connect
Suuberg, E.M.
1993-11-01
A significant amount of time has been devoted during this quarter to preparing the equipment for production of the tars to be measured, and preparing the equipment for measurements by the so-called Knudsen effusion method. This method will be summarized below. The various effusion methods are based on the effusion of the vaporized substance from a surface, or through an orifice [1]. One of these is the Knudsen method [2, 3], in which the substance effuses through small holes of known area. The principal applications of this method have been in the determination of the vapor pressure of metals such as mercury, cadmium, zinc and lead. It has however been equally effective for obtaining the vapor pressure of organic crystals and compounds [4, 5, 6, 7, 8, 99, 20]. The Knudsen method is used for the measurement of low vapor pressures in the range from 1 to 10{sup {minus}6} mm Hg under molecular flow conditions (pressures inside and outside cell are low enough for gas molecules make collisions only with the walls of the cell) and involves measurement of the rate of loss of molecules of the evaporating substance, leaving the opening of an effusion cell. Measurement are made under isothermal conditions, with weight loss being recorded as a function of time simultaneously with sample temperature, and with pressure measured outside the effusion cell. The basic theory of the effusion method was reviewed in the literature [2, 39, 12]. The basic theory of method is based upon the kinetic theory of gases, from which Knudsen derived an expression for the slow isothermal flow out of a cell with a small hole in it. According to Knudsen [1] the vapor pressure of a material in the cell can be calculated from his result, using the equation given.
19. High-Pressure Solvent Vapor Annealing with a Benign Solvent To Rapidly Enhance the Performance of Organic Photovoltaics.
PubMed
Jung, Buyoung; Kim, Kangmin; Eom, Yoomin; Kim, Woochul
2015-06-24
A high-pressure solvent vapor annealing (HPSVA) treatment is suggested as an annealing process to rapidly achieve high-performance organic photovoltaics (OPVs); this process can be compatible with roll-to-roll processing methods and uses a benign solvent: acetone. Solvent vapor annealing can produce an advantageous vertical distribution in the active layer; however, conventional solvent vapor annealing is also time-consuming. To shorten the annealing time, high-pressure solvent vapor is exposed on the active layer of OPVs. Acetone is a nonsolvent for poly(3-hexylthiophene-2,5-diyl) (P3HT), but it can dissolve small amounts of 1-(3-methoxycarbonyl)-propyl-1,1-phenyl-(6,6)C61 (PCBM). Acetone vapor molecules can penetrate into the active layer under high vapor pressure conditions to alter the morphology. HPSVA induces a PCBM-rich phase near the cathode and facilitates the transport of free charge carriers to the electrode. Although P3HT is not soluble in acetone, locally rearranged P3HT crystallites are generated. The performance of OPV films was enhanced after HPSVA; the film treated at 30 kPa for 10 s showed optimum performance. Additionally, this HPSVA method could be adapted for mass production because the temporary exposure of films to high-pressure acetone vapor in ambient conditions also improved performance. PMID:26061813
20. Oxy-Mat Mattress System Development Utilizing Simultaneous Measurement of Interface Pressure and Deep Tissue Oxygen Saturation.
PubMed
Butler, Glenn J; Kenyon, David J; Gorenstein, Scott; Davenport, Thomas; Golembe, Edward; Lee, Bok; Vieweg, Jacques
2015-05-01
The development and management of pressure ulcers (PUs) among hospital and nursing home patients is one of the greatest preventable challenges to healthcare worldwide. For over 50 years, pressure mapping and subjective comfort has been the primary indicators for mattress selection. Our research demonstrates that mattress/patient interface pressure and relative blood/oxygen perfusion do not inversely correlate and pressure is not a meaningful, real-time indicator of tissue ischemia and risk of pressure ulcer development. Developed in our research is a real-time sensor system to simultaneously measure and record these parameters over the anatomical sites at risk for PUs. Measurements focused on the heel, sacrum, trochanter, ischium, scapula and occipital. A modified pressure mapping system is used for interface pressure measurements and integrated with multiple near-infrared sensors to measure specific deep tissue hemoglobin saturated oxygen or rSO2. Testing and mattress design development was done during the period of 2008 to present. Over 200 human tests of commercially available mattresses were conducted in supine, 30 degree, and 70 degree positions, ranging in times of up to four hours. During this time period, we utilized 20 test subjects-eight female and 12 male-with ages ranging from 18 to 65 years. The result of this proprietary off-loading device evaluation and design system shows that the new Oxy-Mat (Off-Loading Technologies, Tarrytown, NY) Non-Powered Mattress System consistently provides optimized tissue perfusion as measured by natural deep tissue oxygen saturation levels. In extensive laboratory and clinical evaluations, the Oxy-Mat was shown to be functionally superior to CMS Group 2 powered mattresses. Another outcome of our research was that a powered mattress system may not be appropriate for most sensate and semi-ambulatory patients. Further research is underway. PMID:26054994
1. Influence of the helium-pressure on diode-pumped alkali-vapor laser
Gao, Fei; Chen, Fei; Xie, Ji-jiang; Zhang, Lai-ming; Li, Dian-jun; Yang, Gui-long; Guo, Jing
2013-05-01
Diode-pumped alkali-vapor laser (DPAL) is a kind of laser attracted much attention for its merits, such as high quantum efficiency, excellent beam quality, favorable thermal management, and potential scalability to high power and so on. Based on the rate-equation theory of end-pumped DPAL, the performances of DPAL using Cs-vapor collisionally broadened by helium are simulated and studied. With the increase of helium pressure, the numerical results show that: 1) the absorption line-width increases and the stimulated absorption cross-section decreases contrarily; 2) the threshold pumping power decreases to minimum and then rolls over to increase linearly; 3) the absorption efficiency rises to maximum initially due to enough large stimulated absorption cross-section in the far wings of collisionally broadened D2 transition (absorption transition), and then begins to reduce; 4) an optimal value of helium pressure exists to obtain the highest output power, leading to an optimal optical-optical efficiency. Furthermore, to generate the self-oscillation of laser, a critical value of helium pressure occurs when small-signal gain equals to the threshold gain.
2. Resonance ionization spectroscopy measurement of the vapor pressure of several molecular species
SciTech Connect
Capelle, G.A.; Jessup, D.A.; Borella, H.M.; Franks, L.A.
1984-01-01
In recent years resonance ionization spectroscopy (RIS) has found increasing application to various problems involving detection of low levels of atomic, and more recently molecular, species. This work demonstrates the usefulness of RIS in measuring vapor pressure curves of molecular species at very low pressures. Specifically, the vapor pressures versus temperature relationship for rubidium iodide (RbI) and potassium iodide (KI) was measured by applying RIS to atomic Rb and K, using a two-laser system. A pulsed molecular nitrogen laser first dissociated the RbI to produce ground-state Rb atoms in the experimental cell. A flashlamp-pumped dye laser then ionized the Rb in a process wherein two photons of the same wavelength are absorbed, the first exciting Rb via an allowed transition to an upper state (5/sup 2/S/sub 1/2/ ..-->.. 6/sup 2//sub 1/2 or 3/2/) lying in energy slightly more than half the distance to the ionization limit, and the second photon ionizing the excited Rb. In the case of KI, an excimer-laser-pumped dye laser was used in a similar way. An applied dc electric field swept the photoelectrons to a proportional counter for subsequent amplification and detection. The photoelectron signal was then related back to RbI and KI concentrations.
3. Optical frequency standard by using a 1560 nm diode laser locked to saturated absorption lines of rubidium vapor
SciTech Connect
Masuda, Shin; Seki, Atsushi; Niki, Shoji
2007-07-20
A robust, compact, highly accurate rubidium optical frequency standard module was developed to overcome the delicate performance of conventional frequency stabilized lasers. A frequency doubled1560 nm distributed feedback diode laser locked to a rubidium D2 saturated absorption line without using an optical amplifier was demonstrated, and dithering-free optical output was obtained. In addition, the sensitivity of the developed optical frequency standard to magnetic fields was investigated. We confirmed that the influence of the magnetic fields on the optical frequency standard can be almost negligible when using appropriate magnetic-shield films. As a result, the magnetic-field-insensitive optical frequency standard, which can be embedded in optical systems,exhibiting uncertainty less than at least 100 kHz, was successfully realized for the first time to the best of our knowledge.
4. Optical frequency standard by using a 1560 nm diode laser locked to saturated absorption lines of rubidium vapor.
PubMed
Masuda, Shin; Seki, Atsushi; Niki, Shoji
2007-07-20
A robust, compact, highly accurate rubidium optical frequency standard module was developed to overcome the delicate performance of conventional frequency stabilized lasers. A frequency doubled 1560 nm distributed feedback diode laser locked to a rubidium D(2) saturated absorption line without using an optical amplifier was demonstrated, and dithering-free optical output was obtained. In addition, the sensitivity of the developed optical frequency standard to magnetic fields was investigated. We confirmed that the influence of the magnetic fields on the optical frequency standard can be almost negligible when using appropriate magnetic-shield films. As a result, the magnetic-field-insensitive optical frequency standard, which can be embedded in optical systems, exhibiting uncertainty less than at least 100 kHz, was successfully realized for the first time to the best of our knowledge. PMID:17609727
5. Estimation of Fracture Toughness of Anisotropic Rocks by Semi-Circular Bend (SCB) Tests Under Water Vapor Pressure
Kataoka, M.; Obara, Y.; Kuruppu, M.
2015-07-01
In order to investigate the influence of water vapor pressure in the surrounding environment on mode I fracture toughness ( K Ic) of rocks, semi-circular bend (SCB) tests under various water vapor pressures were conducted. Water vapor is one of the most effective agents which promote stress corrosion of rocks. The range of water vapor pressure used was 10-2 to 103 Pa, and two anisotropic rock types, African granodiorite and Korean granite, were used in this work. The measurement of elastic wave velocity and observation of thin sections of these rocks were performed to investigate the microstructures of the rocks. It was found that the distribution of inherent microcracks and grains have a preferred orientation. Two types of specimens in different orientations, namely Type-1 and Type-3, were prepared based on the anisotropy identified by the differences in the elastic wave velocity. K Ic of both rock types was dependent on the water vapor pressure in the surrounding environment and decreased with increasing water vapor pressure. It was found that the degree of the dependence is influenced by the orientation and density of inherent microcracks. The experimental results also showed that K Ic depended on the material anisotropy. A fracture process was discussed on the basis of the geometry of fractures within fractured specimens visualized by the X-ray computed tomography (CT) method. It was concluded that the dominant factor causing the anisotropy of K Ic is the distribution of grains rather than inherent microcracks in these rocks.
6. The control of purity and stoichiometry of compound semiconductors by high vapor pressure transport
NASA Technical Reports Server (NTRS)
Bachmann, Klaus J.; Ito, Kazufumi; Scroggs, Jeffery S.; Tran, Hien T.
1995-01-01
In this report we summarize the results of a three year research program on high pressure vapor transport (HPVT) of compound semiconductors. Most of our work focused onto pnictides, in particular ZnGeP2, as a model system. Access to single crystals of well controlled composition of this material is desired for advancing the understanding and control of its point defect chemistry in the contest of remote, real-time sensing of trace impurities, e.g., greenhouse gases, in the atmosphere by ZnGeP2 optical parametric oscillators (OPO's).
7. Track studies in water vapor using a low-pressure cloud chamber. II. Microdosimetric measurements.
PubMed
Stonell, G P; Marshall, M; Simmons, J A
1993-12-01
A low-pressure cloud chamber has been adapted to operate with pure water vapor. Photographs were obtained of tracks arising from the passage of ionizing radiation. The sources used were low-energy X rays, 242Cm alpha particles, and low-energy protons. Distributions of lineal energy, radial distances around an ion track, and interdroplet distances were measured and compared with the predictions of Monte Carlo calculations. After allowing for diffusion and the limitations of the geometry of the system, the measured and calculated distributions were found to be in good agreement. PMID:8278576
8. Solubility parameter and activity coefficient of HDEHP dimer in select organic diluents by vapor pressure osmometry
SciTech Connect
Gray, M.; Nilsson, M.; Zalupski, P.
2013-07-01
A thorough understanding of the non-ideal behavior of the chemical components utilized in solvent extraction contributes to the success of any large-scale spent nuclear fuel treatment. To address this, our current work uses vapor pressure osmometry to characterize the non-ideal behavior of the solvent extraction agent di-(2-ethylhexyl) phosphoric acid (HDEHP), a common extractant in proposed separation schemes. Solubility parameters were fit to data on HDEHP at four temperatures using models based on Scatchard Hildebrand regular solution theory with Flory Huggins entropic corrections. The results are comparable but not identical to the activity coefficients from prior slope analysis in the literature. (authors)
9. Detection and measurement of sulfur mustard (HD) offgassing from the weanling pig following exposure to saturated HD vapor. Technical report, September-October 1994
SciTech Connect
Logan, T.P.; Graham, J.S.; Martin, J.L.; Zallnick, J.E.; Jakubowski, E.M.
1997-11-01
Sulfur mustard (HD) is a chemical warfare agent for which there is neither antidote nor adequate therapeutic protection. Animal models are employed to investigate mechanisms of injury and to evaluate protective measures against HD exposure. Researchers whose experiments involve cutaneous application of HD vapor to animals benefit from the detection and quantitation of HD at the exposed site. The ability to detect and quantify HD enables the researcher to follow safe procedures in handling skin samples. We have designed an experimental procedure to measure HD offgassing from animal models. A Minicams(R), which is a portable gas chromatograph (GC) equipped with a flame photometric detector (FPD) and with online sorbent collection and desorption, was used to monitor the HD concentration. Confirming measurements were made using a two-step process that trapped HD on a Tenax sorbent offline and then transferred the sample by means of an ACEM 900 to a OC equipped with either FPD or a mass spectrometer (MS). We collected data from six experiments in which weanling pigs were exposed to saturated HD vapor via vapor caps containing 10 micro of HD. HD concentration was measured in time-weighted-average (TWA) units at a specific HD application site. The currently recommended exposure value for HD is 3 ng/l, 1 TWA unit. In five of the six experiments, Minicams HD concentration values were less than 0.5 TWA, 2 hours postexposure, and in one of the experiments, TWA Minicams concentration was less than 0.5 TWA, 5 hours post-exposure. OCIMS detection was used in three of the experiments to confirm Minicams data and to provide greater sensitivity and selectivity at 0.1 TWA. GC/MS data confirmed that HD concentrations fell below 0.1 TWA in less than S hours for a specific site.
10. Comparative analysis of deuterium ions implanted and deuterium atoms saturated at high pressure in pure pd and Pd diluted alloys
Didyk, A. Yu.; Kulikauskas, V. S.; Wiśniewski, R.; Wilczynska, T.; Kitowski, K.
2012-01-01
Pd and its diluted alloys (Pd-Ag, Pd-Pt, Pd-Ru, Pd-Rh) were implanted by 25 keV deuterium ions at a fluence interval of (1.2-2.3) × 1022 m-2. The same property alloys were saturated by deuterium atoms using high pressure chamber during long period with temperature stabilization and electrical resistance measurement of standard Pd wire. The post-treatment depth distributions of deuterium and accompanied hydrogen atoms were measured immediately after implantation (ten days) and after definite time period (three months) after saturation with the usage of elastic recoil detection analysis (ERDA). After two months, the measurements were repeated. The comparison of obtained results in both series of studies allowed one to make an important observation of a relative stability of deuterium and hydrogen atoms in pure Pd and its diluted alloys.
11. A vapor-pressure study of the systems formed by polonium with palladium and iridium
SciTech Connect
Abakumou, A.S.; Khokhlou, A.D.; Malysheu, M.L.; Reznikova, N.F.
1985-11-01
Direct thermal vacuum synthesis shows that polonium vapor does not react with iridium when they are heated together to 1000/sup 0/C. Polonium vapor begins to be absorbed appreciably by palladium at 340-350/sup 0/C. The radiotensimetric method has been used in examining the thermal stabilities of polonium-palladium comounds, which has shown that there are three intermetallides PdPo, Pd/sub 2/Po, and Pd/sub 3/Po, which dissociate to release elemental polonium. The dissociation temperature increases as the polonium content of the compound decreases and is in the range 390-700/sup 0/C. The temperature dependence of the polonium vapor pressure in the dissociation is described by the following: PdPo log P /SUB Pa/ = (7.31 + or - 0.08) -- (4520 + or -40)/T, and at 460580/sup 0/C, ..delta..H = 86.3 + or - 0.7 kJ/mol; Pd/sub 2/Po log P /SUB Pa/ = (7.42 + or - 0.01) -- (6080 + or 10)/T at 725900/sup 0/C, ..delta..H = 116 + or - 0.2 kJ/mol; Pd/sub 3/Po log P /SUB Pa/ = (9.18 + or - 0.01) -- (8620 + or 1000/sup 0/C, ..delta..H = 164 + or - 1 kJ/mol. The properties of these compounds are compared with those of the corresponding tellurides and of the polonium-nickel and poloniumplatinum systems.
12. Vapors and Droplets Mixture Deposition of Metallic Coatings by Very Low Pressure Plasma Spraying
Vautherin, B.; Planche, M.-P.; Bolot, R.; Quet, A.; Bianchi, L.; Montavon, G.
2014-04-01
In recent years, the very low pressure plasma-spraying (VLPPS) process has been intensely developed and implemented to manufacture thin, dense and finely structured ceramic coatings for various applications, such as Y2O3 for diffusion barriers, among other examples. This paper aims at presenting developments carried out on metallic coatings. Aluminum was chosen as a demonstrative material due to its "moderate" vaporization enthalpy (i.e., 38.23 KJ cm-3) compared to the one of copper (i.e., 55.33 KJ cm-3), cobalt (i.e., 75.03 KJ cm-3), or even tantalum (i.e., 87.18 KJ cm-3). The objective of this work is primarily to better understand the behavior of a solid precursor injected into the plasma jet leading to the formation of vapors and to better control the factors affecting the coating structure. Nearly dense aluminum coatings were successfully deposited by VLPPS at 100 Pa with an intermediate power plasma torch (i.e., Sulzer Metco F4 type gun with maximum power of 45 kW). Optical emission spectroscopy (OES) was implemented to study and analyze the vapor behavior into the plasma jet. Simplified CFD modeling allowed better understanding of some of the thermo-physical mechanisms. The effect of powder-size distribution, substrate temperature and spray distance were studied. The phase composition and microstructural features of the coatings were characterized by XRD and SEM. Moreover, Vickers microhardness measurements were implemented.
13. Laser scattering diagnostics of an argon atmospheric-pressure plasma jet in contact with vaporized water
Seo, B. H.; Kim, J. H.; You, S. J.; Seong, D. J.
2015-12-01
The radial profiles of the electron density, electron temperature, and molecular rotational temperature are investigated in an argon atmospheric-pressure plasma jet in contact with vaporized water, which is driven by a 13.56 MHz radio frequency by means of the Thomson and Raman laser scattering methods. There is a distinct difference in the radial profiles of the plasma parameters between plasmas in contact with water and those without water contact. In the case of plasmas without vaporized water contact, all the parameters have a single-peak distribution with maximum values at the center of the discharge. In the case of plasmas in contact with vaporized water, all parameters have double-peak distributions; a neighboring peak appears beside the main peak. The new peak may have originated from the ripple of the water surface, which works as a cathode, and the peak of the ripple offers a sharp curvature point, playing the role of a pin. Our experimental results and the underlying physics are described in detail.
14. Vapor pressures and heats of vaporization of primary coal tars. Quarterly technical progress report, 1 October 1993--31 December 1993
SciTech Connect
Suuberg, E.M.
1993-12-31
The vapor pressure correlations that exist at present for coal tars are very crude and they are not considered reliable to even an order of magnitude when applied to tars. Sophisticated general correlative approaches are slowly being developed, based upon group contribution methods, or based upon some key functional features of the molecules. These are as yet difficult to apply to coal tars. The detailed group contribution methods, in which fairly precise structural information is needed, do not lend themselves well for application to very complex, poorly characterized coal tars. The methods based upon more global types of characterizations have not yet dealt much with the question of oxygenated functional groups. In short, only very limited correlations exist, and these are not considered reliable to even an order of magnitude when applied to tars. The present project seeks to address this important gap in the near term by direct measurement of vapor pressures of coal tar fractions, by application of well-established techniques and modifications thereof. The principal objectives of the program are to: (1) obtain data on the vapor pressures and heats of vaporization of tars from a range of ranks of coal, (2) develop correlations based on a minimum set of conveniently measurable characteristics of the tars, (3) develop equipment that would allow performing such measurements in a reliable, straightforward fashion.
15. Vapor pressures and heats of vaporization of primary coal tars. Quarterly technical progress report, 1 July 1993--30 September 1993
SciTech Connect
Suuberg, E.M.; Oja, V.; Lilly, W.D.
1993-12-31
There is significant current interest in general area of coal pyrolysis, particularly with respect to comprehensive models of this complicated phenomenon. This interest derives from the central role of pyrolysis in all thermally driven coal conversion processes -- gasification, combustion, liquefaction, mild gasification, or thermal benefication. There remain several key data needs in these application areas. Among them is a need for more reliable correlation for prediction of vapor pressure of heavy, primary coal tars. Such information is important in design of all coal conversion processes, in which the volatility of tarry products is of major concern. Only very limited correlations exist, and these are not considered reliable to even an order of magnitude when applied to tars. The present project seeks to address this important gap in the near term by direct measurement of vapor pressures of coal tar fractions, by application of well-established techniques and modifications thereof. The principal objectives of the program are to: (1) obtain data on the vapor pressures and heats of vaporization of tars from a range of ranks of coal, (2) develop correlations based on a minimum set of conveniently measurable characteristics of the tars, (3) develop equipment that would allow performing such measurements in a reliable, straightforward fashion. Results of the literature survey are compiled. The experimental tasks have been concerned with setup and calibration.
16. The Vapor Pressure of 1-(2,2,3,3-Tetrafluoropropoxy)-3-(4-sec-butylphenoxy)-2-prop anol
SciTech Connect
Steele, W.V.
2002-01-29
The vapor pressure of the compound 1-(2,2,3,3-tetrafluoropropoxy)-3-(4-sec-butylphenoxy)-2-propanol was measured over the temperature range 62 to 92 C using a Knudsen effusion technique. This compound, known as Cs-7SB, is the modifier component in the caustic-side solvent extraction process solvent. The vapor pressure is related to temperature by the equation ln(p/Pa) = (32.202 {+-} 0.265) - (12154 {+-} 93)/T, where p is the pressure, expressed in pascals; Pa is the reference pressure of 1 pascal; and T is the temperature, expressed in degrees kelvin. The derived heat of vaporization is 101.1 {+-} 0.8{sup kJ{center_dot}mol{sup 1} at 351 K. Because the vapor pressures over the temperature range of 15 to 50 C were lower than the design capabilities of the Knudsen effusion apparatus, the vapor pressures at these temperature limits were obtained by extrapolation. The estimated values are 4.6 {+-} 0.3E-05 (3.5 {+-} 0.2E-07 mm Hg) and 4.5 {+-} 0.1E-03 Pa (3.4 {+-} 0.1E-05 mm Hg) for 15 C and 50 C, respectively.
17. Vapor pressure data for potassium carbonate-potassium bicarbonate solutions for application to multiuse power cycles
Hosler, E. R.; Ghandeharioun, S.
A novel method of generating electric power based on a gas absorption cycle, rather than a normal Rankine steam power cycle, has been developed. This cycle uses carbon dioxide as the working fluid in the turbine and potassium carbonate solutions as the carrier fluid for the absorption part of the cycle. Thermodynamic calculations for typical operating parameters show a cycle efficiency of about 30 percent compared to a Carnot efficiency of about 40 percent and a Rankine cycle efficiency of about 20 percent for the same temperature limits. Thus, the cycle offers a significant thermal efficiency advantage compared to a Rankine cycle. Vapor pressure data have been obtained for various carrier solution concentrations in the high temperature, high pressure region where no previous data existed. This paper summarized these data. The data support the hypothesis that the gas absorption power cycle offers thermal efficiency benefits compared to a conventional steam power cycle.
18. Atmospheric Pressure Plasma Enhanced Chemical Vapor Deposition of Borophosphosilicate Glass Films
Yin, Minghui; Zhao, Lingli; Xu, Xiangyu; Wang, Shouguo
2008-03-01
Borophosphosilicate glass (BPSG) films have been grown on silicon wafers by plasma enhanced chemical vapor deposition at atmospheric pressure (AP-PECVD). Tetraethoxysilane (TEOS), triethylborate (TEB), and trimethylphosphite (TMPI) were adopted as precursors, and argon and oxygen were respectively used as the carrier and reactive gases to produce stable plasma at atmospheric pressure. Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), and refractive index and stress measurements were employed to characterize BPSG films. The effects of input radio-frequency (RF) power and precursor (TEB and TMPI) flow rate on deposition rate were studied. Results indicated that the deposition rate of BPSG films increases with increasing input RF power and precursor flow rate. In addition, reactive gaseous species were detected by optical emission spectroscopy to reveal the possible reaction process of BPSG film deposition.
19. Pressure drop in fully developed, turbulent, liquid-vapor annular flows in zero gravity
NASA Technical Reports Server (NTRS)
Sridhar, K. R.; Chao, B. T.; Soo, S. L.
1992-01-01
The prediction of frictional pressure drop in fully developed, turbulent, annular liquid-vapor flows in zero gravity using simulation experiments conducted on earth is described. The scheme extends the authors' earlier work on dispersed flows. The simulation experiments used two immiscible liquids of identical density, namely, water and n-butyl benzoate. Because of the lack of rigorous analytical models for turbulent, annular flows, the proposed scheme resorts to existing semiempirical correlations. Results based on two different correlations are presented and compared. Others may be used. It was shown that, for both dispersed and annular flow regimes, the predicted frictional pressure gradients in 0-g are lower than those in 1-g under otherwise identical conditions. The physical basis for this finding is given.
20. 46 CFR 154.1836 - Vapor venting as a means of cargo tank pressure and temperature control.
Code of Federal Regulations, 2010 CFR
2010-10-01
... temperature control. 154.1836 Section 154.1836 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY... LIQUEFIED GASES Operations § 154.1836 Vapor venting as a means of cargo tank pressure and temperature... cargo pressure and temperature control system under §§ 154.701 through 154.709 is operating and...
1. 46 CFR 154.1836 - Vapor venting as a means of cargo tank pressure and temperature control.
Code of Federal Regulations, 2014 CFR
2014-10-01
... temperature control. 154.1836 Section 154.1836 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY... LIQUEFIED GASES Operations § 154.1836 Vapor venting as a means of cargo tank pressure and temperature... cargo pressure and temperature control system under §§ 154.701 through 154.709 is operating and...
2. 46 CFR 154.1836 - Vapor venting as a means of cargo tank pressure and temperature control.
Code of Federal Regulations, 2013 CFR
2013-10-01
... temperature control. 154.1836 Section 154.1836 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY... LIQUEFIED GASES Operations § 154.1836 Vapor venting as a means of cargo tank pressure and temperature... cargo pressure and temperature control system under §§ 154.701 through 154.709 is operating and...
3. 46 CFR 154.1836 - Vapor venting as a means of cargo tank pressure and temperature control.
Code of Federal Regulations, 2012 CFR
2012-10-01
... temperature control. 154.1836 Section 154.1836 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY... LIQUEFIED GASES Operations § 154.1836 Vapor venting as a means of cargo tank pressure and temperature... cargo pressure and temperature control system under §§ 154.701 through 154.709 is operating and...
4. 46 CFR 154.1836 - Vapor venting as a means of cargo tank pressure and temperature control.
Code of Federal Regulations, 2011 CFR
2011-10-01
... temperature control. 154.1836 Section 154.1836 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY... LIQUEFIED GASES Operations § 154.1836 Vapor venting as a means of cargo tank pressure and temperature... cargo pressure and temperature control system under §§ 154.701 through 154.709 is operating and...
5. Vapor pressures, thermodynamic stability, and fluorescence properties of three 2,6-alkyl naphthalenes.
PubMed
Santos, Ana Filipa L O M; Oliveira, Juliana A S A; Ribeiro da Silva, Maria D M C; Monte, Manuel J S
2016-03-01
This work reports the experimental determination of relevant thermodynamic properties and the characterization of luminescence properties of the following polycyclic aromatic hydrocarbons (PAHs): 2,6-diethylnaphthalene, 2,6-diisopropylnaphthalene and 2,6-di-tert-butylnaphthalene. The standard (p(o) = 0.1 MPa) molar enthalpies of combustion, ΔcHm(o), of the three compounds were determined using static bomb combustion calorimetry. The vapor pressures of the crystalline phase of 2,6-diisopropylnaphthalene and 2,6-di-tert-butylnaphthalene were measured at different temperatures using the Knudsen effusion method and the vapor pressures of both liquid and crystalline phases of 2,6-diethylnaphthalene were measured by means of a static method. The temperatures and the molar enthalpies of fusion of the three compounds were determined using differential scanning calorimetry. The gas-phase molar heat capacities and absolute entropies of the three 2,6-dialkylnaphthalenes studied were determined computationally. The thermodynamic stability of the compounds in both the crystalline and gaseous phases was evaluated by the determination of the Gibbs energies of formation and compared with the ones reported in the literature for 2,6-dimethylnaphthalene. From fluorescence spectroscopy measurements, the optical properties of the compounds studied and of naphthalene were evaluated in solution and in the solid state. PMID:26716880
6. Fungicide volatilization measurements: inverse modeling, role of vapor pressure, and state of foliar residue.
PubMed
Bedos, Carole; Rousseau-Djabri, Marie-France; Loubet, Benjamin; Durand, Brigitte; Flura, Dominique; Briand, Olivier; Barriuso, Enrique
2010-04-01
Few data sets of pesticide volatilization from plants at the field scale are available. In this work, we report measurements of fenpropidin and chlorothalonil volatilization on a wheat field using the aerodynamic gradient (AG) method and an inverse dispersion modeling approach (using the FIDES model). Other data necessary to run volatilization models are also reported: measured application dose, crop interception, plant foliage residue, upwind concentrations, and meteorological conditions. The comparison of the AG and inverse modeling methods proved the latter to be reliable and hence suitable for estimating volatilization rates with minimized costs. Different diurnal/nocturnal volatilization patterns were observed: fenpropidin volatilization peaked on the application day and then decreased dramatically, while chlorothalonil volatilization remained fairly stable over a week-long period. Cumulated emissions after 31 h reached 3.5 g ha(-1) and 5 g ha(-1), respectively (0.8% and 0.6% of the theoretical application dose). A larger difference in volatilization rates was expected given differences in vapor pressure, and for fenpropidin, volatilization should have continued given that 80% of the initial amount remained on plant foliage for 6 days. We thus ask if vapor pressure alone can accurately estimate volatilization just after application and then question the state of foliar residue. We identified adsorption, formulation, and extraction techniques as relevant explanations. PMID:20199019
7. Predicting temperature-dependent solid vapor pressures of explosives and related compounds using a quantum mechanical continuum solvation model.
PubMed
Alnemrat, Sufian; Hooper, Joseph P
2013-03-01
Temperature-dependent vapor pressures of solid explosives and their byproducts are calculated to an accuracy of 0.32 log units using a modified form of the conductor-like screening model for real solvents (COSMO-RS). Accurate predictions for solids within COSMO-RS require correction for the free energy of fusion as well as other effects such as van der Waals interactions. Limited experimental data on explosives is available to determine these corrections, and thus we have extended the COSMO-RS model by introducing a quantitative structure-property relationship to estimate a lumped correction factor using only information from standard quantum chemistry calculations. This modification improves the COSMO-RS estimate of ambient vapor pressure by more than 1 order of magnitude for a range of nitrogen-rich explosives and their derivatives, bringing the theoretical predictions to within typical experimental error bars for vapor pressure measurements. The estimated temperature dependence of these vapor pressures also agrees well with available experimental data, which is particularly important for estimating environmental transport and gas evolution for buried explosives or environmentally contaminated locations. This technique is then used to predict vapor pressures for a number of explosives and degradation products for which experimental data is not readily available. PMID:23398143
8. The Vapor Pressure of Environmentally Significant Organic Chemicals: A Review of Methods and Data at Ambient Temperature
Delle Site, Alessandro
1997-01-01
The experimental techniques and the prediction procedures for the determination or evaluation of the vapor pressure of environmentally relevant organic compounds are described; with 259 references examined. For each of them the characteristics of precision and accuracy are given, when available from the literature. The experimental methods are classified as "direct" and "indirect." The first class includes all those which can measure directly the vapor pressure, while the second concerns those which need "known" vapor pressures of reference compounds for the calibration. Prediction methods are based on the application of the Clapeyron-Clausius equation or on the quantitative structure-property relationships. Also correlation methods require a suitable calibration. The vapor pressures at ambient temperature for several polycyclic aromatic hydrocarbons, polychlorinated biphenyls, polychlorinated dibenzo-p-dioxins and furans, selected pesticides, and some reference compounds are tabulated together with the vapor pressure equations and the enthalpy values in the temperature range of measurement. A critical comparison, based on a statistical analysis of the data obtained with different methods and derived from 152 references, is also carried out.
9. A unified equation for calculating methane vapor pressures in the CH4-H2O system with measured Raman shifts
USGS Publications Warehouse
Lu, W.; Chou, I.-Ming; Burruss, R.C.; Song, Y.
2007-01-01
A unified equation has been derived by using all available data for calculating methane vapor pressures with measured Raman shifts of C-H symmetric stretching band (??1) in the vapor phase of sample fluids near room temperature. This equation eliminates discrepancies among the existing data sets and can be applied at any Raman laboratory. Raman shifts of C-H symmetric stretching band of methane in the vapor phase of CH4-H2O mixtures prepared in a high-pressure optical cell were also measured at temperatures between room temperature and 200 ??C, and pressures up to 37 MPa. The results show that the CH4 ??1 band position shifts to higher wavenumber as temperature increases. We also demonstrated that this Raman band shift is a simple function of methane vapor density, and, therefore, when combined with equation of state of methane, methane vapor pressures in the sample fluids at elevated temperatures can be calculated from measured Raman peak positions. This method can be applied to determine the pressure of CH4-bearing systems, such as methane-rich fluid inclusions from sedimentary basins or experimental fluids in hydrothermal diamond-anvil cell or other types of optical cell. ?? 2007 Elsevier Ltd. All rights reserved.
10. Pressure-driven gas flow in heated, partially-saturated porous media
SciTech Connect
Dodge, F.T.; Green, R.T.
1994-12-31
Calculations have been made at the Center for Nuclear Waste Regulatory Analyses (CNWRA) to assess the importance of the various driving mechanisms of heat and mass transport at a high-level nuclear waste (HLW) repository located in the unsaturated zone. Scoping measurements of the relative importance of vapor movement by buoyancy forces and by advective forces have been made for a proposed laboratory-scale experiment to be conducted at CNWRA and for a proposed field-scale heater experiment by U.S. Department of Energy (DOE) at Fran Ridge. These scoping measurements are made using a set of dimensionless terms assembled for this analysis. Numerical simulations of the same laboratory- and field-scale experiments are made using VTOUGH. These calculations will be used to predict (and design in the case of the laboratory-scale experiment) the redistribution of moisture in response to the imposition of heat on the two experiments.
11. Influence of Pore-Fluid Pressure on Elastic Wave Velocity and Electrical Conductivity in Water-Saturated Rocks
Higuchi, A.; Watanabe, T.
2013-12-01
Pore-fluid pressure in seismogenic zones can play a key role in the occurrence of earthquakes (e.g., Sibson, 2009). Its evaluation via geophysical observations can lead to a good understanding of seismic activities. The evaluation requires a thorough understanding of the influence of the pore-fluid pressure on geophysical observables like seismic velocity and electrical conductivity. We have studied the influence of pore-fluid pressure on elastic wave velocity and electrical conductivity in water-saturated rocks. Fine grained (100-500?m) biotite granite (Aji, Kagawa pref., Japan) was used as rock samples. The density is 2.658-2.668 g/cm3, and the porosity 0.68-0.87%. The sample is composed of 52.8% plagioclase, 36.0% Quartz, 3.0% K-feldspar, 8.2% biotite. SEM images show that a lot of grain boundaries are open. Few intracrystalline cracks were observed. Following the method proposed by David and Zimmerman (2012), the distribution function of crack aspect ratio was evaluated from the pressure dependence of compressional and shear wave velocities in a dry sample. Cylindrical sample has dimensions of 25 mm in diameter and 30 mm in length, and saturated with 0.01 mol/l KCl aqueous solution. Compressional and shear wave velocities were measured with the pulse transmission technique (PZT transducers, f=2 MHz), and electrical conductivity the two-electrode method (Ag-AgCl electrodes, f=1 Hz-100 kHz). Simultaneous measurements of velocities and conductivity were made using a 200 MPa hydrostatic pressure vessel, in which confining and pore-fluid pressures can be separately controlled. The pore-fluid is electrically insulated from the metal work of the pressure vessel by using a newly designed plastic device (Watanabe and Higuchi, 2013). The confining pressure was progressively increased up to 25 MPa, while the pore-fluid pressure was kept at 0.1 MPa. It took five days or longer for the electrical conductivity to become stationary after increasing the confining pressure. Elastic wave velocities and electrical conductivity showed reproducibly contrasting changes for a small increase in the confining pressure. The elastic wave velocities increased only by 5% as the confining pressure increased from 0.1 MPa to 25 MPa, while the electrical conductivity decreased by an order of magnitude. Based on the SEM examinations, open grain boundaries work as cracks. The changes in elastic wave velocities and electrical conductivity must be caused by the closure of open grain boundaries. Most (80%) of the decrease in electrical conductivity occurred below the confining pressure of 5 MPa. As the confining pressure increased from 0.1 MPa to 5 MPa, cracks with the aspect ratio smaller than 7.510-5 were closed. The decrease in porosity was only 0.0005%. Such a small change in porosity caused a large change in electrical conductivity. The connectivity of fluid was maintained at the confining pressure of 25 MPa by cracks with the aspect ratio larger than 3.710-4. Simultaneous measurements have provided us a lot of information on the microstructure of fluid-bearing rocks.
12. Atmospheric pressure synthesis of photoluminescent hybrid materials by sequential organometallic vapor infiltration into polyethylene terephthalate fibers
SciTech Connect
Akyildiz, Halil I.; Mousa, Moataz Bellah M.; Jur, Jesse S.
2015-01-28
Exposing a polymer to sequential organometallic vapor infiltration (SVI) under low pressure conditions can significantly modify the polymer's chemical, mechanical, and optical properties. We demonstrate that SVI of trimethylaluminum into polyethylene terephthalate (PET) can also proceed readily at atmospheric pressure, and at 60 °C the extent of reaction determined by mass uptake is independent of pressure between 2.5 Torr and 760 Torr. At 120 °C, however, the mass gain is 50% larger at 2.5 Torr relative to that at 760 Torr, indicating that the precursor diffusion in the chamber and fiber matrix decreases at higher source pressure. Mass gain decreases, in general, as the SVI process temperature increases both at 2.5 Torr and 760 Torr attributed to the faster reaction kinetics forming a barrier layer, which prevents further diffusion of the reactive species. The resulting PET/Al-O{sub x} product shows high photoluminescence compared to untreated fibers. A physical mask on the polymer during infiltration at 760 Torr is replicated in the underlying polymer, producing an image in the polymer that is visible under UV illumination. Because of the reduced precursor diffusivity during exposure at 760 Torr, the image shows improved resolution compared to SVI performed under typical 2.5 Torr conditions.
13. Atmospheric pressure synthesis of photoluminescent hybrid materials by sequential organometallic vapor infiltration into polyethylene terephthalate fibers
Akyildiz, Halil I.; Mousa, Moataz Bellah M.; Jur, Jesse S.
2015-01-01
Exposing a polymer to sequential organometallic vapor infiltration (SVI) under low pressure conditions can significantly modify the polymer's chemical, mechanical, and optical properties. We demonstrate that SVI of trimethylaluminum into polyethylene terephthalate (PET) can also proceed readily at atmospheric pressure, and at 60 °C the extent of reaction determined by mass uptake is independent of pressure between 2.5 Torr and 760 Torr. At 120 °C, however, the mass gain is 50% larger at 2.5 Torr relative to that at 760 Torr, indicating that the precursor diffusion in the chamber and fiber matrix decreases at higher source pressure. Mass gain decreases, in general, as the SVI process temperature increases both at 2.5 Torr and 760 Torr attributed to the faster reaction kinetics forming a barrier layer, which prevents further diffusion of the reactive species. The resulting PET/Al-Ox product shows high photoluminescence compared to untreated fibers. A physical mask on the polymer during infiltration at 760 Torr is replicated in the underlying polymer, producing an image in the polymer that is visible under UV illumination. Because of the reduced precursor diffusivity during exposure at 760 Torr, the image shows improved resolution compared to SVI performed under typical 2.5 Torr conditions.
14. CO(2) partial pressure and calcite saturation in springs - useful data for identifying infiltration areas in mountainous environments.
PubMed
Hilberg, Sylke; Brandsttter, Jennifer; Glck, Daniel
2013-04-01
Mountainous regions such as the Central European Alps host considerable karstified or fractured groundwater bodies, which meet many of the demands concerning drinking water supply, hydropower or agriculture. Alpine hydrogeologists are required to describe the dynamics in fractured aquifers in order to assess potential impacts of human activities on water budget and quality. Delineation of catchment areas by means of stable isotopes and hydrochemical data is a well established method in alpine hydrogeology. To achieve reliable results, time series of (at least) one year and spatial and temporal close-meshed data are necessary. In reality, test sites in mountainous regions are often inaccessible due to the danger of avalanches in winter. The aim of our work was to assess a method based on the processes within the carbonic acid system to delineate infiltration areas by means of single datasets consisting of the main hydrochemical parameters of each spring. In three geologically different mountainous environments we managed to classify the investigated springs into four groups. (1) High PCO2 combined with slight super-saturation in calcite, indicating relatively low infiltration areas. (2) Low PCO2 near atmospheric conditions in combination with calcite saturation, which is indicative of relatively high infiltration areas and a fractured aquifer which is not covered by topsoil layers. (3) High PCO2 in combination with sub-saturation in calcite, representing a shallow aquifer with a significant influence of the topsoil layer. (4) The fourth group of waters is characterized by low PCO2 and sub-saturation in calcite, which is interpreted as evidence for a shallow aquifer without significant influence of any hard rock aquifer or topsoil layer. This study shows that CO2-partial pressure can be an ideal natural tracer to estimate the elevation of infiltration areas, especially in non-karstified fractured groundwater bodies. PMID:23429574
15. D0 Silicon Upgrade: Vapor Pressure Thermometry System Near LN2 Subcooler
SciTech Connect
Kuwazaki, Andrew; /Fermilab
1996-07-01
Fermi National Accelerator Laboratory (Fermilab) is in the process of upgrading its detectors. Among these upgrades is the need for more transfer lines containing both liquid nitrogen and helium gas. These two fluids are used to provide the necessary operating cryogenic temperatures for the various detectors, such as the Visible Light Photon Counter (VLPC) and the solenoid inside the detector's calorimeter. With additional piping, it is important to monitor the temperatures to assure that the detectors can operate correctly. This can be done two ways. The first method is to use a Resistance Temperature Device, called a RTD, which is made using either a carbon resistor or a platinum resistor and measures the temperature based on resistance. The second method is to use a vapor-pressure thermometry system. This design will focus on the second method. A nitrogen Vapor Pressure Thermometer (VPT) system is designed to determine the temperature of the liquid nitrogen (LN{sub 2}) supply line, after exiting the LN{sub 2} subcooler, inside the D-Zero Assembly Hall. The operating temperature range is designed from 77 to 300 Kelvin with an initial charge pressure of 100 psia. A cylindrical bulb with a 0.1875-inch diameter and 0.625-inch length allows for minimum cold and warm 1/4-inch O.D. SS 304L tubing lengths, 12-inch and 18-inch respectively, and maintains a liquid level of 50% inside the bulb during cold operation. The amount of nitrogen needed to fill the cylindrical bulb approximately half full is 0.149 grams. In order to conform to the conventional cold volume and warm volume VPT systems, we need to enlarge the existing 1/2-inch x 2-inch SCH. 10 LN{sub 2} supply line over a one foot section to 1-inch x 3-inch SCH. 10 piping.
16. Effect of an oxygen pressure injection (OPI) device on the oxygen saturation of patients during dermatological methyl aminolevulinate photodynamic therapy.
PubMed
Blake, E; Allen, J; Thorn, C; Shore, A; Curnow, A
2013-05-01
Methyl aminolevulinate photodynamic therapy (MAL-PDT) (a topical treatment used for a number of precancerous skin conditions) utilizes the combined interaction of a photosensitizer (protoporphyrin IX (PpIX)), light of the appropriate wavelength, and molecular oxygen to produce singlet oxygen and other reactive oxygen species which induce cell death. During treatment, localized oxygen depletion occurs and is thought to contribute to decreased efficacy. The aim of this study was to investigate whether an oxygen pressure injection (OPI) device had an effect on localized oxygen saturation levels and/or PpIX fluorescence of skin lesions during MAL-PDT. This study employed an OPI device to apply oxygen under pressure to the skin lesions of patients undergoing standard MAL-PDT. Optical reflectance spectrometry and fluorescence imaging were used to noninvasively monitor the localized oxygen saturation and PpIX fluorescence of the treatment area, respectively. No significant changes in oxygen saturation were observed when these data were combined for the group with OPI and compared to the group that received standard MAL-PDT without OPI. Additionally, no significant difference in PpIX photobleaching or clinical outcome at 3 months between the groups of patients was observed, although the group that received standard MAL-PDT demonstrated a significant increase (p<0.05) in PpIX fluorescence initially and both groups produced a significant decrease (p<0.05) after light irradiation. In conclusion, with this sample size, this OPI device was not found to be an effective method with which to improve tissue oxygenation during MAL-PDT. Further investigation is therefore required to find a more effective method of MAL-PDT enhancement. PMID:22926533
17. Peripheral oxygen saturation, heart rate, and blood pressure during dental treatment of children with cyanotic congenital heart disease
PubMed Central
Dutra, Rosane Menezes Faria; Neves, Itamara Lucia Itagiba; Neves, Ricardo Simes; Atik, Edmar; de Paula Santos, Ubiratan
2014-01-01
OBJECTIVES: In this observational study, we evaluated the peripheral oxygen saturation (SpO2), heart rate, and blood pressure of children with cyanotic congenital heart disease who were undergoing dental extraction. METHODS: Forty-four patients between the ages of 6 and 12 years who underwent upper primary tooth extraction were included in the study. Of these, 20 patients were in the cyanotic congenital heart disease group and 24 were in the control group. RESULTS: Peripheral oxygen saturation, heart rate, and systolic blood pressure in the cyanotic congenital heart disease group varied quite significantly during the treatment protocol (p<0.05), with values of 80.5% (7.6) to 82.8% (7.8), 95.3 beats per minute (bpm) (11.3) to 101.3 bpm (9.8), and 93.6 mm Hg (13,3) to 103.8 mm Hg (12.7), respectively. The variations in the control group during the procedure were also significant. CONCLUSIONS: The changes observed during the study protocol, although statistically significant, were mild and lacked clinical relevance. The results indicate that dental treatment of children with cyanotic heart disease using a standardized protocol in decentralized offices without the support of a surgical center is safe. PMID:24838895
18. Organic Dye Effects on DNAPL Entry Pressure in Water Saturated Porous Media
SciTech Connect
Iversen, G.M.
2001-10-02
One of three diazo dyes with the same fundamental structure have been used in most studies of DNAPL behavior in porous media to stain the NAPL: Sudan III, Sudan IV, or Oil-Red-O. The dyes are generally implicitly assumed to not influence DNAPL behavior. That assumption was tested using simple entry pressure experiments.
19. The separation and characterization of a hydrogen getter product mixture: Part 2, measurement of product vapor pressures
SciTech Connect
Fircish, D.W.; Shell, T.R.
1987-06-04
HCPB is the acronym of an organic hydrogen getter compound used in weapon systems. When this material scavenges hydrogen by reacting with it, a number of compounds are formed, each of which is more volatile than HCPB. It is desirable to know the vapor pressure of these products in order to assess their migration potential within the weapon. In this study, individual compounds from a reacted HCPB mixture were isolated and their vapor pressures were measured. Three of the four fractions examined with a modified capacitance manometer were found to have vapor pressures under 1 mtorr; the fourth was measured at 92 +- 15 mtorr. An attempt was made to obtain boiling point data on the two liquid components of the getter mixture, but they decomposed before reaching their boiling points.
20. Track studies in water vapor using a low-pressure cloud chamber. I. Macroscopic measurements.
PubMed
Stonell, G P; Marshall, M; Simmons, J A
1993-12-01
Techniques have been developed to operate a low-pressure cloud chamber with pure water vapor. Photographs have been obtained of the tracks arising in this medium from the passage of ionizing radiation. The sources used were low-energy X rays, 242Cm alpha particles, and low-energy protons. Track lengths of the electrons were similar to those found previously in tissue-equivalent gas. W values of 35.6 +/- 0.4 and 32.6 +/- 0.6 eV per ion pair for carbon and aluminum X rays also compare closely with those in tissue-equivalent gas, but are somewhat higher than the predictions of Monte Carlo calculations. Differential w values were obtained: for alpha particles of energy 5.3 MeV the value was 33.0 +/- 3.0 eV per ion pair; for protons of energy 390, 230, and 85 keV the values were 30.6 +/- 1.9, 31.9 +/- 2.0, and 33.6 +/- 3.4 eV per ion pair. The energy losses of protons in water vapor were measured in a second (dummy) chamber used for energy calibration. Results support Janni's values of stopping power for protons in the energy range 40-480 keV. PMID:8278575
1. Germanium determination by flame atomic absorption spectrometry: an increased vapor pressure-chloride generation system.
PubMed
Kaya, Murat; Volkan, Mürvet
2011-03-15
A new chloride generation system was designed for the direct, sensitive, rapid and accurate determination of the total germanium in complex matrices. It was aimed to improve the detection limit of chloride generation technique by increasing the vapor pressure of germanium tetrachloride (GeCl(4)). In order to do so, a novel joint vapor production and gas-liquid separation unit equipped with a home-made oven was incorporated to an ordinary nitrous oxide-acetylene flame atomic absorption spectrometer. Several variables such as reaction time, temperature and acid concentration have been investigated. The linear range for germanium determination was 0.1-10 ng mL(-1) for 1 mL sampling volume with a detection limit (3s) of 0.01 ng mL(-1). The relative standard deviation (RSD) was 2.4% for nine replicates of a 1 ng mL(-1) germanium solution. The method was validated by the analysis of one non-certified and two certified geochemical reference materials, respectively, CRM GSJ-JR-2 (Rhyolite), and GSJ-JR-1 (Rhyolite), and GBW 07107 (Chinese Rock). Selectivity of the method was investigated for Cd(2+), Co(2+), Cu(2+), Fe(3+), Ga(3+), Hg(2+), Ni(2+), Pb(2+), Sn(2+), and Zn(2+) ions and ionic species of As(III), Sb(III), Te(IV), and Se(IV). PMID:21315908
2. Non-canonical mass laws in equilibrium isotopic fractionations: Evidence from the vapor pressure isotope effect of SF6
Eiler, John; Cartigny, Pierre; Hofmann, Amy E.; Piasecki, Alison
2013-04-01
We report experimental observations of the vapor pressure isotope effect, including 33S/32S and 34S/32S ratios, for SF6 ice between 137 and 173 K. The temporal evolution of observed fractionations, mass-balance of reactants and products, and reversal of the fractionation at one temperature (155 K) are consistent with a subset of our experiments having reached or closely approached thermodynamic equilibrium. That equilibrium involves a reversed vapor pressure isotope effect; i.e., vapor is between 2 and 3 higher in 34S/32S than co-existing ice, with the difference increasing with decreasing temperature. At the explored temperatures, the apparent equilibrium fractionation of 33S/32S ratios is 0.551 0.010 times that for 34S/32S ratioshigher than the canonical ratio expected for mass dependent thermodynamic fractionations (0.515). Two experiments examining exchange between adsorbed and vapor SF6 suggest the sorbate-vapor fractionation at 180-188 K is similar to that for ice-vapor at 150 K. In contrast, the liquid-vapor fractionation at 228-300 K is negligibly small (0.1 for 34S/32S; the mass law is ill defined due to the low amplitude of fractionation). We hypothesize that the observed vapor pressure isotope for SF6 ice and sorbate is controlled by commonly understood effects of isotopic substitution on vibrational energies of molecules, but leads to both an exotic mass law and reversed fractionation due to the competition between isotope effects on intramolecular vibrations, which promote heavy isotope enrichment in vapor, and isotope effects on intermolecular (lattice) vibrations, which promote heavy isotope enrichment in ice. This explanation implies that a variety of naturally important compounds having diverse modes of vibration (i.e., varying greatly in frequency and particularly, reduced mass) could potentially exhibit similarly non-canonical mass laws for S and O isotope fractionations. We examined this hypothesis using a density function model of SF6 vapor and lattice dynamic model of SF6(ice). These models support the direction of the measured vapor pressure isotope effect, but do not quantitatively agree with the magnitude of the fractionation and poorly match the phonon spectrum of SF6 ice. A strict test of our hypothesis must await a more sophisticated model of the isotopic dependence of the phonon spectrum of SF6 ice.
3. Atmospheric Pressure Chemical Vapor Deposition of Graphene Using a Liquid Benzene Precursor.
PubMed
Kang, Cheong; Jung, Da Hee; Lee, Jin Seok
2015-11-01
Graphene has attracted great attention owing to its unique structural and electrical properties. Among various synthetic approaches of the graphene, metal assisted chemical vapor deposition (CVD) is the most reasonable and proper method to produce large-scale and low-defect graphene films. Until now, CVD from gaseous hydrocarbon sources has shown great promises for large-scale graphene growth, but high growth temperature is required for such growth. A recent work by using liquid benzene precursor has shown that monolayer graphene could be obtained at 300 degrees C by low pressure, required for high vacuum equipment. Here, we report the first successful attempt of atmospheric pressure CVD graphene growth on Cu foil using liquid benzene as a precursor. We investigated the effect of hydrogen partial pressure, growth time, and precursor temperature on the domain size of as-grown graphene. Also, micro-Raman analysis confirmed that these reaction parameters influenced the number of layer and uniformity of the graphene. PMID:26726650
4. Determining the stable isotope composition of pore water from saturated and unsaturated zone core: improvements to the direct vapor equilibration laser spectroscopy method
Hendry, M. J.; Schmeling, E.; Wassenaar, L. I.; Barbour, S. L.; Pratt, D.
2015-06-01
A method to measure the ?2H and ?18O composition of pore waters in saturated and unsaturated geologic core samples using direct vapor equilibration and laser spectroscopy (DVE-LS) was first described in 2008, and has since been widely adopted by others. Here, we describe a number of important methodological improvements and limitations encountered in routine application of DVE-LS over several years. Generally, good comparative agreement and accuracy is obtained between core pore water isotopic data obtained using DVE-LS and that measured on water squeezed from the same core. In complex hydrogeologic settings, high-resolution DVE-LS depth profiles provide greater spatial resolution of isotopic profiles compared to long-screened or nested piezometers. When fluid is used during drilling and coring (e.g., water rotary or wet sonic drill methods), spiking the drill fluid with 2H can be conducted to identify core contamination. DVE-LS analyses yield accurate formational isotopic data for fine-textured core (e.g., clay, shale) samples, but are less effective for cores obtained from saturated permeable (e.g., sand, gravels) geologic media or on chip samples that are easily contaminated by wet rotary drilling fluid. Data obtained from DVE-LS analyses of core samples collected using wet (contamination by drill water) and dry sonic (water loss by heating) methods were also problematic. Accurate DVE-LS results can be obtained on core samples with gravimetric water contents < 5 % by increasing the sample size tested. Inexpensive Ziploc gas sampling bags were determined to be as good as, if not better, than other, more expensive bags. Sample storage in gas tight sample bags provides acceptable results for up to 10 days of storage; however, measureable water loss and evaporitic isotopic enrichment occurs for samples stored for up to 6 months. With appropriate care taken during sample collection and storage, the DVE-LS approach for obtaining high resolution pore water isotopic data remains a promising alternative to study the hydrogeology of saturated and unsaturated sediments. Eliminating analytical interferences from volatile organics remains a challenge.
5. A search for chemical laser action in low pressure metal vapor flames. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Zwillenberg, M. L.
1975-01-01
Optical emissions were studied from low pressure (approximately 1 torr) dilute diffusion flames of Ca and Mg vapor with O2, N2O and mixtures of CCl4 and O2. The Ca flames with O2 and N2O revealed high vibrational excitation of the product CaO molecule (up to v=30). The flames with CCl4 revealed extreme nonequilibrium metal atom electronic excitation, up to the metal atom ionization limit (6.1 eV for Ca, 7.6 eV for Mg). The metal atom excited electronic state populations did not follow a Boltzmann distribution, but the excitation rates ('pumping rate') were found to obey an Arrhenius-type expression, with the electronic excitation energy playing the role of activation energy and a temperature of about 5000 K for triplet excited states and 2500 K for singlets (vs. approximately 500 K translational temperature).
6. Reid vapor-pressure regulation of gasoline, 1987-1990. Master's thesis
SciTech Connect
Butters, R.A.
1990-09-30
Although it is generally only a summertime problem, smog, as represented by its criteria pollutant, ozone, is currently the number one air pollution problem in the United States. Major contributors to smog formation are the various Volatile Organic Compounds (VOC's) which react with other chemicals in the atmosphere to form the ozone and other harmful chemicals known as smog. Gasoline is a major source of VOC's, not only as it is burned in car engines, but as it evaporates. Gasoline evaporates in storage tanks, as it is transferred during loading and refueling operations, and in automobiles, both while they are running and while parked in the driveway. In 1987, the United States Environmental Protection Agency began an almost unprecedented effort to reduce the evaporative quality of commercial gasolines by mandating reductions in its Reid Vapor Pressure (RVP).
7. Effect of Vapor Pressure Scheme on Multiday Evolution of SOA in an Explicit Model
Lee-Taylor, J.; Madronich, S.; Aumont, B.; Camredon, M.; Emmons, L. K.; Tyndall, G. S.; Valorso, R.
2011-12-01
Recent modeling of the evolution of Secondary Organic Aerosol (SOA) has led to the critically important prediction that SOA mass continues to increase for several days after emission of primary pollutants. This growth of organic aerosol in dispersing plumes originating from urban point sources has direct implications for regional aerosol radiative forcing. We investigate the robustness of predicted SOA mass growth downwind of Mexico City in the model GECKO-A (Generator of Explicit Chemistry and Kinetics of Organics in the Atmosphere), by assessing its sensitivity to the choice of vapor pressure prediction scheme. We also explore the implications for multi-day SOA mass growth of glassification / solidification of SOA constituents during aging. Finally we use output from the MOZART-4 chemical transport model to evaluate our results in the regional and global context.
8. Partial Pressures for Several In-Se Compositions from Optical Absorbance of the Vapor
NASA Technical Reports Server (NTRS)
Brebrick, R. F.; Su, Ching-Hua
2001-01-01
The optical absorbance of the vapor phase over various In-Se compositions between 33.3-60.99 at.% Se and 673-1418 K was measured and used to obtain the partial pressures of Se2(g) and In2Se(g). The results are in agreement with silica Bourdon gauge measurements for compositions between 50-61 at.%, but significantly higher than those from Knudsen cell and simultaneous Knudsen-torsion cell measurements. It is found that 60.99 at.% Se lies outside the sesquiselenide homogeneity range and 59.98 at.% Se lies inside and is the congruently melting composition. The Gibbs energy of formation of the liquid from its pure liquid elements between 1000-1300 K is essentially independent of temperature and falls between -36 to -38 kJ per g atomic weight for 50 and 56% Se at 1200 and 1300 K.
9. Vapor pressure of three brominated flame retardants determined by using the Knudsen effusion method.
PubMed
Fu, Jinxia; Suuberg, Eric M
2012-03-01
Brominated flame retardants (BFRs) have been used in a variety of consumer products in the past four decades. The vapor pressures for three widely used BFRs, that is, tetrabromobisphenol A (TBBPA), hexabromocyclododecane (HBCD), and octabromodiphenyl ethers (octaBDEs) mixtures, were determined using the Knudsen effusion method and compared with those of decabromodiphenyl ether (BDE209). The values measured extrapolated to 298.15?K are 8.47??10??, 7.47??10??, and 2.33??10?? ?Pa, respectively. The enthalpies of sublimation for these BFRs were estimated using the Clausius-Clapeyron equation and are 143.6??0.4, 153.7??3.1, and 150.8??3.2?kJ/mole, respectively. In addition, the enthalpies of fusion and melting temperatures for these BFRs were also measured in the present study. PMID:22213441
10. Diamond synthesis at atmospheric pressure by microwave capillary plasma chemical vapor deposition
Hemawan, Kadek W.; Gou, Huiyang; Hemley, Russell J.
2015-11-01
Polycrystalline diamond has been synthesized on silicon substrates at atmospheric pressure, using a microwave capillary plasma chemical vapor deposition technique. The CH4/Ar plasma was generated inside of quartz capillary tubes using 2.45 GHz microwave excitation without adding H2 into the deposition gas chemistry. Electronically excited species of CN, C2, Ar, N2, CH, H?, and H? were observed in the emission spectra. Raman measurements of deposited material indicate the formation of well-crystallized diamond, as evidenced by the sharp T2g phonon at 1333 cm-1 peak relative to the Raman features of graphitic carbon. Field emission scanning electron microscopy images reveal that, depending on the growth conditions, the carbon microstructures of grown films exhibit "coral" and "cauliflower-like" morphologies or well-facetted diamond crystals with grain sizes ranging from 100 nm to 10 ?m.
11. Net vapor generation point in boiling flow of trichlorotrifluoroethane at high pressures
NASA Technical Reports Server (NTRS)
Dougall, R. S.; Lippert, T. E.
1973-01-01
The conditions at which the void in subcooled boiling starts to undergo a rapid increase were studied experimentally. The experiments were performed in a 12.7 x 9.5 mm rectangular channel. Heating was from a 3.2 mm wide strip embedded in one wall. The pressure ranged from 9.45 to 20.7 bar, mass velocity from 600 to 7000 kg/sq m sec, and subcooling from 16 to 67 C. Photographs were used to determine when detached bubbles first appeared in the bulk flow. Measurements of bubble layer thickness along the wall were also made. Results showed that the point of net vapor generation is close to the occurrence of fully-developed boiling.
12. The Action of Pressure-Radiation Forces on Pulsating Vapor Bubbles
NASA Technical Reports Server (NTRS)
Hao, Y.; Oguz, N.; Prosperetti, A.
2001-01-01
The action of pressure-radiation (or Bjerknes) forces on gas bubbles is well understood. This paper studies the analogous phenomenon for vapor bubbles, about which much less is known. A possible practical application is the removal of boiling bubbles from the neighborhood of a heated surface in the case of a downward facing surface or in the absence of gravity. For this reason, the case of a bubble near a plane rigid surface is considered in detail. It is shown that, when the acoustic wave fronts are parallel to the surface, the bubble remains trapped due to secondary Bjerknes force caused by an "image bubble." When the wave fronts are perpendicular to the surface, on the other hand, the bubble can be made to slide laterally.
13. The Vapor Pressure of Palladium at Temperatures up to 1973K
NASA Technical Reports Server (NTRS)
Gardner, K. G.; Feguson, F. T.; Nuth, J. A.
2005-01-01
Understanding high-temperature processes is imperative for modeling the formation of the solar system. It is unfortunate that since the 1950 s little has been done in the area of thermodynamics to continue gaining information on metals such as iron (Fe), nickel (Ni), cobalt (Co), palladium (Pd) and many others. Although the vapor pressures of these metals can be extrapolated to higher temperatures, the data is often limited to temperature ranges too low to be applicable to processes that occur during the formation of the solar system (T approx. 2000K). Experimental techniques inhibited the data in the past by restricting the testing of metals to temperatures below their melting point. Today, higher temperature testing is possible by using a Thermo- Cahn Thermogravimetric system that is able to reach temperatures up to 1973K in vacuo and measure a 10 gram change in a sample with mass of up to 100 grams.
14. Vapor Pressure Measurement for 4He Films Adsorbed on 2D Mesoporous Hectorite
Asano, Ryota; Toda, Ryo; Matsushita, Yuki; Hieda, Mitsunori; Matsushita, Taku; Wada, Nobuo
2006-09-01
The vapor-pressure measurement for adsorbed films is equivalent to the measurement of the chemical potential. By the measurement of 4He films adsorbed on two-dimensional (2D) mesoporous Hectorite, we obtained the 2D isothermal compressibility, the isosteric heat, and the effective thickness deduced from the FHH model, mainly above a coverage of 15 ?mol/m2. The compressibility shows two dips at n1 = 17.50.5 ?mol/m2 and n2 = 22.70.5 ?mol/m2 which correspond to the first layer completion and appearance of the quantum-Bose-fluid layer, respectively. For the quantum-Bose-fluid layer, the phonon velocity deduced from the compressibility is on the order of 100 m/s, and it reasonably agrees with that obtained from the 2D phonon heat capacity.
15. Comprehensive characterization of temperature- and pressure-induced bilayer phase transitions for saturated phosphatidylcholines containing longer chain homologs.
PubMed
Goto, Masaki; Endo, Takuya; Yano, Takahiro; Tamai, Nobutake; Kohlbrecher, Joachim; Matsuki, Hitoshi
2015-04-01
Complete elucidation of the phase behavior of phospholipid bilayers requires information on the subtransition from the lamellar crystal (Lc) phase to the gel phase. However, for bilayers of saturated diacylphosphatidylcholines (CnPCs), especially longer chain homologs, equilibration in the Lc phase is known to be very slow. In this study, bilayer phase transitions of three CnPCs with longer acyl chains, C19PC, C20PC and C21PC, were observed by differential scanning calorimetry under atmospheric pressure and by light-transmittance measurements under high pressure. Using lipid samples treated by thermal annealing enabled the observation of the sub-, pre- and main transitions of the C19PC and C20PC bilayers under atmospheric pressure. Only the pre- and main transitions could be observed for the C21PC bilayer due to very slow kinetics of the Lc phase formation for lipids with long acyl chains. The temperature and pressure phase diagrams constructed and phase-transitions quantities (enthalpy, entropy and volume changes) evaluated for these bilayers were compared with one another and with those of bilayers of the CnPC homologs examined in previous studies. These results allowed us (1) to clarify the temperature- and pressure-dependent phase sequence and phase stability of the CnPC (n=12-22) bilayers as a function of the hydrophobicity of the molecules, (2) to prove the presence of a shorter and a longer limit (n=13 and 21) in the acyl chain length for the pressure-induced bilayer interdigitation and (3) to reveal the chain-length dependence of the thermodynamic quantities of the subtransitions including the volume change. PMID:25779604
16. Synthetic fluid inclusions XIX. Experimental determination of the vapor-saturated liquidus of the system H2O-NaCl-FeCl2
Lecumberri-Sanchez, Pilar; Steele-MacInnis, Matthew; Bodnar, Robert J.
2015-01-01
Magmatic-hydrothermal fluids associated with felsic to intermediate composition magmas are generally dominated by (Na K)Cl, but often the fluids also contain significant concentrations of FeCl2. Previously, fluid inclusions containing such fluids were interpreted using the properties of H2O-NaCl because the effect of FeCl2 on the phase equilibrium and volumetric (PVTx) properties of aqueous fluids was essentially unknown. In this study, synthetic fluid inclusion experiments have been conducted to determine the vapor-saturated liquidus phase relations of the system H2O-NaCl-FeCl2. Microthermometric and microanalytical measurements on synthetic fluid inclusions have been combined with the limited existing data, as well as with predictions based on Pitzer's formalism, to determine the ternary cotectic and peritectic phase boundaries and liquidus fields. The liquidus is qualitatively similar to those of other ternary systems of H2O-NaCl plus divalent-cation chlorides (MgCl2 and CaCl2) and has been characterized through empirical equations that represent the liquid salinity on the ice- and halite-liquidus surfaces. The ice and halite liquidi intersect at a metastable cotectic curve, which can be used to determine fluid compositions in this system if metastable behavior is observed. Furthermore, based on the experimentally determined liquidus, bulk salinities of natural fluid inclusions can be determined from the last dissolution temperatures of ice and/or halite using the new empirical equations.
17. The impact of rock and fluid uncertainties in the estimation of saturation and pressure from a 4D petro elastic inversion
Pazetti, Bruno; Davolio, Alessandra; Schiozer, Denis J.; UNICAMP
2015-08-01
The integration of 4D seismic (4DS) attributes and reservoir simulation is used to reduce risks in the management of petroleum fields. One possible alternative is the saturation and pressure domain. In this case, we use estimations of saturation and pressure changes from 4D seismic data as input in history matching processes to yield more reliable production predictions in simulation models. The estimation of dynamic changes from 4DS depends on the knowledge of reservoir rock and fluid properties that are uncertain in the process of estimation. This paper presents a study of the impact of rock and fluid uncertainties on the estimation of saturation and pressure changes achieved through a 4D petro-elastic inversion. The term impact means that the saturation and pressure estimation can be perturbed by the rock and fluid uncertainties. The motivation for this study comes from the necessity to estimate uncertainties in saturation and pressure variation to incorporate them in the history matching procedures, avoiding the use of deterministic values from 4DS, which may not be reliable. The study is performed using a synthetic case with known response from where it is possible to show that the errors of estimated saturation and pressure depend on the magnitude of rock and fluid uncertainties jointly with the reservoir dynamic changes. The main contribution of this paper is to show how uncertain reservoir properties can affect the reliability of pressure and saturation estimation from 4DS and how it depends on reservoir changes induced by production. This information can be used in future projects which use quantitative inversion to integrate reservoir simulation and 4D seismic data.
18. Gas chromatographic vapor pressure determination of atmospherically relevant oxidation products of β-caryophyllene and α-pinene
Hartonen, Kari; Parshintsev, Jevgeni; Vilja, Vesa-Pekka; Tiala, Heidi; Knuuti, Sinivuokko; Lai, Ching Kwan; Riekkola, Marja-Liisa
2013-12-01
Vapor pressures (subcooled liquid, pliquid) of atmospherically relevant oxidation products of β-caryophyllene (β-caryophyllene aldehyde 0.18 ± 0.03 Pa and β-nocaryophyllene aldehyde 0.17 ± 0.03 Pa), and α-pinene (pinonaldehyde 16.8 ± 0.20 Pa, cis-pinic acid 0.12 ± 0.06 Pa, and cis-pinonic acid 0.99 ± 0.19 Pa) at 298 K were obtained by gas chromatography with flame ionization detection (FID) and mass spectrometric (MS) detection. The effects of stationary phase polarity and column film thickness on the vapor pressure values were investigated. Increase in stationary phase polarity provided smaller values, while increase in film thickness gave slightly higher values. Values for vapor pressure were at least two orders of magnitude lower when obtained by a method utilizing vaporization enthalpy (determined by gas chromatography-mass spectrometry) than by retention index method. Finally, the results were compared with values calculated by group contribution theory. For the β-caryophyllene oxidation products, the values measured by gas chromatography were slightly lower than those obtained by theoretical calculations. The opposite trend was observed for the α-pinene oxidation products. The methods based on gas chromatography are concluded to be highly useful for the determination of vapor pressures of semi-volatile compounds. Except for the most polar pinic and pinonic acids, differences between vapor pressure values obtained by GC-FID and GC-MS were small. Since GC-MS provides structural information simultaneously, the use of GC-MS is recommended.
19. A Theoretical Approach Representing Hysteresis in Capillary Pressure-Saturation Relationship Based on Connectivity in Void Space
Cihan, A.; Birkholzer, J. T.; Illangasekare, T. H.; Zhou, Q.
2013-12-01
This study presents a new theoretical model for description of hysteretic constitutive relationships between capillary pressure and saturation under capillary-dominated multiphase flow conditions in porous media. Hysteretic relationships are required for the accurate prediction of the spatial and temporal distribution of multiphase fluids in response to successively occurring drainage and imbibition events in porous media. In addition to contact angle effects, the connectivity of the void space in the porous medium plays a central role for the macroscopic manifestation of hysteresis behavior and capillary entrapment of wetting and non-wetting fluids. The hysteretic constitutive model developed in this work uses void-size distribution and a measure of connectivity of void space to compute the hysteretic curves and to predict entrapped fluid phase saturations. Two functions, the probability of drainage and the probability of wetting, are introduced to characterize connectivity of fluids in void space during drainage and wetting processes. These functions can be estimated through pore-scale simulations in computer-generated porous media or from traditional experimental measurements of primary drainage and main wetting curves. The hysteresis model results are verified by comparing the model predicted scanning curves with 3D pore-scale simulations as well as with actual data sets obtained from column experiments found in the literature.
20. A modeling approach to represent hysteresis in capillary pressure-saturation relationship based on fluid connectivity in void space
Cihan, Abdullah; Birkholzer, Jens; Illangasekare, Tissa H.; Zhou, Quanlin
2014-01-01
This study presents a new model for description of hysteretic constitutive relationships between capillary pressure and saturation under capillary-dominated multiphase flow conditions in porous media. Hysteretic relationships are required for accurate prediction of spatial and temporal distribution of multiphase fluids in response to successively occurring drainage and imbibition events in porous media. In addition to contact angle effects, connectivity of the void space in the porous medium plays a central role for the macroscopic manifestation of hysteresis behavior and capillary entrapment of wetting and nonwetting fluids. The hysteretic constitutive model developed in this work uses void-size distribution and a measure of connectivity for void space to compute the hysteretic curves and to predict entrapped fluid-phase saturations. Two functions, the drainage connectivity function and the wetting connectivity function, are introduced to characterize connectivity of fluids in void space during drainage and wetting processes. These functions can be estimated through pore-scale simulations in computer-generated porous media or from traditional experimental measurements of primary drainage and main wetting curves. The hysteresis model results are verified by comparing the model predicted scanning curves with 3-D pore-scale simulations as well as with actual data sets obtained from column experiments found in the literature.
1. Effects of variable blast pressures on blood flow and oxygen saturation in rat brain as evidenced using MRI.
PubMed
Bir, Cynthia; Vandevord, Pamela; Shen, Yimin; Raza, Waqar; Haacke, E Mark
2012-05-01
It has been recognized that primary blast waves may result in neurotrauma in soldiers in theater. A new type of contrast used in magnetic resonance imaging (MRI), susceptibility-weighted imaging (SWI), has been developed that is based on the different susceptibility levels in diverse tissues and can detect decreases in cerebral blood flow (CBF) using inferred oxygen saturation changes in tissue. In addition, a continuous arterial spin-labeled (ASL) MRI sequence was used as a direct measure of regional CBF within the brain tissue. Animals were subjected to whole-body blast exposures of various overpressures within a gas-driven shock tube. When exposed to low levels of overpressure, most rats demonstrated no obvious changes between pre- and postexposure in the conventional MR images. CBF changes measured by SWI and ASL were significantly higher for the overpressure exposed groups as compared to the sham group and tended to increase with pressure increases at the highest two pressures. In the hippocampus, all blast animals had a reduction in the CBF consistently in the range of 0-27%. In summary, low levels of primary blast pressure exposure demonstrated a significant physiologic effect to the brain up to 72 h postexposure. PMID:22285875
2. Atmospheric-Pressure Chemical Vapor Deposition of Iron Pyrite Thin Films
SciTech Connect
Berry, Nicholas; Cheng, Ming; Perkins, Craig L.; Limpinsel, Moritz; Hemminger, John C.; Law, Matt
2012-10-23
Iron pyrite (cubic FeS{sub 2}) is a promising candidate absorber material for earth-abundant thin-film solar cells. In this report, single-phase, large-grain, and uniform polycrystalline pyrite thin films are fabricated on glass and molybdenum-coated glass substrates by atmospheric-pressure chemical vapor deposition (AP-CVD) using the reaction of iron(III) acetylacetonate and tert-butyl disulfide in argon at 300 C, followed by sulfur annealing at 500--550 C to convert marcasite impurities to pyrite. The pyrite-marcasite phase composition depends strongly on the concentration of sodium in the growth substrate and the sulfur partial pressure during annealing. Phase and elemental composition of the films are characterized by X-ray diffraction, Raman spectroscopy, Auger electron spectroscopy, secondary ion mass spectrometry, Rutherford backscattering spectrometry, and X-ray photoelectron spectroscopy. The in-plane electrical properties are surprisingly insensitive to phase and elemental impurities, with all films showing p-type, thermally activated transport with a small activation energy ({approx}30 meV), a room- temperature resistivity of {approx}1 {Omega} cm, and low mobility. These ubiquitous electrical properties may result from robust surface effects. These CVD pyrite thin films are well suited to fundamental electrical studies and the fabrication of pyrite photovoltaic device stacks.
3. Ultrafine aerosol size distributions and sulfuric acid vapor pressures: Implications for new particle formation in the atmosphere
SciTech Connect
McMurry, P.H.
1992-01-01
This project has two components with different but related objectives. One component deals with measurement of H{sub 2}SO{sub 4} vapor pressures in air under temperature and relative humidity conditions similar to those found in the atmosphere. The second deals with measurement of ultrafine aerosol size distributions. Substantial progress has been made on each of these projects.
4. Vapor pressure and evaporation rate of certain heat-resistant compounds in a vacuum at high temperatures
NASA Technical Reports Server (NTRS)
Bolgar, A. S.; Verkhoglyadova, T. S.; Samsonov, G. V.
1985-01-01
The vapor pressure and evaporation rate of borides of titanium, zirconium, and chrome; and of strontium and carbides of titanium, zirconium, and chrome, molybdenum silicide; and nitrides of titanium, niobium, and tantalum in a vacuum were studied. It is concluded that all subject compounds evaporate by molecular structures except AlB sub 12' which dissociates, losing the aluminum.
5. An Integrated Approach to Introducing Biofuels, Flash Point, and Vapor Pressure Concepts into an Introductory College Chemistry Lab
ERIC Educational Resources Information Center
Hoffman, Adam R.; Britton, Stephanie L.; Cadwell, Katie D.; Walz, Kenneth A.
2011-01-01
Students explore the fundamental chemical concepts of vapor pressure and flash point in a real-world technical context, while gaining insight into the contemporary societal issue of biofuels. Lab activities were developed using a closed-cup instrument to measure the flash point of various biodiesel samples. Pre- and post-tests revealed that the
6. DETERMINATION OF THE VAPOR PRESSURES OF SELECT POLYCHLORINATED DIBENZO-P-DIOXINS AND DIBENZOFURANS AT 75275C
EPA Science Inventory
Vapor pressures were determined for several polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) at 75275C, extending the available literature data to more relevant temperature regions and providing the first experimental data for 2,3,7...
7. An Integrated Approach to Introducing Biofuels, Flash Point, and Vapor Pressure Concepts into an Introductory College Chemistry Lab
ERIC Educational Resources Information Center
Hoffman, Adam R.; Britton, Stephanie L.; Cadwell, Katie D.; Walz, Kenneth A.
2011-01-01
Students explore the fundamental chemical concepts of vapor pressure and flash point in a real-world technical context, while gaining insight into the contemporary societal issue of biofuels. Lab activities were developed using a closed-cup instrument to measure the flash point of various biodiesel samples. Pre- and post-tests revealed that the…
8. COMPUTATIONAL CHEMISTRY METHOD FOR PREDICTING VAPOR PRESSURES AND ACTIVITY COEFFICIENTS OF POLAR ORGANIC OXYGENATES IN PM2.5
EPA Science Inventory
Parameterizations of interactions of polar multifunctional organic oxygenates in PM2.5 must be included in aerosol chemistry models for evaluating control strategies for reducing ambient concentrations of PM2.5 compounds. Vapor pressures and activity coefficients of these compo...
9. 40 CFR 63.7944 - How do I determine the maximum HAP vapor pressure of my remediation material?
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 14 2012-07-01 2011-07-01 true How do I determine the maximum HAP vapor pressure of my remediation material? 63.7944 Section 63.7944 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS (CONTINUED) NATIONAL EMISSION STANDARDS FOR HAZARDOUS AIR POLLUTANTS FOR SOURCE CATEGORIES...
10. Photosynthetic photon flux density, carbon dioxide concentration, and vapor pressure deficit effects on photosynthesis in cacao seedlings
Technology Transfer Automated Retrieval System (TEKTRAN)
Cacao (Theobroma cacao) is a shade plant, native to the under-story of the evergreen rain forest of the Amazon basin and adapted to low levels of photosynthetic photon flux density (PPFD). The influence of PPFD, leaf to air water vapor pressure deficit (VPD) and external carbon dioxide concentration...
11. Stability of streambanks formed in partially saturated soils and effects of negative pore water pressures: the Sieve River (Italy)
Rinaldi, Massimo; Casagli, Nicola
1999-01-01
Streambanks of alluvial channels are usually composed of loose materials, which are unsaturated in ambient conditions. Unsaturated soils are subject to negative pore water pressures, which cause an apparent cohesion. The latter is the main factor in allowing the stability of near-vertical banks. Even during moderate in-bank flow events, the apparent cohesion can be strongly reduced as the material approaches full saturation; therefore, during the drawdown phase, as the confining pressure of the water in the channel disappears, a bank failure is likely to occur. Channel bed-level lowering along the Sieve River, Central Italy, has caused widespread bank instability. A geomorphological reconnaissance of forms and processes was followed by in situ tests to determine the shear strength of the banks. Interpretation of the tests and a streambank stability analysis were based on concepts of soil mechanics for unsaturated soils, in order to obtain relations between bank angle and height in limit equilibrium conditions. A stability chart was obtained with curves for different apparent cohesion values, and a stability analysis was performed taking into account the effects of flow events. In order to investigate the pore pressure effects, a series of piezo-tensiometers were installed in a streambank of the Sieve River. Data from a 1 year monitoring period show variations in pore water pressure and matric suction as a consequence of rainfall, evapotranspiration, and water stage variations. A planar failure with a tension crack occurred in the upper cohesive part of the bank during December 1996. The safety factor has been expressed as a function of the geometry of the bank and of the shear strength of the material. Safety factor variations through time are therefore shown as a function of seasonal variations in matric suction.
12. Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium
USGS Publications Warehouse
Iverson, R.M.
1993-01-01
Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass conservation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameter B, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of Iverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data. ?? 1993 International Association for Mathematical Geology.
13. Comparison of Deposition Characteristics between Triethyl and Trimethyl Borates in an Atmospheric Pressure Chemical Vapor Deposition Equipment with Tetraethyl Orthosilicate and O3
Yamamoto, Yoshito; Ikakura, Hiroshi; Ohgawara, Shoji; Furukawa, Masakazu
1999-09-01
The deposition characteristics of triethyl borate (TEB) and trimethyl borate (TMB) vapors are compared to investigate of boron concentration uniformity and profiles in borophosphosilicate glass (BPSG) films. Film deposition is carried out in an atmospheric pressure equipment with tetraethyl orthosilicate (TEOS) and ozone (O3) under at standard condition and four process parameters are varied around the standard condition. Uniformity values obtained with the TMB vapor at a bubbling temperature of 10C are one-third that with the TEB vapor at the same bubbling temperature, and uniformity changes due to process parameter variations from the standard condition with the TMB vapor are also smaller since the TEB vapor is cleaved by O3 at lower temperature. These results indicate that the deposition characteristics for uniformity using TMB vapor are much better. However, a decrease in the boron concentration profile in films with the TMB vapor is observed between a silicon and silicon-dioxide interface. This decrease is estimated to be due to the fact that TMB bubbling N2 flow rate to suppress the vaporization rate with TMB's higher vapor pressure is one order of magnitude lower than TEB bubbling N2 flow rate. Suppression of TMB vapor to a desired vapor pressure was achieved by cooling the TMB bubbler at -25C. Then, a uniform profile of the TMB vapor was obtained, which was equivalent to the results at 10C.
14. Osmotic virial coefficients of hydroxyethyl starch from aqueous hydroxyethyl starch-sodium chloride vapor pressure osmometry.
PubMed
Cheng, Jingjiang; Gier, Martin; Ross-Rodriguez, Lisa U; Prasad, Vinay; Elliott, Janet A W; Sputtek, Andreas
2013-09-01
Hydroxyethyl starch (HES) is an important industrial additive in the paper, textile, food, and cosmetic industries and has been shown to be an effective cryoprotectant for red blood cells; however, little is known about its thermodynamic solution properties. In many applications, in particular those in biology, HES is used in an aqueous solution with sodium chloride (NaCl). The osmotic virial solution thermodynamics approach accurately captures the dependence of osmolality on molality for many types of solutes in aqueous systems, including electrolytes, sugars, alcohols, proteins, and starches. Elliott et al. proposed mixing rules for the osmotic virial equation to be used for osmolality of multisolute aqueous solutions [Elliott, J. A. W.; et al. J. Phys. Chem. B 2007, 111, 1775-1785] and recently applied this approach to the fitting of one set of aqueous HES-NaCl solution data reported by Jochem and Krber [Cryobiology 1987, 24, 513-536], indicating that the HES osmotic virial coefficients are dependent on HES-to-NaCl mass ratios. The current study reports new aqueous HES-NaCl vapor pressure osmometry data which are analyzed using the osmotic virial equation. HES modifications were measured after dialysis (membrane cut off: 10,000 g/mol) and freeze-drying using vapor pressure osmometry at different mass ratios of HES to NaCl for HES up to 50% and NaCl up to 25% with three different HES modifications (weight average molecular weights [g/mol]/degree of substitution: 40,000/0.5; 200,000/0.5; 450,000/0.7). Equations were then fit to the data to provide a model for HES osmotic virial coefficient dependence on mass ratio of HES to NaCl. The osmolality data of the three HES modifications were accurately described over a broad range of HES-to-NaCl mass ratios using only four parameters, illustrating the power of the osmotic virial approach in analyzing complex data sets. As expected, the second osmotic virial coefficients increase with molecular weight of the HES and increase with HES-to-NaCl mass ratio. PMID:23862979
15. Mercury vapor pressure of flue gas desulfurization scrubber suspensions: effects of pH level, gypsum, and iron.
PubMed
Schuetze, Jan; Kunth, Daniel; Weissbach, Sven; Koeser, Heinz
2012-03-01
Calcium-based scrubbers designed to absorb HCl and SO(2) from flue gases can also remove oxidized mercury. Dissolved mercury halides may have an appreciable partial vapor pressure. Chemical reduction of the dissolved mercury may increase the Hg emission, thereby limiting the coremoval of mercury in the wet scrubbing process. In this paper we evaluate the effects of the pH level, different gypsum qualities, and iron in flue gas desulfurization (FGD) scrubber suspensions. The impact of these parameters on mercury vapor pressure was studied under controlled laboratory conditions in model scrubber suspensions. A major influence is exerted by pH values above 7, considerably amplifying the mercury concentration in the vapor phase above the FGD scrubber suspension. Gypsum also increases the mercury re-emission. Fe(III) decreases and Fe(II) increases the vapor pressure significantly. The consequences of the findings for a reliable coremoval of mercury in FGD scrubbers are discussed. It is shown that there is an increased risk of poor mercury capture in lime-based FGD scrubbers in comparison to limestone FGD scrubbers. PMID:22324514
16. Methods for calculation of engineering parameters for gas separation. [vapor pressure and solubility of gases in organic liquids
NASA Technical Reports Server (NTRS)
Lawson, D. D.
1979-01-01
A group additivity method is generated which allows estimation, from the structural formulas alone, of the energy of vaporization and the molar volume at 25 C of many nonpolar organic liquids. Using these two parameters and appropriate thermodynamic relations, the vapor pressure of the liquid phase and the solubility of various gases in nonpolar organic liquids are predicted. It is also possible to use the data to evaluate organic and some inorganic liquids for use in gas separation stages or liquids as heat exchange fluids in prospective thermochemical cycles for hydrogen production.
17. High-pressure thermal oxidation of n-GaAs in an atmosphere of oxygen and water vapor
Basu, Nandita; Bhat, K. N.
1988-06-01
A low-temperature (250 C) high-pressure oxidation technique is used for the thermal oxidation of gallium arsenide in an ambient of oxygen and water vapor. It is shown that a uniform and chemically stable oxide with high band-gap energy can be grown on GaAs by this process. The role of water vapor and oxygen is studied in detail to obtain information on the oxidation mechanism. The electrical characteristics and the composition of this oxide are presented to demonstrate its suitability for surface passivation and metal-oxide-semiconductor devices.
18. Vaporization of sediments with a pulsed transverse excitation at atmospheric pressure (TEA) CO/sub 2/ laser system
SciTech Connect
Smyrl, N.R.; King, H.G. Jr.
1981-12-31
A transverse excitation at atmospheric pressure (TEA) pulsed CO/sub 2/ laser equipped with an adjunct called a Lasertrace has been used to generate vapor and/or particulates from sediment samples. The material thus obtained can be transferred to analytical systems for analysis making possible the analysis of solids by techniques previously suitable only for liquids or gases. Approximately one milligram of vapor and/or particulates was obtained in a short period of time by this method, suitable for transport to other systems.
19. Exchange of Na+ and K+ between water vapor and feldspar phases at high temperature and low vapor pressure
USGS Publications Warehouse
Fournier, R.O.
1976-01-01
In order to determine whether gas (steam) containing a small amount of dissolved alkali chloride is effective in promoting base exchange of Na+ and K+ among alkali feldspars and coexisting brine or brine plus solid salt, experiments were carried out at 400-700??C and steam densities ranging down to less than 0.05. For bulk compositions rich in potassium, the low pressure results are close to previous high-pressure results in composition of the fluid and coexisting solid phase. However, when the bulk composition is more sodic, alkali feldspars are relatively richer in potassium at low pressure than at high pressure. This behaviour corresponds to enrichment of potassium in the gas phase relative to coexisting brine and precipitation of solid NaCl when the brine plus gas composition becomes moderately sodic. The gas phase is very effective in promoting base exchange between coexisting alkali feldspars at high temperature and low water pressure. This suggests that those igneous rocks which contain coexisting alkali feldspars out of chemical equilibrium either remained very dry during the high-temperature part of their cooling history or that the pore fluid was a gas containing very little potassium relative to sodium. ?? 1976.
20. An improved method for simultaneous determination of frictional pressure drop and vapor volume fraction in vertical flow boiling
NASA Technical Reports Server (NTRS)
Klausner, J. F.; Chao, B. T.; Soo, S. L.
1990-01-01
The two-phase frictional pressure drop and vapor volume fraction in the vertical boiling and adiabatic flow of the refrigerant, R11, have been simultaneously measured by a liquid balancing column and differential magnetic reluctance pressure transducers. An account is given of the experimental apparatus and procedure, data acquisition and analysis, and error estimation employed. All values of two-phase multipliers evaluated on the basis of the measured frictional pressure drop data in vertical upflow fall in the range bounded by the predictions of the Chisholm correlation and the homogeneous model.
1. Threefold atmospheric-pressure annealing for suppressing graphene nucleation on copper in chemical vapor deposition
Suzuki, Seiya; Nagamori, Takashi; Matsuoka, Yuki; Yoshimura, Masamichi
2014-09-01
Chemical vapor deposition (CVD) is a promising method of producing a large single-crystal graphene on a catalyst, especially on copper (Cu), and a further increase in domain size is desirable for electro/optic applications. Here, we report on threefold atmospheric-pressure (ATM) annealing for suppressing graphene nucleation in atmospheric CVD. Threefold ATM annealing formed a step and terrace surface of the underlying Cu, in contrast to ATM annealing. Atomic force microscopy and Auger electron mapping revealed that Si-containing particles existed on threefold-ATM- and ATM-annealed surfaces; particles on Cu had a lower density after threefold ATM annealing than after ATM annealing. The formation of a step and terrace surface and the lower density of particles following the threefold ATM annealing would play a role in reducing graphene nucleation. By combining threefold ATM annealing and electropolishing of Cu, the nucleation of graphene was effectively suppressed, and a submillimeter-sized hexagonal single-crystal graphene was successfully obtained.
2. High vapor pressure deficit drives salt-stress-induced rice yield losses in India.
TOXLINE Toxicology Bibliographic Information
Tack J; Singh RK; Nalley LL; Viraktamath BC; Krishnamurthy SL; Lyman N; Jagadish KS
2015-04-01
Flooded rice is grown across wide geographic boundaries from as far north as Manchuria and as far south as Uruguay and New South Wales, primarily because of its adaptability across diverse agronomic and climatic conditions. Salt-stress damage, a common occurrence in delta and coastal rice production zones, could be heightened by the interactions between high temperature and relative humidity (vapor pressure deficit--VPD). Using temporal and spatial observations spanning 107 seasons and 19 rice-growing locations throughout India with varying electrical conductivity (EC), including coastal saline, inland saline, and alkaline soils, we quantified the proportion of VPD inducing salinity damage in rice. While controlling for time-invariant factors such as trial locations, rice cultivars, and soil types, our regression analysis indicates that EC has a nonlinear detrimental effect on paddy rice yield. Our estimates suggest these yield reductions become larger at higher VPD. A one standard deviation (SD) increase in EC from its mean value is associated with 1.68% and 4.13% yield reductions at median and maximum observed VPD levels, respectively. Yield reductions increase roughly sixfold when the one SD increase is taken from the 75th percentile of EC. In combination, high EC and VPD generate near catastrophic crop loss as predicted yield approaches zero. If higher VPD levels driven by global warming materialize in conjunction with rising sea levels or salinity incursion in groundwater, this interaction becomes an important and necessary predictor of expected yield losses and global food security.
3. Low-temperature-grown continuous graphene films from benzene by chemical vapor deposition at ambient pressure
Jang, Jisu; Son, Myungwoo; Chung, Sunki; Kim, Kihyeun; Cho, Chunhum; Lee, Byoung Hun; Ham, Moon-Ho
2015-12-01
There is significant interest in synthesizing large-area graphene films at low temperatures by chemical vapor deposition (CVD) for nanoelectronic and flexible device applications. However, to date, low-temperature CVD methods have suffered from lower surface coverage because micro-sized graphene flakes are produced. Here, we demonstrate a modified CVD technique for the production of large-area, continuous monolayer graphene films from benzene on Cu at 100–300 °C at ambient pressure. In this method, we extended the graphene growth step in the absence of residual oxidizing species by introducing pumping and purging cycles prior to growth. This led to continuous monolayer graphene films with full surface coverage and excellent quality, which were comparable to those achieved with high-temperature CVD; for example, the surface coverage, transmittance, and carrier mobilities of the graphene grown at 300 °C were 100%, 97.6%, and 1,900–2,500 cm2 V‑1 s‑1, respectively. In addition, the growth temperature was substantially reduced to as low as 100 °C, which is the lowest temperature reported to date for pristine graphene produced by CVD. Our modified CVD method is expected to allow the direct growth of graphene in device manufacturing processes for practical applications while keeping underlying devices intact.
4. Low-temperature-grown continuous graphene films from benzene by chemical vapor deposition at ambient pressure
PubMed Central
Jang, Jisu; Son, Myungwoo; Chung, Sunki; Kim, Kihyeun; Cho, Chunhum; Lee, Byoung Hun; Ham, Moon-Ho
2015-01-01
There is significant interest in synthesizing large-area graphene films at low temperatures by chemical vapor deposition (CVD) for nanoelectronic and flexible device applications. However, to date, low-temperature CVD methods have suffered from lower surface coverage because micro-sized graphene flakes are produced. Here, we demonstrate a modified CVD technique for the production of large-area, continuous monolayer graphene films from benzene on Cu at 100–300 °C at ambient pressure. In this method, we extended the graphene growth step in the absence of residual oxidizing species by introducing pumping and purging cycles prior to growth. This led to continuous monolayer graphene films with full surface coverage and excellent quality, which were comparable to those achieved with high-temperature CVD; for example, the surface coverage, transmittance, and carrier mobilities of the graphene grown at 300 °C were 100%, 97.6%, and 1,900–2,500 cm2 V−1 s−1, respectively. In addition, the growth temperature was substantially reduced to as low as 100 °C, which is the lowest temperature reported to date for pristine graphene produced by CVD. Our modified CVD method is expected to allow the direct growth of graphene in device manufacturing processes for practical applications while keeping underlying devices intact. PMID:26658923
5. Atmospheric Pressure Spray Chemical Vapor Deposited CuInS2 Thin Films for Photovoltaic Applications
Harris, J. D.; Raffaelle, R. P.; Banger, K. K.; Smith, M. A.; Scheiman, D. A.; Hepp, A. F.
2002-10-01
Solar cells have been prepared using atmospheric pressure spray chemical vapor deposited CuInS2 absorbers. The CuInS2 films were deposited at 390 C using the single source precursor (PPh3)2CuIn(SEt)4 in an argon atmosphere. The absorber ranges in thickness from 0.75 - 1.0 micrometers, and exhibits a crystallographic gradient, with the leading edge having a (220) preferred orientation and the trailing edge having a (112) orientation. Schottky diodes prepared by thermal evaporation of aluminum contacts on to the CuInS2 yielded diodes for films that were annealed at 600 C. Solar cells were prepared using annealed films and had the (top down) composition of Al/ZnO/CdS/CuInS2/Mo/Glass. The Jsc, Voc, FF and (eta) were 6.46 mA per square centimeter, 307 mV, 24% and 0.35%, respectively for the best small area cells under simulated AM0 illumination.
6. Prediction of aqueous solubility, vapor pressure and critical micelle concentration for aquatic partitioning of perfluorinated chemicals.
PubMed
Bhhatarai, Barun; Gramatica, Paola
2011-10-01
The majority of perfluorinated chemicals (PFCs) are of increasing risk to biota and environment due to their physicochemical stability, wide transport in the environment and difficulty in biodegradation. It is necessary to identify and prioritize these harmful PFCs and to characterize their physicochemical properties that govern the solubility, distribution and fate of these chemicals in an aquatic ecosystem. Therefore, available experimental data (10-35 compounds) of three important properties: aqueous solubility (AqS), vapor pressure (VP) and critical micelle concentration (CMC) on per- and polyfluorinated compounds were collected for quantitative structure-property relationship (QSPR) modeling. Simple and robust models based on theoretical molecular descriptors were developed and externally validated for predictivity. Model predictions on selected PFCs were compared with available experimental data and other published in silico predictions. The structural applicability domains (AD) of the models were verified on a bigger data set of 221 compounds. The predicted properties of the chemicals that are within the AD, are reliable, and they help to reduce the wide data gap that exists. Moreover, the predictions of AqS, VP, and CMC of most common PFCs were evaluated to understand the aquatic partitioning and to derive a relation with the available experimental data of bioconcentration factor (BCF). PMID:20958003
7. Atmospheric Pressure Spray Chemical Vapor Deposited CuInS2 Thin Films for Photovoltaic Applications
NASA Technical Reports Server (NTRS)
Harris, J. D.; Raffaelle, R. P.; Banger, K. K.; Smith, M. A.; Scheiman, D. A.; Hepp, A. F.
2002-01-01
Solar cells have been prepared using atmospheric pressure spray chemical vapor deposited CuInS2 absorbers. The CuInS2 films were deposited at 390 C using the single source precursor (PPh3)2CuIn(SEt)4 in an argon atmosphere. The absorber ranges in thickness from 0.75 - 1.0 micrometers, and exhibits a crystallographic gradient, with the leading edge having a (220) preferred orientation and the trailing edge having a (112) orientation. Schottky diodes prepared by thermal evaporation of aluminum contacts on to the CuInS2 yielded diodes for films that were annealed at 600 C. Solar cells were prepared using annealed films and had the (top down) composition of Al/ZnO/CdS/CuInS2/Mo/Glass. The Jsc, Voc, FF and (eta) were 6.46 mA per square centimeter, 307 mV, 24% and 0.35%, respectively for the best small area cells under simulated AM0 illumination.
8. High vapor pressure deficit drives salt-stress-induced rice yield losses in India.
PubMed
Tack, Jesse; Singh, Rakesh K; Nalley, Lawton L; Viraktamath, Basavaraj C; Krishnamurthy, Saraswathipura L; Lyman, Nate; Jagadish, Krishna S V
2015-04-01
Flooded rice is grown across wide geographic boundaries from as far north as Manchuria and as far south as Uruguay and New South Wales, primarily because of its adaptability across diverse agronomic and climatic conditions. Salt-stress damage, a common occurrence in delta and coastal rice production zones, could be heightened by the interactions between high temperature and relative humidity (vapor pressure deficit--VPD). Using temporal and spatial observations spanning 107 seasons and 19 rice-growing locations throughout India with varying electrical conductivity (EC), including coastal saline, inland saline, and alkaline soils, we quantified the proportion of VPD inducing salinity damage in rice. While controlling for time-invariant factors such as trial locations, rice cultivars, and soil types, our regression analysis indicates that EC has a nonlinear detrimental effect on paddy rice yield. Our estimates suggest these yield reductions become larger at higher VPD. A one standard deviation (SD) increase in EC from its mean value is associated with 1.68% and 4.13% yield reductions at median and maximum observed VPD levels, respectively. Yield reductions increase roughly sixfold when the one SD increase is taken from the 75th percentile of EC. In combination, high EC and VPD generate near catastrophic crop loss as predicted yield approaches zero. If higher VPD levels driven by global warming materialize in conjunction with rising sea levels or salinity incursion in groundwater, this interaction becomes an important and necessary predictor of expected yield losses and global food security. PMID:25379616
9. Low-temperature-grown continuous graphene films from benzene by chemical vapor deposition at ambient pressure.
PubMed
Jang, Jisu; Son, Myungwoo; Chung, Sunki; Kim, Kihyeun; Cho, Chunhum; Lee, Byoung Hun; Ham, Moon-Ho
2015-01-01
There is significant interest in synthesizing large-area graphene films at low temperatures by chemical vapor deposition (CVD) for nanoelectronic and flexible device applications. However, to date, low-temperature CVD methods have suffered from lower surface coverage because micro-sized graphene flakes are produced. Here, we demonstrate a modified CVD technique for the production of large-area, continuous monolayer graphene films from benzene on Cu at 100-300 °C at ambient pressure. In this method, we extended the graphene growth step in the absence of residual oxidizing species by introducing pumping and purging cycles prior to growth. This led to continuous monolayer graphene films with full surface coverage and excellent quality, which were comparable to those achieved with high-temperature CVD; for example, the surface coverage, transmittance, and carrier mobilities of the graphene grown at 300 °C were 100%, 97.6%, and 1,900-2,500 cm(2) V(-1) s(-1), respectively. In addition, the growth temperature was substantially reduced to as low as 100 °C, which is the lowest temperature reported to date for pristine graphene produced by CVD. Our modified CVD method is expected to allow the direct growth of graphene in device manufacturing processes for practical applications while keeping underlying devices intact. PMID:26658923
10. Chain Assemblies from Nanoparticles Synthesized by Atmospheric Pressure Plasma Enhanced Chemical Vapor Deposition: The Computational View.
PubMed
Mishin, Maxim V; Zamotin, Kirill Y; Protopopova, Vera S; Alexandrov, Sergey E
2015-12-01
This article refers to the computational study of nanoparticle self-organization on the solid-state substrate surface with consideration of the experimental results, when nanoparticles were synthesised during atmospheric pressure plasma enhanced chemical vapor deposition (AP-PECVD). The experimental study of silicon dioxide nanoparticle synthesis by AP-PECVD demonstrated that all deposit volume consists of tangled chains of nanoparticles. In certain cases, micron-sized fractals are formed from tangled chains due to deposit rearrangement. This work is focused on the study of tangled chain formation only. In order to reveal their formation mechanism, a physico-mathematical model was developed. The suggested model was based on the motion equation solution for charged and neutral nanoparticles in the potential fields with the use of the empirical interaction potentials. In addition, the computational simulation was carried out based on the suggested model. As a result, the influence of such experimental parameters as deposition duration, particle charge, gas flow velocity, and angle of gas flow was found. It was demonstrated that electrical charges carried by nanoparticles from the discharge area are not responsible for the formation of tangled chains from nanoparticles, whereas nanoparticle kinetic energy plays a crucial role in deposit morphology and density. The computational results were consistent with experimental results. PMID:26682441
11. Modeling chemical vapor deposition of silicon dioxide in microreactors at atmospheric pressure
Konakov, S. A.; Krzhizhanovskaya, V. V.
2015-01-01
We developed a multiphysics mathematical model for simulation of silicon dioxide Chemical Vapor Deposition (CVD) from tetraethyl orthosilicate (TEOS) and oxygen mixture in a microreactor at atmospheric pressure. Microfluidics is a promising technology with numerous applications in chemical synthesis due to its high heat and mass transfer efficiency and well-controlled flow parameters. Experimental studies of CVD microreactor technology are slow and expensive. Analytical solution of the governing equations is impossible due to the complexity of intertwined non-linear physical and chemical processes. Computer simulation is the most effective tool for design and optimization of microreactors. Our computational fluid dynamics model employs mass, momentum and energy balance equations for a laminar transient flow of a chemically reacting gas mixture at low Reynolds number. Simulation results show the influence of microreactor configuration and process parameters on SiO2 deposition rate and uniformity. We simulated three microreactors with the central channel diameter of 5, 10, 20 micrometers, varying gas flow rate in the range of 5-100 microliters per hour and temperature in the range of 300-800 °C. For each microchannel diameter we found an optimal set of process parameters providing the best quality of deposited material. The model will be used for optimization of the microreactor configuration and technological parameters to facilitate the experimental stage of this research.
12. Stomatal sensitivity to vapor pressure deficit and its relationship to hydraulic conductance in Pinus palustris.
PubMed
Addington, Robert N; Mitchell, Robert J; Oren, Ram; Donovan, Lisa A
2004-05-01
We studied the response of stomatal conductance at leaf (gS) and canopy (GS) scales to increasing vapor pressure deficit (D) in mature Pinus palustris Mill. (longleaf pine) growing in a sandhill habitat in the coastal plain of the southeastern USA. Specifically, we determined if variation in the stomatal response to D was related to variation in hydraulic conductance along the soil-to-leaf pathway (KL) over the course of a growing season. Reductions in KL were associated with a severe growing season drought that significantly reduced soil water content (theta) in the upper 90-cm soil profile. Although KL recovered partially following the drought, it never reached pre-drought values. Stomatal sensitivity to D was well correlated with maximum gS at low D at both leaf and canopy scales, and KL appeared to influence this response by controlling maximum gS. Our results are consistent with the hypothesis that stomatal response to D occurs to regulate minimum leaf water potential, and that the sensitivity of this response is related to changes in whole-plant hydraulics. PMID:14996660
13. The Evolution of Mechanisms Driving the Stomatal Response to Vapor Pressure Deficit1[OPEN
PubMed Central
McAdam, Scott A.M.; Brodribb, Timothy J.
2015-01-01
Stomatal responses to vapor pressure deficit (VPD) are a principal means by which vascular land plants regulate daytime transpiration. While much work has focused on characterizing and modeling this response, there remains no consensus as to the mechanism that drives it. Explanations range from passive regulation by leaf hydration to biochemical regulation by the phytohormone abscisic acid (ABA). We monitored ABA levels, leaf gas exchange, and water status in a diversity of vascular land plants exposed to a symmetrical, mild transition in VPD. The stomata in basal lineages of vascular plants, including gymnosperms, appeared to respond passively to changes in leaf water status induced by VPD perturbation, with minimal changes in foliar ABA levels and no hysteresis in stomatal action. In contrast, foliar ABA appeared to drive the stomatal response to VPD in our angiosperm samples. Increased foliar ABA level at high VPD in angiosperm species resulted in hysteresis in the recovery of stomatal conductance; this was most pronounced in herbaceous species. Increased levels of ABA in the leaf epidermis were found to originate from sites of synthesis in other parts of the leaf rather than from the guard cells themselves. The transition from a passive regulation to ABA regulation of the stomatal response to VPD in the earliest angiosperms is likely to have had critical implications for the ecological success of this lineage. PMID:25637454
14. Numerical study of two-phase flows in porous media : extraction of a capillary pressure saturation curve free from boundary effects
Fiorentino, Eve-Agnès; Moura, Marcel; Jørgen Måløy, Knut; Toussaint, Renaud; Schäfer, Gerhard
2015-04-01
The capillary pressure saturation relationship is a key element in the resolution of hydrological problems that involve the closure partial-flow Darcy relations. This relationship is derived empirically, and the two typical curve fitting equations that are used to describe it are the Brooks-Corey and Van Genüchten models. The question we tackle is the influence of the boundary conditions of the experimental set-up on the measurement of this retention curve, resulting in a non physical pressure-saturation curve in porous media, due the "end effects" phenomenon. In this study we analyze the drainage of a two-phase flow from a quasi 2D random porous medium, and compare it to simulations arising from an invasion percolation algorithm. The medium is initially saturated with a viscous fluid, and as the pressure difference is gradually increased, air penetrates from an open inlet, thus displacing the fluid which leaves the system from the outlet in the opposing side. In the initial stage, the liquid-air interface evolves from a planar front to the fractal structure characteristic of slow drainage processes, giving the initial downward curvature. In the final stage, air spreads all along the filter, and must reach narrower pores, calling for an increase of the pressure difference, reflected by the final upward curvature. Measuring the pressure-saturation (P-S) law in subwindows located at the inlet, outlet and middle of the network, we emphasize that these boundary effects are the fact of a fraction of pores that is likely to be negligible for high scale systems. We analyze the value of the air saturation at the end of the experiment for a series of simulations with different sample geometries : we observe that this saturation converges to a plateau when the distance between the inlet ant outlet increases, and that the value of this plateau is determined by the distance between the lateral walls. We finally show that the pressure difference between the two phases converges to a value determined by the cumulative density function of the capillary pressures distribution, until the filter is reached, triggering the upward curvature of the curve. The boundary effects bring unphysical features to the P-S curve, that may be present in the results of widely used core sample tests. Far from the boundaries, the relationship between pressure and saturation shows a flat profile dominated by a unique constant determined by the capillary pressure distribution of the medium.
15. Beer Law Constants and Vapor Pressures of HgI2 over HgI2(s,l)
NASA Technical Reports Server (NTRS)
Su, Ching-Hua; Zhu, Shen; Ramachandran, N.; Burger, A.; Whitaker, Ann F. (Technical Monitor)
2001-01-01
The optical absorption spectra of the vapor phase over HgI2(s,l) were measured for wavelengths between 200 and 600 nm. The spectra show that the sample sublimed congruently into HgI2 with no Hg or I2 absorption spectrum observed. The Beer's Law constants for 15 wavelengths between 200 and 440 nm were determined. From these constants the vapor pressure of H912, P, was established as a function of temperatures for the liquid and the solid Beta-phases. The expressions correspond to the enthalpies of vaporization and sublimation of 15.30 and 20.17 Kcal/mole, respectively, for the liquid and the Beta-phase HgI2. The difference in the enthalpies gives an enthalpy of fusion of 4.87 Kcal/mole and the intersection of the two expressions gives a melting point of 537 K.
16. Extrapolation of IAPWS-IF97 data: The saturation pressure of H2O in the critical region
Ustyuzhanin, E. E.; Ochkov, V. F.; Shishakov, V. V.; Rykov, A. V.
2015-11-01
Some literature sources and web sites are analyzed in this report. These sources contain an information about thermophysical properties of H2O including the vapor pressure Ps. (Ps,T)-data have a form of the international standard tables named as “IAPWS-IF97 data”. Our analysis shows that traditional databases represent (Ps,T)-data at t > 0.002, here t = (Tc ‑ T)/Tc is a reduced temperature. It is an interesting task to extrapolate IAPWS-IF97 data in to the critical region and to get (Ps,T)-data at t < 0.002. We have considered some equations Ps(t) and estimated that previous models do not follow to the degree laws of the scaling theory (ST). A combined model (CM) is chosen as a form, F(t,D,B), to express a function ln(Ps/Pc) in the critical region including t < 0.002, here D = (α, Pc,Tc,...) are critical characteristics, B are adjustable coefficients. CM has a combined structure with scaling and regular parts. The degree laws of ST are taken into account to elaborate F(t, D, B). Adjustable coefficients (B) are determined by fitting CM to input (Ps,T)-points those belong to IAPWS-IF97 data. Application results are got with a help of CM in the critical region including values of the first and the second derivatives for Ps(T). Some models Ps(T) are compared with CM.
17. Control of Photosynthesis and Stomatal Conductance in Ricinus communis L. (Castor Bean) by Leaf to Air Vapor Pressure Deficit 1
PubMed Central
Dai, Ziyu; Edwards, Gerald E.; Ku, Maurice S. B.
1992-01-01
Castor bean (Ricinus communis L.) has a high photosynthetic capacity under high humidity and a pronounced sensitivity of photosynthesis to high water vapor pressure deficit (VPD). The sensitivity of photosynthesis to varying VPD was analyzed by measuring CO2 assimilation, stomatal conductance (gs), quantum yield of photosystem II (?II), and nonphotochemical quenching of chlorophyll fluorescence (qN) under different VPD. Under both medium (1000) and high (1800 micromoles quanta per square meter per second) light intensities, CO2 assimilation decreased as the VPD between the leaf and the air around the leaf increased. The gs initially dropped rapidly with increasing VPD and then showed a slower decrease above a VPD of 10 to 20 millibars. Over a temperature range from 20 to 40C, CO2 assimilation and gs were inhibited by high VPD (20 millibars). However, the rate of transpiration increased with increasing temperature at either low or high VPD due to an increase in gs. The relative inhibition of photosynthesis under photorespiring (atmospheric levels of CO2 and O2) versus nonphotorespiring (700 microbars CO2 and 2% O2) conditions was greater under high VPD (30 millibars) than under low VPD (3 millibars). Also, with increasing light intensity the relative inhibition of photosynthesis by O2 increased under high VPD, but decreased under low VPD. The effect of high VPD on photosynthesis under various conditions could not be totally accounted for by the decrease in the intercellular CO2 in the leaf (Ci) where Ci was estimated from gas exchange measurements. However, estimates of Ci from measurements of ?II and qN suggest that the decrease in photosynthesis and increase in photorespiration under high VPD can be totally accounted for by stomatal closure and a decrease in Ci. The results also suggest that nonuniform closure of stomata may occur in well-watered plants under high VPD, causing overestimates in the calculation of Ci from gas exchange measurements. Under low VPD, 30C, high light, and saturating CO2, castor bean (C3 tropical shrub) has a rate of photosynthesis (61 micromoles CO2 per square meter per second) that is about 50% higher than that of tobacco (C3) or maize (C4) under the same conditions. The chlorophyll content, total soluble protein, and ribulose-1,5-bisphosphate carboxylase/oxygenase level on a leaf area basis were much higher in castor bean than in maize or tobacco, which accounts for its high rates of photosynthesis under low VPD. PMID:16669054
18. Volatile times for the very first ionic liquid: understanding the vapor pressures and enthalpies of vaporization of ethylammonium nitrate.
PubMed
Emel'yanenko, Vladimir N; Boeck, Gisela; Verevkin, Sergey P; Ludwig, Ralf
2014-09-01
A hundred years ago, Paul Walden studied ethyl ammonium nitrate (EAN), which became the first widely known ionic liquid. Although EAN has been investigated extensively, some important issues still have not been addressed; they are now tackled in this communication. By combining experimental thermogravimetric analysis with time of flight mass spectrometry (TGA-ToF-MS) and transpiration method with theoretical methods, we clarify the volatilisation of EAN from ambient to elevated temperatures. It was observed that up to 419?K, EAN evaporates as contact-ion pairs leading to very low vapour pressures of a few Pascal. Starting from 419?K, the decomposition to nitric acid and ethylamine becomes more thermodynamically favourable than proton transfer. This finding was supported by DFT calculations, which provide the free energies of all possible gas-phase species, and show that neutral molecules dominate over ion pairs above 500?K, an observation that is in nearly prefect agreement with the experimental boiling point of 513?K. This result is crucial for the ongoing practical applications of protic ionic liquids such as electrolytes for batteries and fuel cells because, in contrast to high-boiling conventional solvents, EAN exhibits no significant vapour pressure below 419?K and this property fulfils the requirements for the thermal behaviour of safe electrolytes. Overall, EAN shows the same barely measurable vapour pressures as typical aprotic ionic liquids at temperatures only 70?K lower. PMID:25077820
19. Sulfur concentration of martian basalts at sulfide saturation at high pressures and temperatures - Implications for deep sulfur cycle on Mars
Ding, Shuo; Dasgupta, Rajdeep; Tsuno, Kyusei
2014-04-01
To constrain sulfur concentration at sulfide saturation (SCSS) of martian magmas at mantle conditions, we simulated basalt-sulfide melt equilibria using two synthesized meteorite compositions, i.e., Yamato980459 and NWA2990 in both anhydrous and hydrous conditions at 1-5 GPa and 1500-1700 C. Our experimental results show that SCSS decreases with increasing pressure and increases with increasing temperature. Based on our experimental SCSS and those from previous low-pressure experiments on high-FeO? martian basalts, we developed a parameterization to predict martian basalt SCSS as a function of depth, temperature, and melt composition. Our model suggests that sulfur contents as high as 3500-4300 ppm can be transferred from the martian mantle to the martian exogenic system, and sulfur-rich gases might have caused the greenhouse conditions during the late Noachian. However, modeling of the behavior of sulfur along the liquid line of descent of a primitive martian basalt suggests that a fraction of the magmatic sulfur could precipitate as sulfides in the cumulates during cooling and fractional crystallization of basaltic magmas. Furthermore, the latter case is consistent with the S concentration of martian meteorites, which reflect variable amount of trapped liquid in cumulus mineral assemblage. Furthermore, our model predicts an average S storage capacity of 5700 ppm for the martian magma ocean, whereas the same for Earth is only ?860 ppm. Lastly, high SCSS of martian magma ocean and its inverse correlation with depth along the mantle liquidus could have triggered a sulfur pump where the post-core-formation magma ocean of Mars would gain sulfur through interaction with SO2/H2S rich nascent atmosphere.
20. The dissolution of calcite in CO2-saturated solutions at 25C and 1 atmosphere total pressure
USGS Publications Warehouse
Plummer, L. Neil; Wigley, T.M.L.
1976-01-01
The dissolution of Iceland spar in CO2-saturated solutions at 25C and 1 atm total pressure has been followed by measurement of pH as a function of time. Surface concentrations of reactant and product species have been calculated from bulk fluid data using mass transport theory and a model that accounts for homogeneous reactions in the bulk fluid. The surface concentrations are found to be close to bulk solution values. This indicates that calcite dissolution under the experimental conditions is controlled by the kinetics of surface reaction. The rate of calcite dissolution follows an empirical second order relation with respect to calcium and hydrogen ion from near the initial condition (pH 3.91) to approximately pH 5.9. Beyond pH 5.9 the rate of surface reaction is greatly reduced and higher reaction orders are observed. Calculations show that the rate of calcite dissolution in natural environments may be influenced by both transport and surface-reaction processes. In the absence of inhibition, relatively short times should be sufficient to establish equilibrium.
1. Capillary pressure and saturation relations for supercritical CO2 and brine in sand: High-pressure Pc(Sw) controller/meter measurements and capillary scaling predictions
Tokunaga, Tetsu K.; Wan, Jiamin; Jung, Jong-Won; Kim, Tae Wook; Kim, Yongman; Dong, Wenming
2013-08-01
In geologic carbon sequestration, reliable predictions of CO2 storage require understanding the capillary behavior of supercritical (sc) CO2. Given the limited availability of measurements of the capillary pressure (Pc) dependence on water saturation (Sw) with scCO2 as the displacing fluid, simulations of CO2 sequestration commonly rely on modifying more familiar air/H2O and oil/H2O Pc(Sw) relations, adjusted to account for differences in interfacial tensions. In order to test such capillary scaling-based predictions, we developed a high-pressure Pc(Sw) controller/meter, allowing accurate Pc and Sw measurements. Drainage and imbibition processes were measured on quartz sand with scCO2-brine at pressures of 8.5 and 12.0 MPa (45°C), and air-brine at 21°C and 0.1 MPa. Drainage and rewetting at intermediate Sw levels shifted to Pc values that were from 30% to 90% lower than predicted based on interfacial tension changes. Augmenting interfacial tension-based predictions with differences in independently measured contact angles from different sources led to more similar scaled Pc(Sw) relations but still did not converge onto universal drainage and imbibition curves. Equilibrium capillary trapping of the nonwetting phases was determined for Pc = 0 during rewetting. The capillary-trapped volumes for scCO2 were significantly greater than for air. Given that the experiments were all conducted on a system with well-defined pore geometry (homogeneous sand), and that scCO2-brine interfacial tensions are fairly well constrained, we conclude that the observed deviations from scaling predictions resulted from scCO2-induced decreased wettability. Wettability alteration by scCO2 makes predicting hydraulic behavior more challenging than for less reactive fluids.
2. Aqueous solubilities, vapor pressures, and 1-octanol-water partition coefficients for C9-C14 linear alkylbenzenes
USGS Publications Warehouse
Sherblom, P.M.; Gschwend, P.M.; Eganhouse, R.P.
1992-01-01
Measurements and estimates of aqueous solubilities, 1-octanol-water partition coefficients (Kow), and vapor pressures were made for 29 linear alkylbenzenes having alkyl chain lengths of 9-14 carbons. The ranges of values observed were vapor pressures from 0.002 to 0.418 Pa, log Kow, from 6.83 to 9.95, and aqueous solubilities from 4 to 38 nmol??L-1. Measured values exhibited a relationship to both the alkyl chain length and the position of phenyl substitution on the alkyl chain. Measurement of the aqueous concentrations resulting from equilibration of a mixture of alkylbenzenes yielded higher than expected values, indicating cosolute or other interactive effects caused enhanced aqueous concentrations of these compounds. ?? 1992 American Chemical Society.
3. Vapor pressure deficit controls on fire ignition and fire spread in boreal forest ecosystems
Sedano, F.; Randerson, J. T.
2014-01-01
Climate-driven changes in the fire regime within boreal forest ecosystems are likely to have important effects on carbon cycling and species composition. In the context of improving fire management options and developing more realistic scenarios of future change, it is important to understand how meteorology regulates different fire processes, including ignition, daily fire spread rates, and cumulative annual burned area. Here we combined MODIS active fires (MCD14ML), MODIS imagery (MOD13A1) and ancillary historic fire perimeter information to produce a dataset of daily fire spread maps of Alaska for the period 2002-2011. This approach provided a spatial and temporally continuous representation of fire progression and a precise identification of ignition and extinction locations and dates for each wildfire. The fire-spread maps were analyzed together with daily vapor pressure deficit (VPD) observations from the North American Regional Reanalysis (NARR) and lightning strikes from the Alaska Lightning Detection Network (ALDN). We found a significant relationship between daily VPD and probability that a lightning strike would develop into a fire ignition. In the first 5 days after ignition, above average VPD increased the probability that fires would grow to large or very large sizes. Strong relationships also were identified between VPD and burned area at several levels of temporal and spatial aggregation. As a consequence of regional coherence in meteorology, ignition, daily fire spread rates, and fire extinction events were often synchronized across different fires in interior Alaska. At a regional scale, the sum of positive VPD anomalies during the fire season was positively correlated with annual burned area during the NARR era (1979-2011; R2 = 0.45). Some of the largest fires we mapped had slow initial growth, indicating opportunities may exist for suppression efforts to adaptively manage these forests for climate change. The results of our spatiotemporal analysis provide new information about temporal and spatial dynamics of wildfires and have implications for modeling the terrestrial carbon cycle.
4. Low temperature atmospheric pressure chemical vapor deposition of group 14 oxide films
SciTech Connect
Hoffman, D.M.; Atagi, L.M. |; Chu, Wei-Kan; Liu, Jia-Rui; Zheng, Zongshuang; Rubiano, R.R.; Springer, R.W.; Smith, D.C.
1994-06-01
Depositions of high quality SiO{sub 2} and SnO{sub 2} films from the reaction of homoleptic amido precursors M(NMe{sub 2})4 (M = Si,Sn) and oxygen were carried out in an atmospheric pressure chemical vapor deposition r. The films were deposited on silicon, glass and quartz substrates at temperatures of 250 to 450C. The silicon dioxide films are stoichiometric (O/Si = 2.0) with less than 0.2 atom % C and 0.3 atom % N and have hydrogen contents of 9 {plus_minus} 5 atom %. They are deposited with growth rates from 380 to 900 {angstrom}/min. The refractive indexes of the SiO{sub 2} films are 1.46, and infrared spectra show a possible Si-OH peak at 950 cm{sup {minus}1}. X-Ray diffraction studies reveal that the SiO{sub 2} film deposited at 350C is amorphous. The tin oxide films are stoichiometric (O/Sn = 2.0) and contain less than 0.8 atom % carbon, and 0.3 atom % N. No hydrogen was detected by elastic recoil spectroscopy. The band gap for the SnO{sub 2} films, as estimated from transmission spectra, is 3.9 eV. The resistivities of the tin oxide films are in the range 10{sup {minus}2} to 10{sup {minus}3} {Omega}cm and do not vary significantly with deposition temperature. The tin oxide film deposited at 350C is cassitterite with some (101) orientation.
5. Experiments on two-phase flow in a quasi-2D porous medium: investigation of boundary effects in the measurement of pressure-saturation relationships
Moura, Marcel; Fiorentino, Eve-Agnès; Jørgen Måløy, Knut; Toussaint, Renaud; Schäfer, Gerhard
2015-04-01
We have performed two-phase flow experiments to analyze the drainage from a quasi-2D random porous medium. The medium is transparent, which allows for the visualization of the invasion pattern during the flow and is initially fully saturated with a viscous fluid (a dyed glycerol-water mix). As the pressure in the fluid is gradually reduced, air penetrates from an open inlet, thus displacing the fluid which leaves the system from the outlet in the opposite side. A feedback mechanism was devised to control the experiment: the capillary pressure (difference in pressure between the non-wetting and wetting phases) is continuously increased to be just above the threshold value necessary to drive the invasion process. This mechanism is intended to keep the invasion process slow, in the so-called capillary regime, where capillary forces dominate the dynamics. Pressure measurements and pictures of the flow are recorded and the pressure-saturation relationship is computed. The effects of the boundary conditions to this quantity are verified experimentally by repeatedly performing the analysis using porous media of different sizes. We show that some features of the pressure-saturation curve are strongly affected by boundary effects. The invasion close to the inlet and outlet of the model are particularly influenced by the boundaries and this is reflected in the phases of pressure building up in the pressure-saturation curves, in the beginning and end of the invasion process. Conversely, at the central part of the model (away from the boundaries), the invasion process happens at an essentially constant capillary pressure, which is reflected as a plateau in the pressure-saturation curve. Additionally, the use of a high-resolution camera allows us to analyze the images down to the pore scale. We can directly obtain a distribution of pore-throat sizes in the model (and their associated capillary pressure thresholds) and divide it into distributions of invaded / non-invaded pores. By measuring these separate distributions dynamically, we can show how they evolve with the invasion process.
6. On-line coating of glass with tin oxide by atmospheric pressure chemical vapor deposition.
SciTech Connect
Allendorf, Mark D.; Sopko, J.F. (PPF Industries, Pittsburgh, PA); Houf, William G.; Chae, Yong Kee; McDaniel, Anthony H.; Li, M. (PPF Industries, Pittsburgh, PA); McCamy, J.W.
2006-11-01
Atmospheric pressure chemical vapor deposition (APCVD) of tin oxide is a very important manufacturing technique used in the production of low-emissivity glass. It is also the primary method used to provide wear-resistant coatings on glass containers. The complexity of these systems, which involve chemical reactions in both the gas phase and on the deposition surface, as well as complex fluid dynamics, makes process optimization and design of new coating reactors a very difficult task. In 2001 the U.S. Dept. of Energy Industrial Technologies Program Glass Industry of the Future Team funded a project to address the need for more accurate data concerning the tin oxide APCVD process. This report presents a case study of on-line APCVD using organometallic precursors, which are the primary reactants used in industrial coating processes. Research staff at Sandia National Laboratories in Livermore, CA, and the PPG Industries Glass Technology Center in Pittsburgh, PA collaborated to produce this work. In this report, we describe a detailed investigation of the factors controlling the growth of tin oxide films. The report begins with a discussion of the basic elements of the deposition chemistry, including gas-phase thermochemistry of tin species and mechanisms of chemical reactions involved in the decomposition of tin precursors. These results provide the basis for experimental investigations in which tin oxide growth rates were measured as a function of all major process variables. The experiments focused on growth from monobutyltintrichloride (MBTC) since this is one of the two primary precursors used industrially. There are almost no reliable growth-rate data available for this precursor. Robust models describing the growth rate as a function of these variables are derived from modeling of these data. Finally, the results are used to conduct computational fluid dynamic simulations of both pilot- and full-scale coating reactors. As a result, general conclusions are reached concerning the factors affecting the growth rate in on-line APCVD reactors. In addition, a substantial body of data was generated that can be used to model many different industrial tin oxide coating processes. These data include the most extensive compilation of thermochemistry for gas-phase tin-containing species as well as kinetic expressions describing tin oxide growth rates over a wide range of temperatures, pressures, and reactant concentrations.
7. Fabrication of Ferrite Thin Film using Low Pressure Metalorganic Chemical Vapor Deposition
Yang, Yi
This thesis is based on the research work on the multiferroic material fabrications using low pressure metalorganic chemical vapor deposition (MOCVD). Multiferroic material refers to the ones who have two or more ferroic properties, like ferroelectricity, ferromagnetism, ferroelasticity and ferrotoroidicity. Extensive research findings focused on pure nano scale thin films and composites those were related to presenting both ferroelectricity and ferromagnetism coupling within the material. BiFeO3 (BFO) was known to be the only single phase multiferroic material which exhibited magnetoelectric (ME) coupling effect at room temperature. This coupling effect provided an extra degree of freedom for designs of whole new devices and applications never thought to be possible before. Recently, large ME effect was found in its thin epitaxial-strained films. However, very few papers reported the CVD techniques for depositing BFO thin films so far. Most of these reports used direct liquid injection method to deliver the organometallic reactants during the CVD process (ie. DLICVD). Here, we introduced a novel liquid iron precursor, n-butylferrocene, delivered into the reactor by heating the precursor canisters at certain temperatures for growing BFO thin films. Other crucial MOCVD conditions (reactor's pressure, reactor's temperature, substrates...) were also discussed and optimized. Characterizations for the film composition, crystallinity, ferroelectricity, ferromagnetism and the magneto-dielectric coupling effect were analyzed in detail. The results confirmed that BFO film had multiferroic properties and could be potentially used in future tunable high-frequency devices. Although single-phase BFO exhibited ME effect, this suffered from problems such as current leakages, weak ME coupling and low ordering temperatures. Doping or ion substitution was a limited way to enhance the ME property since the compounds had definite compositions. Therefore, heterostructures such as bilayered/multilayered thin films, nanoparticles/nanopillars embedded in different materials and nanowires became more promising for the future on-chip integration applications because the coupling in such structures was many orders of magnitude stronger. Another research scientists interested in was the heterostructural magnetostrictive NiFe2O4 (NFO) with piezoelectric materials. NFO was a promising magnetic phase for ME heterostructures due to its low anisotropy, high permeability with high resistivity, low eddy current losses and smaller coercive field. In this study, the nickel ferrite thin films had been deposited using computer controlled MOCVD setup in both co-deposition mode and cyclic-deposition mode. Conditions for CVD process were discussed and optimized for growing NFO thin film. The thin films showed NFO composition, uniformity in chemical states and thickness, trevorite crystalline form, free from carbon contamination and similar magnetic property as other literature reported.
8. Effusion Cell Measurements of the Vapor Pressure of Cobalt at Temperatures up to 2000K; Comparisons with Iron and Nickel
NASA Technical Reports Server (NTRS)
Nuth, J. A.; Ferguson, F. T.; Johnson, N. M.
2004-01-01
It has become increasingly clear over the past decade that high temperature processes played important roles in the Primitive Solar Nebula. Unfortunately, basic data, such as the vapor pressures of Fe, Ni, Co or SiO have not been measured over the appropriate temperature range (near T approx. 2000K), but must be extrapolated from lower temperature measurements often made more than 50 years ago. The extrapolation of the available data to higher temperatures can be quite complex (e.g., see [1] for SiO vapor pressures) and can depend on other factors such as the oxygen fugacity or the presence of hydrogen gas not accounted for in the original measurements. Moreover, modern technology has made possible more accurate measurements of such quantities over a wider temperature range. We have acquired a commercial Thermo-Cahn Thermogravimetric system capable of vacuum operation to 1700C and measurement of a 10g change in sample mass using up to a 100g sample, with microgram accuracy. With this new system we have initiated a series of basic vapor pressure measurements on simple metals such as Fe[2] and Ni[3] with the intention to extend such measurements to more complex systems once we gain sufficient experience.
9. Evaluation of Vapor Pressure and Ultra-High Vacuum Tribological Properties of Ionic Liquids (2) Mixtures and Additives
NASA Technical Reports Server (NTRS)
Morales, Wilfredo; Koch, Victor R.; Street, Kenneth W., Jr.; Richard, Ryan M.
2008-01-01
Ionic liquids are salts, many of which are typically viscous fluids at room temperature. The fluids are characterized by negligible vapor pressures under ambient conditions. These properties have led us to study the effectiveness of ionic liquids containing both organic cations and anions for use as space lubricants. In the previous paper we have measured the vapor pressure and some tribological properties of two distinct ionic liquids under simulated space conditions. In this paper we will present vapor pressure measurements for two new ionic liquids and friction coefficient data for boundary lubrication conditions in a spiral orbit tribometer using stainless steel tribocouples. In addition we present the first tribological data on mixed ionic liquids and an ionic liquid additive. Post mortem infrared and Raman analysis of the balls and races indicates the major degradation pathway for these two organic ionic liquids is similar to those of other carbon based lubricants, i.e. deterioration of the organic structure into amorphous graphitic carbon. The coefficients of friction and lifetimes of these lubricants are comparable to or exceed these properties for several commonly used space oils.
10. Interactive response of photosynthetic characteristics in Haloxylon ammodendron and Hedysarum scoparium exposed to soil water and air vapor pressure deficits.
PubMed
Gong, Chunmei; Wang, Jiajia; Hu, Congxia; Wang, Junhui; Ning, Pengbo; Bai, Juan
2015-08-01
C4 plants possess better drought tolerance than C3 plants. However, Hedysarum scoparium, a C3 species, is dominant and widely distributed in the desert areas of northwestern China due to its strong drought tolerance. This study compared it with Haloxylon ammodendron, a C4 species, regarding the interactive effects of drought stress and different leaf-air vapor pressure deficits. Variables of interest included gas exchange, the activity levels of key C4 photosynthetic enzymes, and cellular anatomy. In both species, gas exchange parameters were more sensitive to high vapor pressure deficit than to strong water stress, and the net CO2 assimilation rate (An) was enhanced as vapor pressure deficits increased. A close relationship between An and stomatal conductance (gs) suggested that the species shared a similar response mechanism. In H. ammodendron, the activity levels of key C4 enzymes were higher, including those of phosphoenolpyruvate carboxylase (PEPC) and nicotinamide adenine dinucleotide phosphate-malate enzyme (NADP-ME), whereas in H. scoparium, the activity level of nicotinamide adenine dinucleotide-malate enzyme (NAD-ME) was higher. Meanwhile, H. scoparium utilized adaptive structural features, including a larger relative vessel area and a shorter distance from vein to stomata, which facilitated the movement of water. These findings implied that some C4 biochemical pathways were present in H. scoparium to respond to environmental challenges. PMID:26257361
11. High-pressure vapor-liquid equilibria for propane + 2-butanol, propylene + 2-butanol, and propane + 2-butanol + 2-propanol
SciTech Connect
Gros, H.P.; Zabaloy, M.S.; Brignole, E.A.
1996-03-01
The use of dual effect solvents (near critical extractant and high-pressure water entrainer), for the recovery and dehydration of alcohols from dilute aqueous solutions, has been proposed by Brignole et al. (1987). The present work is part of an experimental program undertaken to confirm the applicability of light hydrocarbons for this separation problem. Vapor-liquid equilibria have been measured for propane + 2-butanol, propylene + 2-butanol, and propane + 2-butanol + 2-propanol in the temperature range of (328.1 to 368.1) K and at pressures up to 44.45 bar. The data were correlated using a group contribution equation of state for associating mixtures.
12. Measurements of seismic attenuation and transient fluid pressure in partially saturated Berea sandstone: evidence of fluid flow on the mesoscopic scale
Tisato, Nicola; Quintal, Beatriz
2013-10-01
A novel laboratory technique is proposed to investigate wave-induced fluid flow on the mesoscopic scale as a mechanism for seismic attenuation in partially saturated rocks. This technique combines measurements of seismic attenuation in the frequency range from 1 to 100 Hz with measurements of transient fluid pressure as a response of a step stress applied on top of the sample. We used a Berea sandstone sample partially saturated with water. The laboratory results suggest that wave-induced fluid flow on the mesoscopic scale is dominant in partially saturated samples. A 3-D numerical model representing the sample was used to verify the experimental results. Biot's equations of consolidation were solved with the finite-element method. Wave-induced fluid flow on the mesoscopic scale was the only attenuation mechanism accounted for in the numerical solution. The numerically calculated transient fluid pressure reproduced the laboratory data. Moreover, the numerically calculated attenuation, superposed to the frequency-independent matrix anelasticity, reproduced the attenuation measured in the laboratory in the partially saturated sample. This experimental-numerical fit demonstrates that wave-induced fluid flow on the mesoscopic scale and matrix anelasticity are the dominant mechanisms for seismic attenuation in partially saturated Berea sandstone.
13. Determination of vapor-liquid equilibrium data in microfluidic segmented flows at elevated pressures using Raman spectroscopy.
PubMed
Luther, Sebastian K; Stehle, Simon; Weihs, Kristian; Will, Stefan; Braeuer, Andreas
2015-08-18
A fast, noninvasive, and efficient analytical measurement strategy for the characterization of vapor-liquid equilibria (VLE) is presented, which is based on phase (state of matter) selective Raman spectroscopy in multiphase flows inside microcapillay systems (MCS). Isothermal VLE data were measured in binary and ternary mixtures composed of acetone, water, carbon dioxide or nitrogen at elevated pressures up to 10 MPa and temperatures up to 333 K. For validation, the obtained data were compared with literature data and reference measurements in a high-pressure variable volume cell. Additionally, the mixtures were investigated at temperatures and pressures where no data is available in literature to extend the high-pressure VLE database. PMID:26171990
14. Influence of the synthesis conditions of silicon nanodots in an industrial low pressure chemical vapor deposition reactor
Cocheteau, V.; Scheid, E.; Mur, P.; Billon, T.; Caussat, B.
2008-03-01
Experiments conducted in an industrial tubular low pressure chemical vapor deposition (LPCVD) reactor have demonstrated the reproducibility and spatial uniformity of silicon nanodots (NDs) area density and mean radius. The wafer to wafer uniformity was satisfactory (density and radius standard deviations <10%) for the whole conditions tested except for low silane flow rates, high silane partial pressures and short run durations (<20 s). Original synthesis conditions have then been searched to reach both excellent wafer to wafer uniformities along the industrial load of wafers and high NDs densities. From previous results, it was deduced that the key was to markedly increase run duration in decreasing temperature and in increasing silane pressure. At 773 K, run durations as long as 180 and 240 s have thus allowed to reach NDs densities respectively equal to 9 10 11 and 6.5 10 11 NDs/cm 2 for the two highest silane pressures tested in the range 60-150 Pa.
15. Change in form of palladium plate during one-sided saturation with hydrogen: I. Effect of rate of increase in gaseous-hydrogen pressure
Gol'tsova, M. V.; Lyubimenko, E. N.
2012-11-01
The effect of the rate of gaseous-hydrogen pressure rise on changes in the form of a palladium plate has been studied during its one-sided saturation with hydrogen in the α region of the Pd-H system under isothermal conditions at temperatures of 170-320°C. The dependences of the principal characteristics of hydrogen-induced changes in the form of a plate on the rate of gaseous hydrogen pressure rise were determined. The decrease in the rate of increase in hydrogen pressure was found to lead to a decrease in the maximum bend of the plate.
16. Speciation of High-Pressure Carbon-Saturated COH Fluids at Buffered fO2 Conditions: An Experimental Approach
Tumiati, S.; Tiraboschi, C.; Recchia, S.; Poli, S.
2014-12-01
The quantitative assessment of species in COH fluids is crucial in modelling mantle processes. For instance, H2O/CO2 ratio in the fluid phase influences the location of the solidus and of carbonation/decarbonation reactions in peridotitic systems . In the scientific literature, the speciation of COH fluids has been generally assumed on the basis of thermodynamic calculations using equations of state of simple H2O-non-polar gas systems (e.g., H2O-CO2-CH4). Only few authors dealt with the experimental determination of high-pressure COH fluid species at different conditions, using diverse experimental and analytical approaches (e.g., piston cylinder+capsule-piercing+gas-chromatography/mass-spectrometry; cold-seal+silica glass capsules+Raman). We performed experiments on COH fluids using a capsule-piercing device coupled with a quadrupole mass spectrometry. This type of analyzer ensures superior performances in terms of selectivity of molecules to be detected, high acquisition rates and extended linear response range. Experiments were carried out in a rocking piston cylinder apparatus at pressure of 1 GPa and temperatures from 800 to 900C. Carbon-saturated fluids were generated through the addition of oxalic acid dihydrate and graphite. Single/double capsules and different packing materials (BN and MgO) were used to evaluate the divergence from the thermodynamic speciation model. Moreover, to assess the effect of solutes on COH fluid speciation we also performed a set of experiments adding synthetic forsterite to the charge. To determine the speciation we assembled a capsule-piercing device that allows to puncture the capsule in a gas-tight vessel at 80C. The extraction Teflon vessel is composed of a base part, where the capsule is allocated on a steel support, and a top part where a steel drill is mounted. To release the quenched fluids from the capsule, the base part of vessel is hand-tighten to the top part, allowing the steel pointer to pierce the capsule. The evolved gases are then convoyed to a quadrupole mass spectrometer through a heated line to avoid the condensation of water. Our results suggest that fluid speciation can diverge considerably compared to the thermodynamic model depending on the experimental strategies adopted and on the presence of solutes in complex COH systems.
17. Effect of Addition of Water Vapor on OH Radical Concentration in an Atmospheric Pressure Microwave Argon Plasma Jet
Srivastava, Nimisha; Wang, Chuji; Harper, Sterling
2010-11-01
In recent years, role of reactive plasma species such as OH and O in various plasma treatments and combustion applications are topics of investigation and debate. Quantitative study of OH radicals in atmospheric plasma jets can contribute to the better understanding of OH generation mechanism and to optimization of plasma treatment processing and plasma source designs. A 2.45 GHz microwave plasma source was used to study the effect on OH radical generation in an argon atmospheric pressure plasma jet with addition of H2O vapor. OH radical number densities were measured along the plasma jet axis using UV cavity ringdown spectroscopy of OH (A--X) (1 -- 0) band at 308 nm. Addition of water vapor results in reduction of plasma column jet length and increases gas temperature. Optical emission spectroscopy clearly shows that dominant reactive species in pure Ar plasma jet changed from N2 to OH with the addition of water vapor. The absolute number densities of OH varied along the jet axis from 7.4x10^14 to 3.7x10^16, 4.3x10^14 to 5.0x10^16, and 4.6x10^14 to 3.4x10^16 molecule/cm^3 for the addition of 0 ppm, 4 ppm, and 7 ppm water vapor, respectively.
18. Vapor pressures and evaporation coefficients for melts of ferromagnesian chondrule-like compositions
Fedkin, A. V.; Grossman, L.; Ghiorso, M. S.
2006-01-01
To determine evaporation coefficients for the major gaseous species that evaporate from silicate melts, the Hertz-Knudsen equation was used to model the compositions of residues of chondrule analogs produced by evaporation in vacuum by Hashimoto [Hashimoto A. (1983) Evaporation metamorphism in the early solar nebula-evaporation experiments on the melt FeO-MgO-SiO 2-CaO-Al 2O 3 and chemical fractionations of primitive materials. Geochem. J. 17, 111-145] and Wang et al. [Wang J., Davis A. M., Clayton R. N., Mayeda T. K., Hashimoto A. (2001) Chemical and isotopic fractionation during the evaporation of the FeO-MgO-SiO 2-CaO-Al 2O 3-TiO 2 rare earth element melt system. Geochim. Cosmochim. Acta 65, 479-494], in vacuum and in H 2 by Yu et al. [Yu Y., Hewins R. H., Alexander C. M. O'D., Wang J. (2003) Experimental study of evaporation and isotopic mass fractionation of potassium in silicate melts. Geochim. Cosmochim. Acta 67, 773-786], and in H 2 by Cohen et al. [Cohen B. A., Hewins R. H., Alexander C. M. O'D. (2004) The formation of chondrules by open-system melting of nebular condensates. Geochim. Cosmochim. Acta 68, 1661-1675]. Vapor pressures were calculated using the thermodynamic model of Ghiorso and Sack [Ghiorso M. S., Sack R. O. (1995) Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures. Contrib. Mineral. Petrol. 119, 197-212], except for the late, FeO-free stages of the Wang et al. (2001) and Cohen et al. (2004) experiments, where the CMAS activity model of Berman [Berman R. G. (1983) A thermodynamic model for multicomponent melts, with application to the system CaO-MgO-Al 2O 3-SiO 2. Ph.D. thesis, University of British Columbia] was used. From these vapor pressures, evaporation coefficients ( α) were obtained that give the best fits to the time variation of the residue compositions. Evaporation coefficients derived for Fe (g), Mg (g), and SiO (g) from the Hashimoto (1983) experiments are similar to those found by Alexander [Alexander C. M. O'D. (2004) Erratum. Meteoritics Planet. Sci. 39, 163] in his EQR treatment of the same data and also adequately describe the FeO-bearing stages of the Wang et al. (2001) experiments. From the Yu et al. (2003) experiments at 1723 K, αNa = 0.26 ± 0.05, and αK = 0.13 ± 0.02 in vacuum, and αNa = 0.042 ± 0.020, and αK = 0.017 ± 0.002 in 9 × 10 -5 bar H 2. In the FeO-free stages of the Wang et al. (2001) experiments, αMg and αSiO are significantly different from their respective values in the FeO-bearing portions of the same experiments and from the vacuum values obtained at the same temperature by Richter [Richter F. M., Davis A. M., Ebel D. S., Hashimoto A. (2002) Elemental and isotopic fractionation of Type B calcium-, aluminum-rich inclusions: experiments, theoretical considerations, and constraints on their thermal evolution. Geochim. Cosmochim. Acta 66, 521-540] for CMAS compositions much lower in MgO. When corrected for temperature, the values of αMg and αSiO that best describe the FeO-free stages of the Wang et al. (2001) experiments also adequately describe the FeO-free stage of the Cohen et al. (2004) H 2 experiments, but αFe that best describes the FeO-bearing stage of the latter experiment differs significantly from the temperature-corrected value derived from the Hashimoto (1983) vacuum data.
19. Response of effluent-irrigated Eucalyptus grandis and Pinus radiata to salinity and vapor pressure deficits.
PubMed
Myers, B. J.; Benyon, R. G.; Theiveyanathan, S.; Criddle, R. S.; Smith, C. J.; Falkiner, R. A.
1998-01-01
Effects of high vapor pressure deficit (VPD) and soil salinity on growth and physiology of Pinus radiata D. Don and Eucalyptus grandis Hill ex Maiden were studied in a five-year-old plantation irrigated with salt-enhanced effluent (2.2 dS m(-1)) or freshwater (0.2 dS m(-1)) for 14 weeks during spring and summer. Salt was then rapidly leached by over-irrigation with low-salinity effluent. Soil water and salinity, tree water stress, sap flux, substrate carbon conversion efficiency, foliage and stem growth, and foliar cations and chloride were monitored throughout the study. An average of 9 and 1 Mg ha(-1) of salt with an average hydraulic load of 660 and 780 mm was applied to the salt and control plots, respectively. Maximum soil salinity in the root zone was 5.8 and 6.8 dS m(-1) in the eucalypt and pine plots, respectively. Predawn water potential was more than twice as sensitive to increasing salinity in E. grandis as in P. radiata. The salt treatment reduced rates of leaf and stem growth of the eucalypts by 60 to 70% but had no effect on leaf and stem growth of the pines. In the eucalypts, salinity decreased mean leaf area by 26% and increased specific leaf area by 12% compared with control values, indicating less biomass per unit leaf area in the salt treatment. Salinity had no effects on these two parameters in pine. The salt treatment significantly increased mean foliar concentrations of Na and Cl in both species, and of K in the pines. Foliar Na concentration was 6-10 times higher in the eucalypts than in the pines. Lowered water potential and increased Na concentration in the eucalypts in response to salinity resulted in about a 50% reduction in the efficiency of conversion of carbon into biomass; however, three weeks after leaching the salt, there was no significant difference in efficiency of conversion of carbon into biomass between the treatments. Salinity had no effect on water use by eucalypts, but caused a nonsignificant decrease (7%) in water use by pines. As evaporative demand increased, crop factor (transpiration divided by pan evaporation) declined by up to 50 and 60% in the pines and eucalypts, respectively. We conclude that stomatal response to high VPD, not soil salinity, accounts for most of the reduction in summertime water use. PMID:12651343
20. Does Spatial Variation in Soil Characteristics Affect Tree Transpiration Responses to Vapor Pressure Deficit?
Traver, E.; Ewers, B. E.; Loranty, M.; Mackay, D. S.
2006-12-01
Forest canopy transpiration (Ec) both depends on and influences the local and regional atmospheric conditions. Because soil is the source of water for Ec, the soil's chemical and physical properties are also likely to be drivers of transpiration. The objective of this study is to spatially quantify the relationship between the soil's chemical and physical characteristics and Ec across environmental gradients. The two study sites are in northern Wisconsin, in mixed hardwood forest. In one site, the environmental gradient runs from a dry upland dominated by aspen (Populus tremuloides) to a wetland dominated by alders (Alnus rugosa). The second site has little elevational variation, is well-drained, and is dominated by sugar maple (Acer saccharum) bisected by a swath of red pine (Pinus resinosa). Ec data have been collected over three summers on the same set of trees using Granier sensors, while the soil samples were collected in 2006 from the same plots as the measured trees. Both of the approximately 120 m x 120 m plots have been sampled in 10 m x 10 m subplots based on a 3/7 cyclic sampling scheme to maximize spatially explicit information with a minimum number of sampled points. Roughly 150 trees were measured in each plot. We have previously shown an inverse relationship between the spatial autocorrelation of Ec and vapor pressure deficit (D). We thus hypothesize that a significant amount of this relationship can be explained by soil properties. Preliminary analysis of soil data from a representative transect in the aspen site show that soil texture, carbon (C) content, and nitrogen (N) content change along the gradient. From the upland through the wetland, Ec declined significantly, and, while all the soils were a sandy loam, the sand content showed a decreasing trend, while the silt content increased nearly two-fold. Across the same (upland to wetland) gradient, the C:N ratio showed a slightly increasing trend, but the total percentage values of the two elements increased nearly 25 fold: from C of 0.884 and N of 0.060 to C of 22.34 and N of 1.283. We hypothesize that the maple site will show less variability in Ec because of its more uniform soil characteristics. Ongoing work of soil moisture release curves, bulk density, and root biomass will provide additional explanations of the spatial relationships between Ec and D. Our analytical approach, then, provides a first step in explaining the processes behind spatial patterns in transpiration.
1. A combined droplet train and ambient pressure photoemission spectrometer for the investigation of liquid/vapor interfaces
SciTech Connect
Starr, David E.; Wong, Ed K.; Worsnop, Douglas R.; Wilson, Kevin R.; Bluhm, Hendrik
2008-05-01
We describe a combined ambient pressure photoelectron spectroscopy/droplet train apparatus for investigating the nature and heterogeneous chemistry of liquid/vapor interfaces. In this instrument a liquid droplet train with typical droplet diameters from 50...150 {micro}m is produced by a vibrating orifice aerosol generator (VOAG). The droplets are irradiated by soft X-rays (100...1500 eV) in front of the entrance aperture of a differentially pumped electrostatic lens system that transfers the emitted electrons into a conventional hemispherical electron analyzer. The photoemission experiments are performed at background pressures of up to several Torr, which allows the study of environmentally important liquid/vapor interfaces, in particular aqueous solutions, under equilibrium conditions. The exposure time of the droplet surface to the background gases prior to the XPS measurement can be varied, which will allow future kinetic measurements of gas uptake on liquid surfaces. As an example, a measurement of the surface composition of a {chi} = 0.21 aqueous methanol solution is presented. The concentration of methanol at the vapor/liquid interface is enhanced by a factor of about 3 over the bulk value, while the expected bulk value is recovered at depths larger than about 1.5 nm.
2. A combined droplet train and ambient pressure photoemission spectrometer for the investigation of liquid/vapor interfaces.
PubMed
Starr, David E; Wong, Ed K; Worsnop, Douglas R; Wilson, Kevin R; Bluhm, Hendrik
2008-06-01
We describe a combined ambient pressure photoelectron spectroscopy/droplet train apparatus for investigating the nature and heterogeneous chemistry of liquid/vapor interfaces. In this instrument a liquid droplet train with typical droplet diameters from 50-150 mum is produced by a vibrating orifice aerosol generator (VOAG). The droplets are irradiated by soft X-rays (100-1500 eV) in front of the entrance aperture of a differentially pumped electrostatic lens system that transfers the emitted electrons into a conventional hemispherical electron analyzer. The photoemission experiments are performed at background pressures of up to several Torr, which allows the study of environmentally important liquid/vapor interfaces, in particular aqueous solutions, under equilibrium conditions. The exposure time of the droplet surface to the background gases prior to the XPS measurement can be varied, which will allow future kinetic measurements of gas uptake on liquid surfaces. As an example, a measurement of the surface composition of a chi = 0.21 aqueous methanol solution is presented. The concentration of methanol at the vapor/liquid interface is enhanced by a factor of about 3 over the bulk value, while the expected bulk value is recovered at depths larger than about 1.5 nm. PMID:18688373
3. Graphene chemical vapor deposition at very low pressure: The impact of substrate surface self-diffusion in domain shape
SciTech Connect
Cunha, T. H. R.; Ek-Weis, J.; Lacerda, R. G.; Ferlauto, A. S.
2014-08-18
The initial stages of graphene chemical vapor deposition at very low pressures (<10{sup −5 }Torr) were investigated. The growth of large graphene domains (∼up to 100 μm) at very high rates (up to 3 μm{sup 2} s{sup −1}) has been achieved in a cold-wall reactor using a liquid carbon precursor. For high temperature growth (>900 °C), graphene grain shape and symmetry were found to depend on the underlying symmetry of the Cu crystal, whereas for lower temperatures (<900 °C), mostly rounded grains are observed. The temperature dependence of graphene nucleation density was determined, displaying two thermally activated regimes, with activation energy values of 6 ± 1 eV for temperatures ranging from 900 °C to 960 °C and 9 ± 1 eV for temperatures above 960 °C. The comparison of such dependence with the temperature dependence of Cu surface self-diffusion suggests that graphene growth at high temperatures and low pressures is strongly influenced by copper surface rearrangement. We propose a model that incorporates Cu surface self-diffusion as an essential process to explain the orientation correlation between graphene and Cu crystals, and which can clarify the difference generally observed between graphene domain shapes in atmospheric-pressure and low-pressure chemical vapor deposition.
4. Effects of capillarity and vapor adsorption in the depletion of vapor-dominated geothermal reservoirs
SciTech Connect
Pruess, Karsten; O'Sullivan, Michael
1992-01-01
Vapor-dominated geothermal reservoirs in natural (undisturbed) conditions contain water as both vapor and liquid phases. The most compelling evidence for the presence of distributed liquid water is the observation that vapor pressures in these systems are close to saturated vapor pressure for measured reservoir temperatures (White et al., 1971; Truesdell and White, 1973). Analysis of natural heat flow conditions provides additional, indirect evidence for the ubiquitous presence of liquid. From an analysis of the heat pipe process (vapor-liquid counterflow) Preuss (1985) inferred that effective vertical permeability to liquid phase in vapor-dominated reservoirs is approximately 10{sup 17} m{sup 2}, for a heat flux of 1 W/m{sup 2}. This value appears to be at the high end of matrix permeabilities of unfractured rocks at The Geysers, suggesting that at least the smaller fractures contribute to liquid permeability. For liquid to be mobile in fractures, the rock matrix must be essentially completely liquid-saturated, because otherwise liquid phase would be sucked from the fractures into the matrix by capillary force. Large water saturation in the matrix, well above the irreducible saturation of perhaps 30%, has been shown to be compatible with production of superheated steam (Pruess and Narasimhan, 1982). In response to fluid production the liquid phase will boil, with heat of vaporization supplied by the reservoir rocks. As reservoir temperatures decline reservoir pressures will decline also. For depletion of ''bulk'' liquid, the pressure would decline along the saturated vapor pressure curve, while for liquid held by capillary and adsorptive forces inside porous media, an additional decline will arise from ''vapor pressure lowering''. Capillary pressure and vapor adsorption effects, and associated vapor pressure lowering phenomena, have received considerable attention in the geothermal literature, and also in studies related to geologic disposal of heat generating nuclear wastes, and in the drying of porous materials. Geothermally oriented studies were presented by Chicoine et al. (1977), Hsieh and Ramey (1978, 1981), Herkelrath et al. (1983), and Nghiem and Ramey (1991). Nuclear waste-related work includes papers by Herkelrath and O'Neal (1985), Pollock (1986), Eaton and Bixler (1987), Pruess et al. (1990), Nitao (1990), and Doughty and E'ruess (1991). Applications to industrial drying of porous materials have been discussed by Hamiathy (1969) arid Whitaker (1977). This paper is primarily concerned with evaluating the impact of vapor pressure lowering (VPL) effects on the depletion behavior of vapor-dominated reservoirs. We have examined experimental data on vapor adsorption and capillary pressures in an effort to identify constitutive relationships that would be applicable to the tight matrix rocks of vapor-dominated systems. Numerical simulations have been performed to evaluate the impact of these effects on the depletion of vapor-dominated reservoirs.
5. CVD mullite coatings in high-temperature, high-pressure air-H{sub 2}O[Chemical Vapor Deposition
SciTech Connect
Haynes, J.A.; Lance, M.J.; Cooley, K.M.; Ferber, M.K.; Lowden, R.A.; Stinton, D.P.
2000-03-01
Crystalline mullite was deposited by chemical vapor deposition (CVD) onto SiC/SiC composites overlaid with CVD SiC. Specimens were exposed to isothermal oxidation tests in high-pressure air +H{sub 2}O at 1,200 C. Unprotected CVD SiC formed silica scales with a dense amorphous inner layer and a thick, porous, outer layer of cristobalite. Thin coatings ({approximately}2{mu}m) of dense CVD mullite effectively suppressed the rapid oxidation of CVD SiC. No microstructural evidence of mullite volatility was observed under these temperature, pressure, and low-flow-rate conditions. Results of this preliminary study indicate that dense, crystalline, high-purity CVD mullite is stable and protective in low-velocity, high-pressure, moisture-containing environments.
6. Vapor-liquid partitioning of alkaline earth and transition metals in NaCl-dominated hydrothermal fluids: An experimental study from 360 to 465 °C, near-critical to halite saturated conditions
Pester, Nicholas J.; Ding, Kang; Seyfried, William E.
2015-11-01
Multi-phase fluid flow is a common occurrence in magmatic hydrothermal systems; and extensive modeling efforts using currently established P-V-T-x properties of the NaCl-H2O system are impending. We have therefore performed hydrothermal flow experiments (360-465 °C) to observe vapor-liquid partitioning of alkaline earth and first row transition metals in NaCl-dominated source solutions. The data allow extraction of partition coefficients related to the intrinsic changes in both chlorinity and density along the two-phase solvus. The coefficients yield an overall decrease in vapor affinity in the order Cu(I) > Na > Fe(II) > Zn > Ni(II) ⩾ Mg ⩾ Mn(II) > Co(II) > Ca > Sr > Ba, distinguished with 95% confidence for vapor densities greater than ∼0.2 g/cm3. The alkaline earth metals are limited to purely electrostatic interactions with Cl ligands, resulting in an excellent linear correlation (R2 > 0.99) between their partition coefficients and respective ionic radii. Though broadly consistent with this relationship, relative behavior of the transition metals is not well resolved, being likely obscured by complex bonding processes and the potential participation of Na in the formation of tetra-chloro species. At lower densities (at/near halite saturation) partitioning behavior of all metals becomes highly non-linear, where M/Cl ratios in the vapor begin to increase despite continued decreases in chlorinity and density. We refer to this phenomenon as "volatility", which is broadly associated with substantial increases in the HCl/NaCl ratio (eventually to >1) due to hydrolysis of NaCl. Some transition metals (e.g., Fe, Zn) exhibit volatility prior to halite stability, suggesting a potential shift in vapor speciation relative to nearer critical regions of the vapor-liquid solvus. The chemistry of deep-sea hydrothermal fluids appears affected by this process during magmatic events, however, our results do not support suggestions of subseafloor halite precipitation recorded in currently available field data. Ca-Cl systematics in vent fluids are specifically explored, revealing behavior consistent with partitioning due to phase separation. Interestingly, the effect of variable chloride on dissolved Na/Ca ratios associated with plagioclase solubility (in single-phase solutions) appears fundamentally similar to that of phase separation on vapor compositions such that vapors evolved in hydrothermal systems may naturally remain near equilibrium with the host lithology. Conversely, residual liquids/brines left behind in the crust may be undersaturated with metals, enhancing the rate and extent of hydrothermal alteration.
7. Realization of the 3He Vapor-Pressure Temperature Scale and Development of a Liquid-He-Free Calibration Apparatus
Shimazaki, T.; Toyoda, K.; Tamura, O.
2011-12-01
The 3He vapor-pressure temperature scale was realized using an apparatus based on a continuously operating 3He cryostat at the National Metrology Institute of Japan (NMIJ), National Institute of Advanced Industrial Science and Technology (AIST). The cryostat has two operational modes: a 3He circulation mode and a 1 K pot mode. The 3He circulation mode can be used for 3He vapor-pressure measurements below 1.6 K, and the 1 K pot mode can be used for measurements above 1.3 K. Either mode can be selected for measurements from 1.3 K to 1.6 K. The realization of the 3He vapor-pressure temperature scale in this study fully covers its defined temperature range from 0.65 K to 3.2 K in the International Temperature Scale of 1990. The latest realization results are presented in this article. In addition, a liquid-He-free calibration apparatus was developed. It does not require liquid helium as a cryogen, which usually entails cumbersome handling and periodic refilling. The apparatus was designed for the calibration of capsule-type resistance thermometers from 0.65 K to 24.5561 K (the triple point of neon). The cooling system of the apparatus consists of a commercially available pulse-tube refrigerator and a 3He Joule-Thomson (JT) cooling circuit developed at NMIJ/AIST. The pulse-tube refrigerator is used in a pre-cooling stage and cools the apparatus to approximately 5 K. The 3He JT cooling circuit is used to cool the apparatus from 5 K to below 0.65 K. Since the 3He JT cooling circuit is a closed circuit, the apparatus can run continuously with only simple maintenance required. The basic characteristics of the apparatus are described.
8. Very long single- and few-walled boron nitride nanotubes via the pressurized vapor/condenser method
Smith, Michael W.; Jordan, Kevin C.; Park, Cheol; Kim, Jae-Woo; Lillehei, Peter T.; Crooks, Roy; Harrison, Joycelyn S.
2009-12-01
A new method for producing long, small-diameter, single- and few-walled, boron nitride nanotubes (BNNTs) in macroscopic quantities is reported. The pressurized vapor/condenser (PVC) method produces, without catalysts, highly crystalline, very long, small-diameter, BNNTs. Palm-sized, cotton-like masses of BNNT raw material were grown by this technique and spun directly into centimeters-long yarn. Nanotube lengths were observed to be 100 times that of those grown by the most closely related method. Self-assembly and growth models for these long BNNTs are discussed.
9. Very Long Single and Few-Walled Boron Nitride Nanotubes via the Pressurized Vapor/Condenser Method
NASA Technical Reports Server (NTRS)
Smith, Michael W.; Jordan, Kevin C.; Park, Cheol; Kim, Jae-Woo; Lillehei, Peter T.; Crooks, Roy; Harrison, Joycelyn S.
2009-01-01
A new method for producing long, small diameter, single and few-walled, boron nitride nanotubes (BNNTs) in macroscopic quantities is reported. The pressurized vapor/condenser (PVC) method produces, without catalysts, highly crystalline, very long, small diameter, BNNTs. Palm-sized, cotton-like masses of BNNT raw material were grown by this technique and spun directly into centimeters-long yarn. Nanotube lengths were observed to be 100 times that of those grown by the most closely related method. Self-assembly and growth models for these long BNNTs are discussed.
10. Very long single- and few-walled boron nitride nanotubes via the pressurized vapor/condenser method
SciTech Connect
Michael W. Smith, Kevin Jordan, Cheol Park, Jae-Woo Kim, Peter Lillehei, Roy Crooks, Joycelyn Harrison
2009-11-01
Boron nitride nanotubes (BNNTs) are desired for their exceptional mechanical, electronic, thermal, structural, textural, optical, and quantum properties. A new method for producing long, small-diameter, single- and few-walled, boron nitride nanotubes (BNNTs) in macroscopic quantities is reported. The pressurized vapor/condenser (PVC) method produces, without catalysts, highly crystalline, very long, small-diameter, BNNTs. Palm-sized, cotton-like masses of BNNT raw material were grown by this technique and spun directly into centimeters-long yarn. Nanotube lengths were observed to be 100 times that of those grown by the most closely related method. Self-assembly and growth models for these long BNNTs are discussed.
11. Physical and electrical properties of graphene grown under different hydrogen flow in low pressure chemical vapor deposition
PubMed Central
2014-01-01
Hydrogen flow during low pressure chemical vapor deposition had significant effect not only on the physical properties but also on the electrical properties of graphene. Nucleation and grain growth of graphene increased at higher hydrogen flows. And, more oxygen-related functional groups like amorphous and oxidized carbon that probably contributed to defects or contamination of graphene remained on the graphene surface at low H2 flow conditions. It is believed that at low hydrogen flow, those remained oxygen or other oxidizing impurities make the graphene films p-doped and result in decreasing the carrier mobility. PMID:25332692
12. Strength and ductility of room-dry and water-saturated igneous rocks at low pressures and temperatures to partial melting. Final report
SciTech Connect
Friedman, M.; Handin, J.; Higgs, N.G.; Lantz, J.R.; Bauer, S.J.
1980-11-01
Rock types that are likely candidates for drilling were tested. Reported herein are the short-time ultimate strengths and ductilities determined at temperatures of 25/sup 0/ to 1050/sup 0/C and a strain rate of 10/sup -4/s/sup -1/ of (a) room-dry Mt. Hood Andesite, Cuerbio Basalt, and Charcoal (St. Cloud Gray) Granodiorite at confining pressures of 0, 50, and 100 MPa, (b) water-saturated specimens of the same three rocks at zero effective pressure (both pore and confining pressures of 50 MPa), and (c) room-dry Newberry Rhyolite Obsidian at 0 and 50 MPa. These strengths are then compared with the stresses developed at the wall of a borehole in an elastic medium at the appropriate temperatures and mean pressures to assess the problem of borehole stability. (MHR)
13. Solvent vapor recovery by pressure swing adsorption. 1: Experimental transient and periodic dynamics of the butane-activated carbon system
SciTech Connect
Liu, Y.; Holland, C.E.; Ritter, J.A.
1998-11-01
An experimental investigation was carried out for the separation and recovery of butane vapor (10 to 40 vol%) from nitrogen using Westvaco BAX activated carbon in a twin-bed pressure swing adsorption (PSA) system utilizing a 4-step Skarstrom-type cycle. Twenty-four runs, covering a broad range of process and initial column conditions, were performed to investigate the transient and period process dynamics. In all cases the approach to the periodic state was very slow, taking up to 160 cycles depending on the initial condition of the beds; and peak bed temperatures of up to 105 C were observed depending on both the initial condition of the beds and the process conditions. Also, the periodic state of each run was unique when approaching a new periodic state from less contaminated beds. The uniqueness of the periodic states, together with the exceedingly high peak temperatures, inferred much about the practice of preconditioning beds to avoid high temperature excursions. The periodic enriched butane vapor concentration histories also gave considerable insight into new cycle designs for improved solvent vapor enrichment.
14. Spatial and temporal variability of water vapor pressure in the arid region of northwest China, during 1961-2011
Yao, Junqiang; Chen, Yaning; Yang, Qing
2015-01-01
This paper investigated the spatial and temporal variations of the water vapor pressure (WVP) of the arid region of northwest China (ARNC) from 1961 to 2011. The original daily temperature and relative humidity data were collected from 96 meteorological stations in the region and analyzed by a Mann-Kendall test and linear trend. The results showed that (1) the WVP possesses vertical zonality and longitude zonality, which decreased from the low to high with the elevation increasing, and the WVP changed obviously from the northwest and southeast to the middle of the ARNC. (2) WVP exhibited an abrupt increasing trend in most of the stations over the past 51 years; only four meteorological stations displayed upward trend in the ARNC. The WVP in the desert increased most rapidly, followed by the oasis and mountainous area. (3) The northwest of Xinjiang and northwest of the Hexi Corridor were sensitive to the water vapor change. Thus, further studies should be performed on the relations between the land use and cover and the water vapor change.
15. Spatial and temporal variability of water vapor pressure in the arid region of northwest China, during 1961-2011
Yao, Junqiang; Chen, Yaning; Yang, Qing
2016-02-01
This paper investigated the spatial and temporal variations of the water vapor pressure (WVP) of the arid region of northwest China (ARNC) from 1961 to 2011. The original daily temperature and relative humidity data were collected from 96 meteorological stations in the region and analyzed by a Mann-Kendall test and linear trend. The results showed that (1) the WVP possesses vertical zonality and longitude zonality, which decreased from the low to high with the elevation increasing, and the WVP changed obviously from the northwest and southeast to the middle of the ARNC. (2) WVP exhibited an abrupt increasing trend in most of the stations over the past 51 years; only four meteorological stations displayed upward trend in the ARNC. The WVP in the desert increased most rapidly, followed by the oasis and mountainous area. (3) The northwest of Xinjiang and northwest of the Hexi Corridor were sensitive to the water vapor change. Thus, further studies should be performed on the relations between the land use and cover and the water vapor change.
16. Beer Law Constants and Vapor Pressures of HgI2 over HgI2(s,l)
NASA Technical Reports Server (NTRS)
Su, Ching-Hua; Zhu, Shen; Ramachandran, N.; Burger, A.
2002-01-01
Optical absorption spectra of the vapor phase over HgI2(s,l) were measured at sample temperatures between 349 and 610 K for wavelengths between 200 and 600 nm. The spectra show the samples sublimed congruently into HGI2 without any observed Hg or I2 absorption spectra. The Beer's Law constants for 15 wavelengths between 200 and 440 nm were derived. From these constants the vapor pressure of HgI2, P, was found to be a function of temperature for the liquid and the solid beta-phases: ln P(atm) = -7700/T(K) + 12.462 (liquid phase) and ln P(atm) = -10150/T(K) + 17.026 (beta-phase). The expressions match the enthalpies of vaporization and sublimation of 15.30 and 20.17 kcal/mole respectively, for the liquid and the beta-phase HgI2. The difference in the enthalpies gives an enthalpy of fusion of 4.87 kcal/mole, and the intersection of the two expressions gives a melting point of 537 K.
17. Effects of water-saturation on strength and ductility of three igneous rocks at effective pressures to 50 MPA and temperatures to partial melting
SciTech Connect
Bauer, S.J.; Friedman, M.; Handin, J.
1981-01-01
The short-term failure strengths and strains at failure of room-dry and water-saturated, cylindrical specimens (2 by 4 cm) of Charcoal Granodiorite (CG), Mt. Hood Andesite (MHA), and Cuerbio Basalt (CB) at a strain rate of 10/sup -4/s/sup -1/, at effective confining pressures of 0, 50, and 100 MPa and at temperatures to partial melting were investigated. Data from water-saturated specimens of the granodiorite and andesite, compared to room-dry counterparts, indicate (1) the pore pressures are essentially communicated throughout each test specimen so that they are fully effective; (2) at P/sub e/ = 0 and 50 MPa the granodiorite does not water-weaken; (3) at these same effective pressures the more porous and finer-grained andesite begins to exhibit water-weakening at about 600/sup 0/C; (4) at P/sub e/ = 0 and 870 to 900/sup 0/C the andesite's strength averages 20 MPa while the strength of dry specimens at the same P and T exhibit a strength of 100 MPa; (5) at P/sub e/ = 50 MPa compared to 160 MPa dry; (6) the basalt at P/sub e/ = 0, appears to be water-weakened at 800/sup 0/C; (7) water saturated specimens deformed at temperatures less than that of melting exhibit ultimate strengths at less than 2% shortening and then work-soften along faults; (8) again as do the dry counterparts, the wet specimens deform primarily by microscopic fracturing that coalesces into one or more macroscopic faults; and (9) the temperature for incipient melting of the andesite is decreased >150/sup 0/C in the water-saturated tests.
18. Normative Values of Retinal Oxygen Saturation in Rhesus Monkeys: The Beijing Intracranial and Intraocular Pressure (iCOP) Study
PubMed Central
Li, Jing; Yang, Yiquan; Yang, Diya; Liu, Xiangxiang; Sun, Yunxiao; Wei, Shifei; Wang, Ningli
2016-01-01
Objective To study the normal values of the retinal oxygen saturation in Rhesus monkeys and to evaluated repeatability and reproducibility of retinal oxygen saturation measurements. Methods Eighteen adult Rhesus macaque monkeys were included in this experimental study. An Oxymap T1 retinal oximeter (Oxymap, Reykjavik, Iceland) was used to perform oximetry on all subjects. Global arterial (SaO2) and venous oxygen saturation (SvO2), arteriovenous difference in SO2 were measured. In the first examination, each eye was imaged three times. At the following two examinations, each eye was imaged once. All examinations were finished in one month. P values were calculated to evaluate the difference between the measurements during three visits by performing an ANOVA. Intra-visit and inter-visit intraclass correlation coefficient (ICC) was determined. Results At baseline, the average SaO2 and SvO2 were 89.48 ± 2.64% and 54.85 ± 2.18%, respectively. The global A-V difference was 34.63 ± 1.91%. The difference between the three visits was not significant (p>0.05). The highest A-V difference in SO2 and lowest saturations were found in the inferotemporal quadrant. Intra-session and inter-visit repeatability were both high. For all oxygen saturation parameters, the ICC values of the intra-session repeatability ranged between 0.92 and 0.96. As found previously, a relatively high ICC value for inter-visit repeatability also was found for all oxygen saturation measurements, ranging between 0.86 and 0.94, with the lowest values in the infero-nasal quadrant. Conclusions Our study is the first to describe retinal SO2 in healthy Rhesus monkeys. In normal monkey eyes, the reproducibility and repeatability of retinal oximetry oxygen saturation measurements were high in the retinal arterioles and venules. Our results support that Oxymap T1 retinal oximetry is a suitable and reliable technique in monkey studies. PMID:26930659
19. Vapor pressures of 1,3-dialkylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids with long alkyl chains
Rocha, Marisa A. A.; Coutinho, Joo A. P.; Santos, Lus M. N. B. F.
2014-10-01
This work presents the vapor pressure at several temperatures for the 1,3-dialkylimidazolium bis(trifluoromethylsulfonyl)imide series, [CN/2CN/2im][NTf2] (N = 14, 16, 18, and 20), measured by a Knudsen effusion method combined with a quartz crystal microbalance. The thermodynamic properties of vaporization of the ionic liquids under study are analysed together with the results obtained previously for the shorter alkyl chain length [CN/2CN/2im][NTf2] (N = 2, 4, 6, 8, 10, and 12), in order to evaluate the effect of the alkyl side chains of the cation and to get additional insights concerning the nanostructuration of ionic liquids. The symmetry effect is explored, based on the comparison with the asymmetric imidazolium based ionic liquids, [CN-1C1im][NTf2]. A trend shift on the thermodynamic properties of vaporization along the alkyl side chains of the extended symmetric ionic liquids, around [C6C6im][NTf2], was detected. An intensification of the odd-even effect was observed starting from [C6C6im][NTf2], with higher enthalpies and entropies of vaporization for the odd numbered ionic liquids, [C7C7im][NTf2] and [C9C9im][NTf2]. Similar, but less pronounced, odd-even effect was found for the symmetric ionic liquids with lower alkyl side chains length, [CN/2CN/2im][NTf2] (with N = 4, 6, 8, 10, and 12). This effect is related with the predominant orientation of the terminal methyl group of the alkyl chain to the imidazolium ring and their influence in the cation-anion interaction. The same Critical Alkyl length at the hexyl, (C6C1and C6C6) was found for both asymmetric and symmetric series indicating that the nanostructuration of the ionic liquids is related with alkyl chain length.
20. 3D transient multiphase model for keyhole, vapor plume, and weld pool dynamics in laser welding including the ambient pressure effect
Pang, Shengyong; Chen, Xin; Zhou, Jianxin; Shao, Xinyu; Wang, Chunming
2015-11-01
The physical process of deep penetration laser welding involves complex, self-consistent multiphase keyhole, metallic vapor plume, and weld pool dynamics. Currently, efforts are still needed to understand these multiphase dynamics. In this paper, a novel 3D transient multiphase model capable of describing a self-consistent keyhole, metallic vapor plume in the keyhole, and weld pool dynamics in deep penetration fiber laser welding is proposed. Major physical factors of the welding process, such as recoil pressure, surface tension, Marangoni shear stress, Fresnel absorptions mechanisms, heat transfer, and fluid flow in weld pool, keyhole free surface evolutions and solid-liquid-vapor three phase transformations are coupling considered. The effect of ambient pressure in laser welding is rigorously treated using an improved recoil pressure model. The predicated weld bead dimensions, transient keyhole instability, weld pool dynamics, and vapor plume dynamics are compared with experimental and literature results, and good agreements are obtained. The predicted results are investigated by not considering the effects of the ambient pressure. It is found that by not considering the effects of ambient pressure, the average keyhole wall temperature is underestimated about 500 K; besides, the average speed of metallic vapor will be significantly overestimated. The ambient pressure is an essential physical factor for a comprehensive understanding the dynamics of deep penetration laser welding.
1. Growth of verically aligned carbon nanofibers by low-pressure inductively coupled plasma-enhanced chemical vapor deposition
SciTech Connect
Caughman, John B; Baylor, Larry R; Guillorn, Michael A; Merkulov, Vladimir I; Lowndes, Douglas H; Allard Jr, Lawrence Frederick
2003-08-01
Vertically aligned carbon nanofibers (VACNFs) have been grown using a low-pressure, plasma-enhanced, chemical vapor deposition process. The nanofibers are grown from a nickel catalyst that can be patterned to form arrays of individual, isolated VACNFs. The fibers are grown at pressures below 100 mTorr, using an inductively coupled plasma source with a radio-frequency bias on the sample substrate to allow for independent control of the ion energies. Plasma conditions are related to growth results by comparing optical emission from the plasma to the physical structure of the nanofibers. We find that the ratio of etching species in the plasma to depositing species is critical to the final shape of the carbon structures that are formed.
2. Substrate control for large area continuous films of monolayer MoS2 by atmospheric pressure chemical vapor deposition
Wang, Shanshan; Pacios, Merce; Bhaskaran, Harish; Warner, Jamie H.
2016-02-01
Growing monolayer MoS2 films that are continuous with large domain sizes by chemical vapor deposition is one of the major challenges in 2D materials research at the moment. Here, we explore how atmospheric pressure CVD can be used to grow centimeter scale continuous films of monolayer MoS2 films directly on Si substrates with an oxide layer whilst also obtaining large domain sizes exceeding 20 μm within the films. This is achieved by orientating the growth substrate in a vertical position to improve the uniformity of precursor feed-stock compared to horizontally orientated growth substrates. This leads to continuous films of monolayer MoS2 over a significantly larger area without the need for low-pressure vacuum systems or volatile precursors. This provides important insights into novel approaches for maximizing domain sizes within MoS2 films, with concomitant large area uniform coverage.
3. Substrate control for large area continuous films of monolayer MoS2 by atmospheric pressure chemical vapor deposition.
PubMed
Wang, Shanshan; Pacios, Merce; Bhaskaran, Harish; Warner, Jamie H
2016-02-26
Growing monolayer MoS2 films that are continuous with large domain sizes by chemical vapor deposition is one of the major challenges in 2D materials research at the moment. Here, we explore how atmospheric pressure CVD can be used to grow centimeter scale continuous films of monolayer MoS2 films directly on Si substrates with an oxide layer whilst also obtaining large domain sizes exceeding 20 μm within the films. This is achieved by orientating the growth substrate in a vertical position to improve the uniformity of precursor feed-stock compared to horizontally orientated growth substrates. This leads to continuous films of monolayer MoS2 over a significantly larger area without the need for low-pressure vacuum systems or volatile precursors. This provides important insights into novel approaches for maximizing domain sizes within MoS2 films, with concomitant large area uniform coverage. PMID:26821123
4. Analysis and modeling of low pressure chemical vapor deposition of phosphorus-doped polysilicon in commercial scale reactor
Shimizu, Ryosuke; Ogino, Masaaki; Sugiyama, Masakazu; Shimogaki, Yukihiro
2004-07-01
In a commercial scale low pressure chemical vapor deposition (CVD) reactor, we analyzed the elementary reaction of silane based CVD with the doping gas of phosphine. The variation of conductivity in the radial direction over a monitor wafer became significant as the phosphine gas partial pressure decreased, and it reached up to about 30% at 6.510-4 Pa. The radial distribution of phosphorus fraction in a film, however, was smaller than 7%. On the basis of the diffusion model of chemical species into the wafer gaps, we found that the sticking probability of phosphine is 2-510-5, which is 1 order of magnitude larger than the one of silane. The reaction kinetics of both silane and phosphine seems almost linear, but slight nonlinearity at high phosphine concentration range was also indicated. .
5. Absolute integrated intensities of vapor-phase hydrogen peroxide (H202) in the mid-infrared at atmospheric pressure
SciTech Connect
Johnson, Timothy J.; Sams, Robert L.; Burton, Sarah D.; Blake, Thomas A.
2009-09-01
We report quantitative broadband infrared spectra of vapor-phase hydrogen peroxide (H2O2) with all spectra pressure broadened to atmospheric pressure. The spectra were generated by flowing a concentrated solution (83 weight%) of H2O2 into a gently heated disseminator and diluting with a flow of pure nitrogen carrier gas. The water vapor lines were subtracted from the resulting spectra to yield the spectrum of pure H2O2. Comparison with previous results for the ?6 band strength (including hot bands) compares favorably with the results of Klee et al. [(1999) J. Mol. Spectr. 195, 154] as well as HITRAN. The present results are 433 and 467 cm-2 atm-1 (8% and 3% at 298 and 323 K, respectively) for the band strength, matching well the Klee value (S = 467 cm-2 atm-1 at 296 K) for the integrated band. Other bands in the 520-7500 cm-1 interval and their potential for atmospheric monitoring are discussed.
6. Chemical vapor deposition of hexagonal boron nitride films in the reduced pressure
SciTech Connect
Choi, B.J.
1999-12-01
Hexagonal boron nitride (h-BN) films were deposited onto a graphite substrate in reduced pressure by reacting ammonia and boron tribromide at 800--1,200 C. The growth rate of h-BN films was dependent on the substrate temperature and the total pressures. The growth rate increased with increasing the substrate temperature at the pressure of 2 kPa, while it showed a maximum value at the pressures of 4 and 8 kPa. The temperature at which the maximum growth rate occurs decreased with increasing total pressure. With increasing the substrate temperature and total pressure, the apparent grain size increased and the surface morphology showed a rough, cauliflower-like structure.
7. Liquid-vapor phase equilibrium in a tin-selenium system
Volodin, V. N.; Burabaeva, N. M.; Trebukhov, S. A.
2014-12-01
Based on the pressure of the saturated vapor and components over liquid alloys in a tin-selenium system, determined using the boiling points approach (isothermal variant), its boiling point and corresponding vapor phase composition are calculated in the region of liquid solutions. The phase diagram is supple-mented with the liquid-vapor phase transition under atmospheric pressure and in vacuums of 100 and 10 Pa with the boundaries of the region in which the regions of liquid and vapor coexist being determined.
8. 40 CFR 61.242-4 - Standards: Pressure relief devices in gas/vapor service.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 8 2010-07-01 2010-07-01 false Standards: Pressure relief devices in... (CONTINUED) AIR PROGRAMS (CONTINUED) NATIONAL EMISSION STANDARDS FOR HAZARDOUS AIR POLLUTANTS National Emission Standard for Equipment Leaks (Fugitive Emission Sources) 61.242-4 Standards: Pressure...
9. Vapor pressures and calculated heats of vaporization of concentrated nitric acid solutions in the composition range 71 to 89 percent nitrogen dioxide, 1 to 10 percent water, and in the temperature range 10 to 60 degrees C
NASA Technical Reports Server (NTRS)
Mckeown, A B; Belles, Frank E
1954-01-01
Total vapor pressures were measured for 16 acid mixtures of the ternary system nitric acid, nitrogen dioxide, and water within the temperature range 10 degrees to 60 degrees Celsius, and with the composition range 71 to 89 weight percent nitric acid, 7 to 20 weight percent nitrogen dioxide, and 1 to 10 weight percent water. Heats of vaporization were calculated from the vapor pressure measurements for each sample for the temperatures 25, 40, and 60 degrees Celsius. The ullage of the apparatus used for the measurements was 0.46. Ternary diagrams showing isobars as a function of composition of the system were constructed from experimental and interpolated data for the temperatures 25, 40, 45, and 60 degrees C and are presented herein.
10. Growth of non-polar ZnO thin films with different working pressures by plasma enhanced chemical vapor deposition
Chao, Chung-Hua; Wei, Da-Hua
2014-11-01
Non-polar coexisting m-plane (10\\bar{1}0) and a-plane (11\\bar{2}0) zinc oxide (ZnO) thin films have been synthesized onto commercial silicon (100) substrates by using plasma enhanced chemical vapor deposition (PECVD) system at different working pressures. The effects of the working pressure on crystal orientation, microstructure, surface morphology, and optical properties of the ZnO thin films were investigated. From the X-ray diffraction patterns, the non-polar ZnO thin films were successfully synthesized at the working pressures of 6 and 9 Torr, respectively. The non-polar ZnO thin films showed stripes-like surface morphology and with smooth surface roughness (˜3.53 nm) was performed by field emission scanning electron microscope (FE-SEM) and atomic force microscope (AFM), respectively. All the ZnO films show a remarkable near-band-edge (NBE) emission peak located at ultraviolet (UV) band accompanying a negligible deep-level (DL) emission at visible region detected by photoluminescence (PL) spectra at room temperature. From the above systematic measurement analysis, indicating the better crystallinity and optical character of ZnO thin film was improved with reducing the working pressure. The wettability of non-polar ZnO thin films was also explored in this presented article.
11. Bridgman-type apparatus for the study of growth-property relationships - Arsenic vapor pressure-GaAs property relationship
NASA Technical Reports Server (NTRS)
Parsey, J. M.; Nanishi, Y.; Lagowski, J.; Gatos, H. C.
1982-01-01
A precision Bridgman-type apparatus is described which was designed and constructed for the investigation of relationships between crystal growth parameters and the properties of GaAs crystals. Several key features of the system are highlighted, such as the use of a heat pipe for precise arsenic vapor pressure control and seeding without the presence of a viewing window. Pertinent growth parameters, such as arsenic source temperature, thermal gradients in the growing crystal and in the melt, and the macroscopic growth velocity can be independently controlled. During operation, thermal stability better than + or - 0.02 C is realized; thermal gradients can be varied up to 30 C/cm in the crystal region, and up to 20 C/cm in the melt region; the macroscopic growth velocity can be varied from 50 microns/hr to 6.0 cm/hr. It was found that the density of dislocations depends critically on As partial pressure; and essentially dislocation-free, undoped, crystals were grown under As pressure precisely controlled by an As source maintained at 617 C. The free carrier concentration varied with As pressure variations. This variation in free carrier concentration was found to be associated with variations in the compensation ratio rather than with standard segregation phenomena.
12. Real-time explosives/narcotics vapor enhancement and collection systems for use with the atmospheric pressure ionization time-of-flight mass spectrometer
Hintze, M. Marx; Hansen, Byron L.; Heath, Russell L.
1992-05-01
This paper is a companion document to the Atmospheric Pressure Ionization Time-of-Flight Mass Spectrometer (API TOFMS) presentation (Lee, et al., 1992). Two significant technique challenges related to design and implementation of vapor collection systems are addressed. They are as follows: (1) freeing deposited or trapped explosive material particles or vapor; and (2) transportation of sample specimen from the pickup point to the detector. Addressed in this dissertation will be both hand-held collection and air shower booth accumulation.
13. Capillary pressure-saturation relations for supercritical CO2 and brine in limestone/dolomite sands: implications for geologic carbon sequestration in carbonate reservoirs.
PubMed
Wang, Shibo; Tokunaga, Tetsu K
2015-06-16
In geologic carbon sequestration, capillary pressure (Pc)-saturation (Sw) relations are needed to predict reservoir processes. Capillarity and its hysteresis have been extensively studied in oil-water and gas-water systems, but few measurements have been reported for supercritical (sc) CO2-water. Here, Pc-Sw relations of scCO2 displacing brine (drainage), and brine rewetting (imbibition) were studied to understand CO2 transport and trapping behavior under reservoir conditions. Hysteretic drainage and imbibition Pc-Sw curves were measured in limestone sands at 45 C under elevated pressures (8.5 and 12.0 MPa) for scCO2-brine, and in limestone and dolomite sands at 23 C (0.1 MPa) for air-brine using a new computer programmed porous plate apparatus. scCO2-brine drainage and imbibition curves shifted to lower Pc relative to predictions based on interfacial tension, and therefore deviated from capillary scaling predictions for hydrophilic interactions. Fitting universal scaled drainage and imbibition curves show that wettability alteration resulted from scCO2 exposure over the course of months-long experiments. Residual trapping of the nonwetting phases was determined at Pc = 0 during imbibition. Amounts of trapped scCO2 were significantly larger than for those for air, and increased with pressure (depth), initial scCO2 saturation, and time. These results have important implications for scCO2 distribution, trapping, and leakage potential. PMID:25945400
14. Simultaneous measurements of elastic wave velocities and electrical conductivity in a brine-saturated granitic rock under confining pressures and their implication for interpretation of geophysical observations
Watanabe, Tohru; Higuchi, Akiyoshi
2015-12-01
Simultaneous measurements of elastic wave velocity and electrical conductivity in a brine-saturated granitic rock were conducted under confining pressures of up to 180 MPa. Contrasting changes in velocity and conductivity were observed. As the confining pressure increased to 50 MPa, compressional and shear wave velocities increased by less than 10 %. On the other hand, electrical conductivity decreased by an order of magnitude. Both changes must be caused by the closure of cracks under pressures. Microstructural examinations showed that most cracks were open grain boundaries. In reality, a crack is composed of many segments with different apertures. If crack segments have a similar length, segments with small apertures are closed at low pressures to greatly reduce conductivity, while those with wide apertures are open even at high pressures. The latter must form an interconnected fluid path to maintain the electrical conduction through fluid. A power law distribution of apertures causes a steep decrease in conductivity at low pressures. An empirical relation between the crack density parameter and normalized conductivity was obtained. The normalized conductivity is the ratio of bulk conductivity to the conductivity of a pore fluid. This relation should be a basis for quantitative interpretation of observed seismic velocity and electrical conductivity.
15. Thermodynamic properties of saturated liquid parahydrogen charted for important temperature range
NASA Technical Reports Server (NTRS)
Mc Carty, R. D.; Roder, H. M.
1967-01-01
Six entropy diagrams for parahydrogen in or near the saturated liquid state cover the temperature range from 29.16 degrees to 42.48 degrees R with pressures to 100 psia and mixtures of the liquid and vapor phases to 0.003 quality. The diagrams are printed in color, are 19 by 30 inches in size, and are suitable for wall mounting.
16. Transport properties of nonelectrolyte liquid mixturesV. Viscosity coefficients for binary mixtures of benzene plus alkanes at saturation pressure from 283 to 393 K
Dymond, J. H.; Young, K. J.
1981-09-01
Viscosity coefficient measurements at saturation pressure are reported for benzene + n-hexane, benzene + n-octane, benzene + n-decane, benzene + n-dodecane, benzene + n-hexadecane, and benzene + cyclohexane at temperatures from 283 to 393 K. The characteristic parameter G in the Grunberg and Nissan equation 10765_2004_Article_BF00504187_TeX2GIFE1.gif ell n? = x_1 ell n? _1 + x_2 ell n? _2 + x_1 x_2 G is found to be both composition and temperature dependent for benzene + n-alkane mixtures, but it is independent of composition for the system benzene + cyclohexane.
17. The saturation pressure for different objects in reduced variables and the justification of some empirical relations set from the van der Waals equation
Apfelbaum, E. M.; Vorob'ev, V. S.
2014-01-01
We analyse the saturation pressure (SP) behaviour along the coexistence curve liquid-gas in reduced variables, containing only the Zeno line parameters. Using experimental and simulation data for substances (Ar, N2, Hg, Cs) and two models (van der Waals and Lennard-Jones) we create a global 3D picture of SP dependence on temperature and density. We also show that the well-known empirical Timmermans relation and partly Riedel equation are the consequences of the van der Waals equation and the rectilinear diameter law.
18. Mass Spectrometric Identification of Si-O-H(g) Species from the Reaction of Silica with Water Vapor at Atmospheric Pressure
NASA Technical Reports Server (NTRS)
Opila, Elizabeth J.; Fox, Dennis S.; Jacobson, Nathan S.
1997-01-01
A high-pressure sampling mass spectrometer was used to detect the volatile species formed from SiO2 at temperatures between 1200C and 1400C in a flowing water vapor/oxygen gas mixture at 1 bar total pressure. The primary vapor species identified was Si(OH)4. The fragment ion Si(OH)3+,' was observed in quantities 3 to 5 times larger than the parent ion Si(OH)4+. The Si(OH)3+ intensity was found to have a small temperature dependence and to increase with the water vapor partial pressure as expected. In addition, SiO(OH)+ believed to be a fragment of SiO(OH)2, was observed. These mass spectral results were compared to the behavior of silicon halides.
19. Compact electron-beam source for formation of neutral beams of very low vapor pressure materials
NASA Technical Reports Server (NTRS)
Rutherford, J. A.; Vroom, D. A.
1978-01-01
In order to form metal vapors for neutral beam studies, an electron-beam heater and a power supply have been designed. The source, which measures about 30 x 50 x 70 mm, consists of a filament, accelerating plate (defined by pole pieces), and a supported target. The electrons from the filament are focused by the field penetration through a 2 mm slit in the high-voltage cage. They are then accelerated to about 5 kV to a ground plate. The electrons then follow a path in the magnetic field and strike the sample to be heated on its front surface. The assembly is attached to a water-cooled base plate. The electron beam source has produced beams of Ta and C particles with densities of about 10 to the 8th power/cu cm.
20. Vapor pressures of solid hydrates of nitric acid - Implications for polar stratospheric clouds
NASA Technical Reports Server (NTRS)
Worsnop, Douglas R.; Fox, Lewis E.; Zahniser, Mark S.; Wofsy, Steven C.
1993-01-01
Thermodynamic data are presented for hydrates of nitric acid: HNO3.H2O, HNO3.2H2O, HNO3.3H2O, and a higher hydrate. Laboratory data indicate that nucleation and persistence of metastable HNO3.2H2O may be favored in polar stratospheric clouds over the slightly more stable HNO3.3H2O. Atmospheric observations indicate that some polar stratospheric clouds may be composed of HNO3.2H2O and HNO3.3H2O. Vapor transfer from HNO3.2H2O to HNO3.3H2O could be a key step in the sedimentation of HNO3, which plays an important role in the depletion of polar ozone.
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|
https://mathematica.stackexchange.com/questions/65258/dayround-rounding-valuesno-difference-between-preceding-and-following
|
# DayRound Rounding Values:No difference between “Preceding” and “Following”?
On Mathematica 10.0.1 both
DayRound[{1980, 2, 29}, "EndOfMonth", "Preceding"]
and
DayRound[{1980, 2, 29}, "EndOfMonth", "Following"]
produce
DateObject[List[1980,2,29],Rule[CalendarType,"Gregorian"]]
Is that correct? I would expect that the first one would produce the January 31 and the later one to produce March 31.
This is documented behavior. From the docs on DayRound >> Details and Options:
In DayRound[date, daytype, rounding]
If date is of daytype, DayRound has no effect.
So, since {1980, 2, 29} an "EndOfMonth" day, its "rounded" form is itself. And
DayRound[{1980, 2, 28}, "EndOfMonth","Preceding"]
return DateObject[{1980, 1, 31}, CalendarType -> "Gregorian"] as expected. However, you need
DayRound[{1980, 3, 1}, "EndOfMonth","Following"]
to get DateObject[{1980, 3, 31}, CalendarType -> "Gregorian"].
• thanks. Yet I still struggle to understand the logic of "Preceding" and "Following" having no effect. – iav Nov 9 '14 at 18:29
• @iav, i agree it does feel puzzling. Perhaps it helps to try to think of "Preceding" and "Following" in the weak inequality (LessEqual and GreaterEqual) sense. – kglr Nov 9 '14 at 18:37
|
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|
https://forum.polymake.org/viewtopic.php?p=782
|
installation on OS X 10.7
Discussions on installation issues go here.
folderol
Posts: 3
Joined: 26 Jun 2012, 12:01
installation on OS X 10.7
I'm trying to install polymake for someone who has been unable to do it on their own. I personally have no idea what polymake is for or what it does, but I know how to install software.
That said, I cannot for the life of me get this thing going. Even simply following the noodly appendages of the hacked flowchart that is the installation instructions has been maddening, so I'm turning to you guys to maybe restart from square one.
Initially, I tried to compile polymake without fink. Hours later, I realized this is nigh impossible.
So, I uninstalled all the stuff I managed to successfully install, then tried again with fink.
Hours later, I got all of the prerequisites installed, but polymake still won't compile, neither 2.11 with the patch nor 2.12 without it. I've tried 3 different gcc versions, but no dice.
The binary installation allegedly doesn't work for 10.7. I see there is supposed to be some sort of "app", but there's nothing in any of the folders labeled "apps" that looks appy.
So.
Let's start over.
What should I be doing to make this work? Which version should I try?
The place where I last gave up is this...fink is installed, along with all the necessary packages (maybe).
./configure output for 2.12 says:
Code: Select all
Could not compile a test program checking for the GNU Multiprecision Library (GMP). The most probable reasons are that the library is installed at a non-standard location, lacking developer's subpackage or missing at all. Please refer to the installation instructions at http://polymake.mathematik.tu-darmstadt.de/doku.php/howto/install. The complete error log follows: dyld: Library not loaded: /usr/local/lib/libppl_c.4.dylib Referenced from: /usr/local/libexec/gcc/x86_64-apple-darwin11.4.0/4.7.1/cc1plus Reason: image not found g++: internal compiler error: Trace/BPT trap: 5 (program cc1plus) Please submit a full bug report, with preprocessed source if appropriate. See <http://gcc.gnu.org/bugs.html> for instructions.
"fink install gmp" doesn't work because there's no package called gmp, but I did install gmp5. Is this the problem, or another wild goose chase?
paffenholz
Developer
Posts: 186
Joined: 24 Dec 2010, 13:47
Re: installation on OS X 10.7
I assume that you use a Mac with Mac OS 10.7.
polymake has been successfully compiled both with and without fink. Take 2.12, there is no reason that 2.11 should make something easier, but you miss a lot of new features.
There are binaries on the download page, that should work in all but very few cases. New ones will probably appear in the next one or two weeks. The "polymake app" is not a true and native app, it just contains a precompiled polymake with all dependencies and a script that starts a terminal, sets some ENV variables and starts polymake inside this terminal. But it should start by clicking the app-folder.
Compiling polymake:
In any case: the gcc apple includes in Xcode only shares the name with the real gcc. You need to have your own. The one of fink would be okay. You can compile your own, but don't take any of the 4.5.*. And maybe also don't take a 4.7.*, in the past those with odd minor numbers tend to not work well. Supply CC=<path-to-your>/gcc CXX=<path-to-your>/g++ to configure. clang is too buggy.
with fink:
- you are right, it should be gmp5. From the given error message I assume this is not found. Has fink installed ppl ("fink list ppl" should have an "i" in front of some "ppl")? I don't think apple ships a libppl, but I currently don't have a 10.7 to check. Is "sw/*" in your \$PATH, and comes before apples directories? Otherwise call ". /sw/bin/init.sh" in the shell, or supply "FINK=/sw/bin/fink" to configure. If nothing helps you could put /sw/{lib,include} into LDFLAGS, CFLAGS
- You have to compile everything for the same architecture as fink was built. But that seems to be the case.
EDIT: the error message more likely suggest that your privately installed gcc does not find your libppl. Is that installed at a place where it can be found?
without fink:
- You have to supply "--with-fink=no" to configure. Otherwise polymake tries to deduce some parameters from the fink script
- the self-compiled gmp,... must provide the same architecture (x86_64 recommended). Provide CFLAGS="-arch x86_64" ARCHFLAGS='-arch x86_64' if needed.
- and they must be found, e.g. by placing them into CFLAGS and LDFLAGS, or use the --with-* statements.
------------------------
Apologies for the lengthy installtion instructions, but they try to take care of every possible extra wishes various people had for installing polymake.
folderol
Posts: 3
Joined: 26 Jun 2012, 12:01
Re: installation on OS X 10.7
Hmmm, well, I was hoping for directions on a more specific path (please, limit my options!), but thank you very much for all the work.
I am currently away from the machine, but just want to make sure I understand all your advice before I get back to it...
So, I should be able to just double-click on the "app" folder and it should Just Work? Without any installation of all the other stuff? I'm not a Mac person, so I didn't know that was a reasonable thing to try.
As for the binaries, is it also true that I should just be able to download those and have them Just Work without gmp and mpfr and all those other consonants? The instructions I saw said to do a "dpkg -i" on the binaries files, but I've never used dpkg and it wasn't clear to me that it would work on a Mac. Pretty sure they also said that I'd need to install Xcode and fink to make that work, and by "Xcode" they meant "some other version of gcc", which needs all that other stuff...which seems like it wouldn't involve any time savings.
If you need to do all that heavy lifting, you might as well just compile it and be sure it will work, right? Although, I guess I haven't had any success at compiling...
Anyway, as for where I got stuck...OK, it at least seems like I'm on the right track. I had gcc 4.7 installed, but then thought it might be too new, so I went back to 4.6. gmp5 and some version of ppl are installed.
I put ". /sw/bin/init.sh" in the .profile, and fink itself seemed to be working fine.
Everything is installed at whereever fink decided the best place was. I didn't make any changes to the default configurations.
Let's just forget about "without fink", because I couldn't get half of the packages to compile without it.
Whew, OK. I think that's everything. At least I seem to be in the neighborhood of knowing what's going on.
Again, thanks very much for all your help.
paffenholz
Developer
Posts: 186
Joined: 24 Dec 2010, 13:47
Re: installation on OS X 10.7
I wasn't sure about what you were trying and what you would prefer...
So, I should be able to just double-click on the "app" folder and it should Just Work? Without any installation of all the other stuff? I'm not a Mac person, so I didn't know that was a reasonable thing to try. As for the binaries, is it also true that I should just be able to download those and have them Just Work without gmp and mpfr and all those other consonants?
This applies to the thing you can download here (or with the "bundle" link on the downloads page). If you mount it (double click) it contains a compiled version of polymake that you can just drag to the /Application/ folder. Then you can double click it like any other program. No further installation necessary. The other things in the dmg are there for license reasons.
The drawback: Currently it comes with gmp 5.0.2, and that has a bug that may sometimes cause polymake running into an infinite loop. I'm switching to 5.0.5, but this may take another couple of days. You can wait, or just replace the polymake.app in /Application later. The only trace apart the thing in /Application that polymake leaves on the computer is a hidden directory in the home folder for customization.
The instructions I saw said to do a "dpkg -i" on the binaries files, but I've never used dpkg and it wasn't clear to me that it would work on a Mac. Pretty sure they also said that I'd need to install Xcode and fink to make that work, and by "Xcode" they meant "some other version of gcc", which needs all that other stuff...which seems like it wouldn't involve any time savings.
That only applies to older versions of Mac OS. The many changes between 10.6 and 10.7 made the installation description a bit messy. Basically Mac OS is a unix variant, and fink uses package management similar to debian.
Anyway, as for where I got stuck...OK, it at least seems like I'm on the right track. I had gcc 4.7 installed, but then thought it might be too new, so I went back to 4.6. gmp5 and some version of ppl are installed.
I put ". /sw/bin/init.sh" in the .profile, and fink itself seemed to be working fine.
That sound like everything should be okay. Then I currently can't explain the lacking libppl that your gcc complains about. Is there a libppl at the place where cc1plus wants to find it? Is is somewhere else? Are the gmpxx header and lib in /sw/{lib,include}? It seems that you are using your own version of gcc, not one of fink. But this should not be a problem.
I'll think about it again. I don't have a 10.7 available right now, but when I have I will try installation with fink myself.
Whew, OK. I think that's everything. At least I seem to be in the neighborhood of knowing what's going on.
Again, thanks very much for all your help.
I really hope you get it running, and I am really sorry for all the problems. Apple dropping support for gcc and switching to an unfinished version of clang came unexpected.
folderol
Posts: 3
Joined: 26 Jun 2012, 12:01
Re: installation on OS X 10.7
I wasn't sure about what you were trying and what you would prefer...
All I wanted to do was install it and make it work. I only tried all that complicated stuff because the documentation seemed to indicate that it was necessary.
Ah, if I'd understood that initially, I would not have troubled you at all! That seems to work, thank you.
Basically Mac OS is a unix variant, and fink uses package management similar to debian.
I understood the basic premise, but misunderstood the documentation. Where it says...
Except for the 10.7 app bundle you first have to install Xcode.
...I interpreted the "Except for" as "However", which is poor grammar but that's how it sounded in my head.
Also I didn't think there would be pages of complex explanation if there were a simple "app". Note that in the "Installing the App Bundle" section, there's no actual link to the bundle itself. I didn't notice it hidden in the large compatibility chart.
I would suggest that the "polymake on the Mac" page have an explicit note at the top that says if you have 10.7, just download this .dmg file and go to town.
If all you want to do is make it work, everything else is just noise.
It seems that you are using your own version of gcc, not one of fink. But this should not be a problem.
Nope, I just used the gcc46 package on fink. (Although I initially tried installing it without fink, and also tried gcc47 with fink.)
At any rate, thanks for the help. I see that updating in the future (and future installations) will be trivial, so I appreciate all your hard work. My issue was with the documentation, not the engineering.
Success!
paffenholz
Developer
Posts: 186
Joined: 24 Dec 2010, 13:47
Re: installation on OS X 10.7
All I wanted to do was install it and make it work. I only tried all that complicated stuff because the documentation seemed to indicate that it was necessary.
Ah, if I'd understood that initially, I would not have troubled you at all! That seems to work, thank you.
Also I didn't think there would be pages of complex explanation if there were a simple "app". Note that in the "Installing the App Bundle" section, there's no actual link to the bundle itself. I didn't notice it hidden in the large compatibility chart.
Some people prefer to compile themselves, and some want to be able to add own code, etc. So they are not happy with a binary version... I tried to make this point more clear on the installation page.
Sorry for the complications. Enjoy.
paffenholz
Developer
Posts: 186
Joined: 24 Dec 2010, 13:47
Re: installation on OS X 10.7
I have updated the binaries for 10.7 and polymake 2.12 with gmp 5.0.5. Hopefully this solves toe problem with infinte loops caused by some commands.
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http://math.stackexchange.com/questions/256886/a-p-adic-jacobi-sum-with-an-unramified-character
|
# A $p$-adic “Jacobi sum” with an unramified character
Working over a $p$-adic field with absolute value $|\cdot|$, let $\chi$ be a character on ${\mathfrak o}^\times$ with conductor $n\ge 1$, meaning that $n$ is the smallest integer such that $\chi$ is trivial on $U_n=1+{\mathfrak p}^n$. I'm trying to calculate the integral, with ${\rm Re}(s)\gg 1$, $$J(\chi,|\cdot|^s)=\int_{\mathfrak o^\times}\chi(x)|x-1|^s\ dx$$ Note that if we replace $|\cdot|^s$ with a character $\chi'$ with conductor $n$, this would reduce to the typical Jacobi sum, and we'd have the formula $$J(\chi,\chi')={G(\chi,\psi)G(\chi',\psi)\over G(\chi\chi',\psi)}$$ where $\psi$ is an additive character with conductor $n$ and $G(\chi,\psi)$ is the Gauss sum $$G(\chi,\psi)=\int_{\mathfrak o^\times}\chi(x)\psi(x)\ dx$$ Of course, this formula wouldn't work for $\chi'$ unramified.
Is anyone aware of how to calculate this sort of Jacobi sum?
-
I think I've figured out how to do it. It's essentially the same argument as in the "classical" case, just interpreted slightly differently. Here's the sketch, which may lose some change-of-measure constants. $$J(\chi,|\cdot|^s)=\int_{\mathfrak o^\times}\chi(x)|x-1|^s\ dx$$ Extend $\chi$ by zero to all of $k$ and apply Fourier inversion to get $$=\int_{\mathfrak o^\times}\int_k |x-1|^s\psi(-ax)\int_{\mathfrak o^\times}\chi(y)\psi(ay)\ dy\ da\ dx$$ where $\psi$ has conductor $0$. The integral over $y$ vanishes unless ${\rm ord}(a)=-n$, so the integral becomes $$=\int_{\mathfrak o^\times}\int_{\mathfrak o^\times}|x-1|^s\psi(-\varpi^{-n}ux)\int_{\mathfrak o^\times}\chi(y)\psi(\varpi^{-n}uy)\ dy\ du\ dx$$ $$=\int_{\mathfrak o^\times}\int_{\mathfrak o^\times}|x-1|^s\psi(-\varpi^{-n}ux)\bar\chi(u)\int_{\mathfrak o^\times}\chi(y)\psi(\varpi^{-n}y)\ dy\ du\ dx$$ $$=G(\chi,\psi_{\varpi^{-n}})\int_{k}\int_{\mathfrak o^\times}{\bf 1}_{\mathfrak o^\times}(x)|x-1|^s\psi(-\varpi^{-n}ux)\bar\chi(u)\ du\ dx$$ $$=G(\chi,\psi_{\varpi^{-n}})\int_{k}\int_{\mathfrak o^\times}{\bf 1}_{\mathfrak o^\times}(1+x)|x|^s\psi(-\varpi^{-n}ux)\psi(-\varpi^{-n}u)\bar\chi(u)\ du\ dx$$ $$=q^{-ns-1}G(\chi,\psi_{\varpi^{-n}})\int_{k}\int_{\mathfrak o^\times}{\bf 1}_{\mathfrak o^\times}(1-\varpi^{n}u^{-1}x)|x|^s\psi(x)\bar\psi(\varpi^{-n}u)\bar\chi(u)\ du\ dx$$ Now, as a function of $x$, the characteristic function ${\bf 1}_{\mathfrak o^\times}(1-\varpi^{n}u^{-1}x)$ differs from ${\bf 1}_{\mathfrak o}(\varpi^{n}x)$ only on a set of measure zero, so we have $$J(\chi,|\cdot|^s)=q^{-ns-1}\big|G(\chi,\psi_{\varpi^{-n}})\big|^2\int_{\varpi^{-n}\mathfrak o}|x|^s\psi(x)\ dx$$ This final integral can be calculated using the well-known formula for $\int_{|x|=p^i}\psi(x)\ dx$, giving (if I did everything correctly), $$J(\chi,|\cdot|^s)=q^{-ns-1}\big|G(\chi,\psi_{\varpi^{-n}})\big|^2{2-q^s\over 1-q^{-s}}$$
And, of course, the norm-square of the Gauss sum is $q^{-n}$. – B R Dec 12 '12 at 22:52
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https://how-to.aimms.com/Articles/129/129-MSACCESS-32bit-64bit.html
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# Install Side-by-Side Drivers¶
Note
Some years ago, before Microsoft Office 2010, life was – in some sense – easier for developers: Office was 32-bit, period. In our days, since the release of Microsoft Office 2010, things are a bit more complicated, as users can now have a machine with a 64-bit native version of Office installed as well. This means, for instance, that a 32-bit application using an ODBC driver to connect to an Access database might not work anymore, since the 32-bit ODBC driver might not exist on a machine with a 64-bit Office installation. In such a case, even though the user has a valid Office installation on his or her machine, the application may still display an error regarding the installation or the registration of the proper drivers on the local machine.
In order to address such problems, Microsoft released a redistributable named Microsoft Access Database Engine 2010 Redistributable. This redistributable provides a 32-bit or a 64-bit version of the Microsoft Access Database Engine, which can be downloaded from the Microsoft Download Center:
So, for example, if you have a 32-bit application using a 32-bit ODBC driver on a machine with a 64-bit installation of Office 2010, you will need to install the 32-bit version of the Microsoft Access Database Engine as well.
Please note that launching the installation of a Microsoft Access Database Engine in the usual way, on a machine with an Office installation architecture different from the current one (e.g. 32-bit on 64-bit), may cause the installation to fail. To have it run properly, you need to launch it from a command line with the /passive argument specified:
• To install the Microsoft Access Database Engine 32-bit on a machine running Office 2010 64-bit:
> AccessDatabaseEngine.exe /passive
• To install the Microsoft Access Database Engine 64-bit on a machine running Office 2010 32-bit:
> AccessDatabaseEngine_X64.exe /passive
In order to use the new driver from your AIMMS project for connecting to an Access database, you need to adjust the Data Source Name (.dsn) file associated with your Access database. Typically that .dsn file contains something like:
[ODBC]
DRIVER=Microsoft Access Driver (*.mdb)
DBQ=MyDB.mdb
DriverId=25
FIL=MS Access
SafeTransactions=0
This should be changed to look like (where the changes are highlighted):
[ODBC]
DRIVER=Microsoft Access Driver (*.mdb, *.accdb)
DBQ=.MyDB.mdb
DriverId=25
FIL=MS Access
SafeTransactions=0
In order to use the new driver from your AIMMS project for reading CSV files by using ODBC, you need to adjust the DSN file associated with your (sub-) folder containing the CSV files. Typically that DSN file contains something like:
[ODBC]
DRIVER=Microsoft Text Driver (*.txt; *.csv)
DBQ=DATA
UserCommitSync=Yes
SafeTransactions=0
PageTimeout=5
MaxScanRows=16
MaxBufferSize=2048
FIL=text
DriverId=27
In this example, Data is the subfolder of your AIMMS Project directory containing the CSV files.
For the new driver this should be changed to look like (where the changes are highlighted):
[ODBC]
DRIVER=Microsoft Access Text Driver (*.txt, *.csv)
DBQ=.DATA
UserCommitSync=Yes
SafeTransactions=0
PageTimeout=5
MaxScanRows=16
MaxBufferSize=2048
FIL=text
DriverId=27
Extensions=txt,csv,tab,asc
Please note that the above is applicable to Office 2010 as well as to Office 2013. In case of Office 2013, the installation steps above should suffice. However, when Office 2010 32-bit is natively installed and the user tries to install the 64-bit version of the Microsoft Access Database Engine, he or she might still get an error regarding the registration of the proper drivers on the local machine. Should such a situation occur, please try the following workaround:
• Check the 64-bit registry key HKEY_LOCAL_MACHINESOFTWAREMicrosoftOffice14.0CommonFilesPaths before installing the 64-bit version of the Microsoft Access Database Engine 2010 redistributable.
• If it does not contain the mso.dll registry value, then you will need to rename or delete the value after installing the 64-bit version of the Microsoft Access Database Engine 2010 redistributable on a system with a 32-bit version of MS Office installed.
• Use the /passive command line parameter to install the redistributable, e.g. "C:directory pathAccessDatabaseEngine_x64.exe" /passive
• Delete or rename the mso.dll registry value, which contains the path to the 64-bit version of mso.dll (and should not be used by 32-bit MS Office versions).
• Now you can start a 32-bit MS Office application without the “re-configuring” issue.
Note that the mso.dll registry value will already be present if a 64-bit version of MS Office is installed. In this case the value should not be deleted or renamed.
Last Updated: March, 2020
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http://www.energsustainsoc.com/content/2/1/21
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Original article
# Greenhouse gas emission reductions as a motivator of e85 purchases across market segments
Adrienne E Marra, Kimberly L Jensen*, Christopher D Clark, Burton C English and Dustin K Toliver
Author Affiliations
Department of Agricultural & Resource Economics, University of Tennessee, 308F Morgan Hall, 2621 Morgan Circle, Knoxville, TN, 37996, USA
For all author emails, please log on.
Energy, Sustainability and Society 2012, 2:21 doi:10.1186/2192-0567-2-21
The electronic version of this article is the complete one and can be found online at: http://www.energsustainsoc.com/content/2/1/21
Received: 19 March 2012 Accepted: 3 September 2012 Published: 17 October 2012
© 2012 Marra et al.; licensee Springer.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
### Abstract
#### Background
Climate change has become a concern of both policy makers and consumers. Transportation constitutes a key source of greenhouse gas (GHG) emissions; hence, alternative transportation fuels with reduced GHG emissions are of increasing interest as a potential strategy for decreasing emissions. However, consumer views on achieving emission reductions through the use of alternative fuels have not been widely studied. Understanding consumer preferences related to alternative fuels is relevant as new fuel options become available.
#### Methods
This study uses a two-step cluster analysis of opinion variables to segment consumers into four market segments (Potential activists, Environmentals, Neutrals, and National interests). Cluster profiles are examined based on demographics and opinion variables related to concerns about national security, food versus fuel, perceived effects of personal actions, perceived effects of other's actions, and environmental issues. Willingness to pay (WTP) for reductions in GHG emissions through purchases of ethanol blends is estimated via conjoint analysis from a national survey.
#### Results
Estimates reveal that WTP varies in significance and magnitude across the four segments. In particular, the Environmentals market cluster is the only cluster consistently willing to pay a premium for emission reductions.
#### Conclusions
Market opinion clusters play a significant role in WTP for emission reductions through purchases of E85. Results suggest the existence of a potential niche market consisting of consumers with strong environmental concerns who are willing to pay a premium for renewable fuels in order to reduce GHG emissions.
##### Keywords:
Market opinion clusters; Willingness to pay; Emission reductions
### Background
The US Environmental Protection Agency estimated that the transportation sector was the largest contributor to US greenhouse gas (GHG) emissions in 2010, contributing about 30.4% of US CO2 emissions [1]. In 2009, the USA was responsible for nearly 18% of the world's CO2 emissions [2]. Consumers have become increasingly aware of their role in contributing to GHG emissions, as evidenced by the 73% of surveyed consumers who were aware of the term carbon footprint in 2010 [3]. Public opinion polls have indicated concerns about GHG and the environment, but have provided mixed opinions on the most effective means to reduce GHG emissions. A June 2010 Pew Research Center Poll revealed that about two-thirds of the respondents favored limits on CO2 and other greenhouse gas emissions [4]. Furthermore, while 37% favored keeping energy prices low as the most important priority, about 56% favored protecting the environment as the most important priority. However, an earlier poll by Stanford University and Resources for the Future found that US consumers tended to favor policies directed at the electricity sector rather than at transportation, with transportation emission taxes receiving little support [5]. In addition, a 2007 Gallup poll showed that 55% did not favor a policy that would ban vehicles averaging less than 12.75-km/l fuel efficiency [6].
Accumulating evidence of the link between GHG emissions and climate change has prompted the adoption of an array of policies designed to reduce GHG emissions. In the USA, many of these policies have focused on the transportation sector, given its importance to GHG emissions [7]. Some of these policies have been designed to reduce GHG emissions by improving automotive fuel efficiency. For example, the Energy Independence and Security Act of 2007 [8] raised the Corporate Average Fuel Economy standards for passenger cars and light trucks for the first time since 1975. Other policies are designed to promote the production and consumption of alternatives to petroleum-based gasoline.
Several US renewable fuel policies have focused on promoting production and consumption of ethyl alcohol (ethanol). Ethanol is a renewable fuel made from various plant materials, which are collectively referred to as ‘biomass’. Most of the gasoline sold in the USA is blended with ethanol to oxygenate the fuel and reduce air pollution [9]. In general, the ethanol content is limited to 10% (E10) or less. However, flexible fuel vehicles (FFVs) can safely operate on a blend of up to 85% ethanol (E85). As a renewable fuel made from biomass, ethanol has the potential to reduce net GHG emissions associated with transportation. Ethanol production and consumption is subsidized in the USA through a tax credit equal to $0.12/l of pure ethanol blended into gasoline. Also, a 2005 federal law created a Renewable Fuels Standard (RFS) requiring 2.84 × 1010 l of renewable fuel to be blended into the transportation fuel on an annual basis by 2012. The RFS was amended in 2007 to increase the requirement to 1.36 × 1011 l by 2022. Production of ethanol in the USA has increased significantly over time with production rising from 6.62 × 108 l in 1980 to 5.26 × 1011 l in 2011 [10]. Despite these preferential policies, ethanol will ultimately have to compete for its share of the transportation fuel market. In particular, for consumers to purchase E85 and E85-compatible vehicles, they will need to perceive benefits from consuming this fuel compared with either regular gasoline (E0) or other lower-level ethanol blends such as E10. One attribute that may influence consumer decision making in selecting a fuel, whether an ethanol blend or conventional gasoline, is the level of emissions generated when using the fuel. The objectives of this study are to estimate willingness to pay (WTP) for GHG emission reductions through the use of E85 and analyze how WTP is influenced by demographics and attitudes toward renewable energy, fuel security, and the environment. Data on consumer preferences are collected with a conjoint analysis exercise that asks respondents to choose among fuel varieties that are differentiated along the dimensions of price (Price), ethanol blend (E85, E10, and E0), percent imported (Imports), availability (Inconvenience), and reductions in GHG emissions (Reduce). WTP for GHG emission reductions through the use of E85 are estimated using the random parameters logit (RPL) model to analyze the data from the conjoint exercise. The effects of consumer demographics and attitudes toward the environment and fuel security on WTP for emissions reductions are incorporated in the analysis through interactions with the emission reduction attribute. One might argue that two of the primary ‘benefits’ of ethanol consumption relative to gasoline, improved environmental performance and increased domestic production, are externalities that primarily accrue to a broader set of individuals than the set of ethanol consumers. As a result, in the absence of any price advantage, the market for ethanol might be expected to be a niche market, driven largely by consumer attitudes toward issues such as the environment, fuel security, and food security. To explore these attitudes, a cluster analysis is used to group respondents on the basis of their responses to a variety of attitudinal questions. The resulting clusters are used to analyze how differences in attitudes may impact WTP for GHG emission reductions. #### Market segmentation Smith's pioneering article [11] emphasized the role of the consumer in the market and discussed the strategy of market segmentation over 5 decades ago. In the years since, market segmentation has become a commonly utilized marketing tool to identify the preferences and needs of distinct market segments for new products and to address these needs with specific marketing strategies [12,13]. Classification of consumers into groups or market segments is often used in order to gain a better understanding of consumer needs and motivations in order to facilitate the marketing of a product [11,14]. A common way of segmenting markets is through clustering. Clustering is a basic investigative technique that involves grouping similar objects together based on a set of characteristics [15]. It is the art of finding groups in data and relies on the meaningful interpretation of the researcher or classifier [16]. Simply stated, clustering involves gathering similar objects (data) into distinct clusters that are internally homogeneous and externally heterogeneous. A popular approach to finding clusters in a data set is to employ a hierarchical method followed by a non-hierarchical method [17-19]. Van de Velde et al. [20] used such a two-step process to cluster consumers based on their perceptions of the importance of fuel characteristics and beliefs about biofuels. The first step involved a hierarchical cluster method that was used to create an agglomeration schedule and dendrogram from which a four-cluster solution was determined to be optimal. The second step used the cluster centers from the hierarchical method to refine the solution using a k-means cluster analysis. Clusters were identified as performance-oriented, society-oriented, environment-oriented, and convenience-oriented consumers. #### WTP for GHG emission reductions and ethanol blends Several studies have focused on attitudes toward and WTP for GHG emission reductions. Jeanty and Hitzhusen [21] used a contingent valuation exercise to estimate WTP for air pollution reduction from the use of biodiesel in diesel engines. More specifically, they valued the benefits of reducing CO2 emissions by 75%, fine particulates by 47%, sulfur emissions by 100%, and volatile organic compounds by 56%. They reported premiums of$0.02/l, $0.05/l,$0.08/l depending on the statistical model used. Achtnicht [22] used a stated preference exercise to estimate WTP for the abatement of CO2 emissions among German car buyers and to examine whether CO2 emissions per kilometer is a relevant attribute when choosing a vehicle. The results revealed that CO2 emissions were a significant attribute related to vehicle choice and that women, younger respondents, and those who possessed a Higher Education Entrance Qualification were willing to pay more for CO2 reductions. MacKerron et al. [23] examined airline passengers' WTP for emission offsets for their airline flights. They estimated that passengers were willing to pay about $39.10 per flight to offset associated emissions. While they found females were more likely to buy the offsets than males, neither income nor having children had a significant effect. O'Connor et al. [24] reported the results of a mail survey of 623 residents of Central Pennsylvania on support for policies to reduce GHG emissions. Ordinary least squares analysis revealed that respondents who could correctly identify the causes of climate change and who expected negative consequences from climate change were likely to support both government initiatives that were focused on replacing fossil fuels and voluntary actions to do the same. Economic circumstances and concerns were not found to be significant predictors of support for such policies. The belief that environmental protection efforts do not threaten jobs, limit personal freedoms, or hurt the economy was a strong predictor for support of the GHG mitigation policies. Overall, respondents wanted to reduce emissions if they understood the causes of climate change, perceived climate change to be a significant risk, or felt that climate change mitigation policies would not reduce employment opportunities. Roe et al. [25] examined consumer WTP for emission reductions from electricity production when there is no change in fuel source and when the fuel source is renewable. Their results suggest that many population segments are willing to pay for decreases in air emissions. They also found that several groups were willing to pay significantly more when the emission reductions were generated by increased use of renewable fuels. Significant differences in WTP were found across regions and income levels. Dietz et al. [26] examined social influences on the support for climate change policies and found political orientation, income, race, gender, and age to be influential. Similarly, Berrens et al. [27] estimated WTP for various climate change policies and found that political ideology had a significant influence. Several studies have focused specifically on consumer preferences for ethanol blends [28-31]. Petrolia et al. [28] used a contingent valuation exercise to examine WTP for E10 and E85 among US consumers. They found that demand for E85 is more price inelastic than E10, with much stronger preferences for E85 than E10. Their results suggested that more educated people are more likely to be accepting of E10, but less likely to pay a premium. However, politically ‘liberal’ respondents were more likely to pay a premium for both E10 and E85. Solomon and Johnson [29] conducted a study of Michigan, Wisconsin, and Minnesota residents to determine how these residents valued climate protection through the potential purchase and consumption of cellulosic ethanol. Using a multi-part, split-sample contingent valuation method, the authors found that 83.8% of the respondents were willing to pay higher fuel prices for cellulosic ethanol. Variables that were significant determinants of WTP were household income, political views, gender, climate change concerns and beliefs, and whether the premium would go towards reducing climate change. Aguilar and Thompson [30] examined attitudes toward ethanol use and WTP for ethanol blends among Missouri consumers. They found widespread agreement with statements suggesting that ethanol could benefit farmers, reduce dependence on fossil fuels, and improve the environment (i.e., ‘The use of ethanol as a motor vehicle fuel benefits U.S. farmers’, ‘The use of ethanol as a motor vehicle fuel helps reduce U.S. dependence on fossil fuels’, and ‘The use of ethanol as a motor vehicle fuel has a positive impact on the environment’). However, their estimated WTP for ethanol blends of 20% (E20) was lower but statistically indistinguishable from WTP for E0 or E10. They examined the fuel attributes of price, octane rating, feedstock source, and blend but did not include emission reductions as an attribute in their modeling. Finally, Jensen et al. [31] examined WTP for E85 from corn, switchgrass, and wood residues compared with E10, using some of the same survey data used in this analysis. Results from their study suggest consumers are willing to pay a premium for E85 with switchgrass as the ethanol feedstock as opposed to E10 with corn as the ethanol feedstock. They also found that consumer concerns about land use for fuel instead of food production had a negative impact on WTP for E85 from corn grain, while greater concerns about fuel security relative to the environment had a positive impact. They also estimated WTP for emission reductions from E85 compared with E10 from corn to be about 0.0043 cents/km for each percent in emission reductions (0.036 cents/l for a vehicle with a fuel efficiency of 8.50 km/l) However, their study neither examined the effects of attitudes or demographics on WTP for emission reductions nor did it consider consumer preferences for E0. While several studies ([21-26]) have examined WTP for emission reductions or for ethanol blends ([28-31]), these studies have not examined WTP for emission reductions as an attribute of E85 within the context of conjoint analysis. This study will extend the literature by estimating how WTP for emission reductions through E85 purchases vary across market segments using cluster analysis to identify the market segments, conjoint analysis to estimate WTP, and data from a nationwide US survey. ### Methods #### Economic model of willingness to pay Consumers are assumed to maximize utility and that when presented with a set of alternatives, they will select the alternative that provides the greatest amount of utility relative to the other alternatives. It is also assumed that the utility received from any alternative is related to a set of observable attributes associated with that alternative. Thus, the utility that individual n receives from the jth alternative (Unj) can be expressed as Unj= θZj+ εnj, where Zj is a vector of observed attributes of the jth alternative, θ is a vector of unobserved parameters to be estimated, and εnj is an error term. Under certain conditions, a conditional logit model [32] can be used to estimate this model, in which case the probability of selecting alternative j can be expressed as: (1) Mean WTP for attribute l is calculated using: (2) where is the estimated coefficient for l, a non-price attribute, and is the estimated coefficient for price. However, the conditional logit is limited in that it assumes homogeneity of individuals, implying that there is homogeneity of preferences across the sample. Heterogeneity of preferences across consumers can be incorporated into the model using a random parameter model [33]. Individual utility within this framework can be expressed as: (3) where is a vector of the mean parameters to be estimated across the n individuals, and σn is the vector of individual deviations from the population mean . Mean WTP can be estimated using [34]: (4) The attribute for price is assumed to be constant across respondents to avoid problems associated with individual coefficient estimates that are the same sign as [35] or are near zero [36]. Heterogeneity of preferences can also be incorporated into the model by including demographic and attitudinal variables in a ‘mixed’ model [37]. When the fixed parameter model is modified to include these demographic and attitudinal variables, utility can be expressed as: (5) where Yn are individual characteristics or taste indicators, and ϕ are their associated parameters. The individual characteristics enter the model as interactions with the product attributes. Mean WTP for attribute l, calculated at the sample mean, becomes: (6) This mixed model is modified by Lavin and Hanemann [38] to enable the incorporation of the taste indicators of the consumers into the random parameters model. Utility in this model can be expressed as: (7) where Yn are taste indicators and ϕ are their associated parameters. Again, is a vector of the mean parameters, and σ is the vector of individual deviations from the mean. This model becomes the RPL with individual characteristics or taste indicators interacted with the product attributes. If the demographic and attitudinal variables are interacted with non-price variables, then the individual-level estimate for WTP for attribute l becomes: (8) The individual-level WTP is calculated according to Equation 8 using the individual-level parameters for the non-price attributes, respondent characteristics, and the fixed parameters on these characteristics, along with the fixed parameter on price. Mean WTP can be calculated at the means of the random parameters and the demographic and attitudinal variables using [39]: (9) In this analysis, the attitudinal variables and individual characteristics are interacted with the emission reduction attribute (Reduce). The parameters on the fuel attributes other than fuel price are randomized, while the parameters on price and on the interactions of the emission reduction variable (Reduce) with the demographic and attitudinal variables are held fixed. The coefficient on emission reductions (Reduce) is hypothesized to be positive [21]. The coefficients on percentage of imported fuel (Import), on fuel that is less widely available (Inconvenience), and on fuel price (Price) are expected to be negative. The RPL is estimated with simulated maximum likelihood and, in this case, using Halton draws with 1,000 replications. The randomized parameters are assumed to follow a normal distribution. #### Survey The data were obtained through an online survey conducted in January and February of 2009. The survey sample and online services were provided by Knowledge Networks® (KN). The sample was drawn from an online research panel maintained by KN and designed to be representative of the US population. More information on the online research panel and recruitment methodology can be found in KN [40]. The sample was a simple random sample of panel members 18 years of age or older. The survey was fielded to 2,851 panel members, and 1,909 responses were received before the survey was closed to further responses. The survey instrument began with two screening questions. If the household did not currently own or lease at least one automobile or the household automobile the respondent drove the most often did not have a gasoline or gasoline/electric engine, the respondent was screened out of the survey. Out of the 1,909 respondents, 1,727 passed the screening and provided useable responses to the survey. Out of these 1,727 responses, 1,668 were used for the cluster analysis based on the completeness of responses to the clustering questions. A survey weight designed to compensate for non-response to the survey was calculated by comparing respondent demographics with benchmark demographics (i.e., gender, age, race/ethnicity, education, Census Region, metropolitan area, and internet access) from the Current Population Survey. The weight was calculated with an iterative proportional fitting procedure [38]. The distribution of the calculated weights was examined to identify and, if needed, trim outliers at the extreme upper and lower tails of the weight distribution. The post-stratified and trimmed weights were then scaled to the sum of the total sample size. All results presented in this paper have been weighed with the resulting weights. In addition to the screening questions, the survey instrument provided respondents with some basic information on ethanol blends and feedstocks. This information was provided on eight different ‘information screens’. The information screens were interspersed with questions covering such issues as vehicle ownership, driving patterns, and familiarity and experience with ethanol and FFVs. Following the information screens was a conjoint analysis exercise where respondents were asked to choose between three different varieties of E85 and, depending on the survey version, either E0 or E10 produced with corn grain ethanol. Participants were asked to assume that their automobile was compatible with E85 when responding to the conjoint analysis questions. Following the conjoint analysis exercise, respondents were asked a number of attitudinal and behavioral questions on a variety of topics related to ethanol production and consumption, including fuel security, fuel consumption behavior, the food vs. fuel debate, climate change, and the environment. Finally, responses to the survey questions were supplemented with demographic information from the panel member profile maintained by KN. The conjoint analysis exercise consisted of 14 different choice tasks, although three of these were fixed or holdout tasks that were constant across all respondents.a Each choice task had four alternative combinations of fuel attributes, and respondents were asked to select their most preferred alternative from these four. Three of the alternatives were an E85 blend with differing levels of attributes while the remaining alternative was either E0 or E10 from corn, depending on the survey version. The levels of the attributes for the three E85 blends differed from one alternative to another and from one choice task to another, while the levels of the attributes for the E0 or E10 alternative were constant across all choice tasks. bSee Figure 1 for an example of the choice task presented to respondents. Figure 1. Example of choice task.a Price levels offered in this example are 7.8, 7.4, and 7 cents/mile driven. These prices convert to 4.8, 4.6, and 4.4 cents/km. Assuming 8.5 km/l, the prices per liter are$0.41/l, $0.39, and$0.37 for E85 and $.53 for gasoline. The attributes included in the choice task were fuel price (stated both in dollars per gallon and dollars per mile or$/l and $/km), feedstock for the ethanol, percent of fuel from imported sources, level of GHG emission reductions relative to either E0 or E10 (depending on survey version), and availability of the fuel. For the analysis presented in this study, the ethanol feedstock types are aggregated to E85 from a biomass feedstock to focus on willingness to pay for emission reductions. Price per kilometer was calculated using an example vehicle that gets 8.5 km/l with E85. For the E0 survey, the price levels used for the E85 alternatives were 3.9, 4.1, 4.3, 4.6, and 4.8 cents/km driven, while the E0 alternative was priced at 4.4 cents/km. These prices per kilometer convert to$0.33, $0.35,$0.37, $0.39, and$0.41/l for E85 and $.53/l for E0. For the E10 survey, the price levels used for the E85 alternatives were 4.2, 4.4, 4.7,4.9, and 5.2 cents/km driven, with the E10 alternative priced at 4.7 cents/km. These prices per mile convert to$0.35, $0.38,$0.40, $0.42, and$0.44/l for E85 and \$.53/l for E10 on an energy equivalent basis.
The levels of emission reductions for the E85 alternatives were 10%, 50%, and 73% compared with E0 or E10 (the percent reduction for E0 or E10 was obviously zero). The percentages of E85 fuel imported were 10%, 33%, and 50%, with the E0 alternative listed as being 67% imported and the E10 alternative listed as being 60% imported. Availability of the E85 alternative was stated as being located at a fuel station that was ‘on your way’ or either 2 or 5 min ‘out of your way’. The E0 and E10 alternatives were presented as being 2 min out of the way.
The resulting fuel attribute variable definitions are provided in Table 1. These fuel attributes include price (Price), blend (E85), minutes out of the consumer's way that he or she must travel to purchase the fuel (Inconvenience), percent of GHG emission reductions from E10 or E0 (Reduce), and percent of fuel from imported sources (Import).
Table 1. Names, definitions, and hypothesized signs of variables used in the models
The experimental design used to determine how the levels of the attributes of the E85 alternatives varied across alternatives and choice tasks were generated using Sawtooth Software's CBC/Web software (UT, USA). The design was a randomized design created using the Balanced Overlap design strategy. The Balanced Overlap strategy prohibits duplicate alternatives within the same choice task but does not strictly minimize the number of times a particular attribute level is shown in a single task. Allowing some overlap of attribute levels within a choice task improves the researcher's ability to analyze interactions between the attributes [41] and may outperform strategies that minimize level overlap [42]. Although the software can produce a unique design for each respondent, the need to import the design into KN's web architecture rendered such a large number of alternative designs infeasible. Instead, 20 different designs were created, and each respondent was randomly assigned to one of the 20 designs.
#### Cluster analysis
Market segments were identified using a cluster analysis of responses to the series of 15 attitudinal and behavioral questions that followed the conjoint analysis exercise. These questions were actually statements where the respondents were asked to list their level of agreement with the statement using a five-point Likert scale ranging from ‘strongly disagree’ (1) to ‘strongly agree’ (5). These statements pertained to attitudes and behaviors related to fuel security, the food vs. fuel debate, environmental concern, perceived consumer effectiveness (PCE)c, and faith in the efficacy of others (FIO)d. A complete list of variables used in the cluster analysis can be found in Table 2. Several of the variables in Table 2 were based upon [26]. A popular two-stage cluster method in which a hierarchical cluster method is followed by a non-hierarchical method was chosen for this analysis [17-20]. Ward's minimum variance method was the hierarchical method used to determine the optimal number of clusters. This method minimizes the within-cluster sum of squares [43]. At each stage of the analysis, joining of every possible pair of clusters is considered, and the two clusters whose union results in the minimum increase in ‘information loss’ are combined [15]. The number of clusters was determined based on inspection of the dendrograms and interpretation of the relevance of three, four, and five cluster solutions. The number of clusters was also ascertained using the Duda-Hart Je(2)/Je(1) index for which larger values indicate more distinct clustering [44].e Based on these observations, a four-cluster solution emerged as optimal. Cluster centroids were saved from the Ward's analysis to be used as starting seeds for the k-means analysis. It is widely recognized in the literature that the performance of the k-means method depends largely on the initial seeds used to begin the clustering process [19,44,45]. Steinley [46] cautions about the starting seeds used in the k-means procedure and notes that researchers have often chosen to use starting seeds from a hierarchical method like Ward's minimum variance to obtain the starting seeds for the k-means method [47,48]. The results from the Ward's method analysis were refined using the k-means non-hierarchical method. The k-means method is a simple, non-parametric clustering method that minimizes within-cluster variability and maximizes between cluster variability.
Table 2. Names and descriptions of variables used in cluster analysis
To investigate associations between clusters and demographics and other survey questions, analyses of variance were conducted to determine differences in mean opinion ratings across the four clusters for each of the opinion variables. The analyses of variance were calculated based on an approach suggested by Kennedy [49]. In this case, dummy variables are created for three of the four clusters. The variable of interest is then regressed on the three cluster dummy variables. In this method, the coefficients for the dummy variables are the means for the variable for each cluster. The analysis of variance F-test is the same as testing whether or not the dummy variable coefficients (means) are significantly different from each other [49]. It was necessary to use this method so that the post-stratification weight could be applied to the data. Mean comparison tests (t tests) were conducted by omitting one cluster dummy variable at a time and evaluating the significance of the coefficients on the other dummy variables by examining the t-statistics associated with each estimated coefficient. Names for the four clusters (Potential Activist, Environmental, Neutral, and National Interest) were based on inspection and interpretation of the mean responses to the clustering variables.
The effects of demographic characteristics on market opinions were examined using a multinomial logit with the Neutral cluster as a base. The demographics examined included gender, age, education level, income, region of residence, political views, and race/ethnicity. The definitions of these variables are shown at the bottom of Table 3.
Table 3. Multinomial logit of market opinion clusters on demographic variablesa,b
#### Conjoint analysis
WTP for emission reductions is estimated using responses to the conjoint analysis tasks. Conjoint analysis has been used extensively in consumer research as a means of predicting consumer preferences among multi-attribute alternatives since the early 1970s [50]. The type of conjoint analysis used in this study is also referred to as contingent choice. With contingent choice, respondents choose a preferred product defined along a set bundle of product attributes from among two or more product choices. The set of attributes for all products is the same, but the attribute levels differ among the product varieties. This method was chosen because of its similarity to the actual purchase decisions faced by consumers. The inclusion of price as a product attribute in this survey allows WTP to be estimated for changes in levels of non-price attributes such as GHG emission reductions.
### Results and discussion
#### Market opinion clusters
As stated earlier, the cluster analysis revealed four clusters: the Potential activist, Environmental, Neutral, and National interest clusters. Table 4 displays the overall F-tests for differences in the mean opinion ratings among these four clusters. In each case, statistically significant differences among the mean ratings across clusters were observed. Further examination of the t tests revealed that significant differences existed among most of the means across the clusters. A description of each cluster is provided below.
Table 4. Mean market opinion ratings across clustersa,b
#### Potential activist cluster
The Potential activist cluster is the largest of the four and contains 560 respondents. As can be seen in Table 4, while the members of the Potential activist cluster feel strongly about several of the clustering questions, they tend not to have either the highest or lowest mean responses. Issues surrounding climate change are of greater importance to this cluster than the National interest and Neutral clusters, but not greater than the Environmental cluster. The Potential activists are also second behind the Environmentals when it comes to environmental concerns both now and in the future; however, the Potential activists led all clusters in agreement with the statement that they do not have enough information to make well-informed decisions about environmental issues. The Potential activists have varying opinions about consumer effectiveness – they tend to disagree that personal actions do not have any significant effect on the environment, but they are also the most likely out of the four clusters to agree that most people are not willing to make sacrifices to protect the environment. Finally, the Potential activists are the second most likely behind the National interests to agree that science and technology will solve environmental problems.
#### Environmental cluster
The Environmental cluster is the second largest cluster with 459 respondents and its members are the most likely to agree that climate change is occurring and that it will lead to environmental and health problems around the world. As shown in Table 4, this cluster strongly disagrees that there is no urgent need to take measures to prevent climate change. The Environmentals are the second most likely behind the National interests cluster to agree that US farmland should be used to produce food and not fuel and that increased corn ethanol production will lead to higher food prices. This cluster believes that the USA should reduce its dependence on foreign oil, but does not believe that it is more important than protecting the environment. The Environmentals are the least likely to support opening up more US lands for oil drilling. Concerns for the loss of the world's forests are highest in this cluster as well as concern for the state of the environment both present and in the future. Members of the Environmental cluster disagree, more than any other cluster, with the statement that their personal actions do not have an effect on the quality of the environment; however, like Potential activists, they are likely to agree that most people are not willing to make sacrifices to protect the environment. They are second behind the National interest cluster in disagreeing with the statement that they do not have enough information to make well-informed decisions on environmental issues. Not surprisingly, the Environmentals feel a greater responsibility to protect the environment for future generations than the other clusters.
#### Neutral cluster
The Neutral cluster is the third largest with 410 respondents. The Neutral cluster is so named because its means are clustered around the value of three, which represents neutral in the Likert scale range used. As a result, the Neutral cluster lags the other clusters in agreeing with a number of the statements (i.e., farmland should be devoted to food and not fuel, increasing ethanol production from corn will lead to higher food prices, reducing dependence on foreign oil more important than improving national security, science and technology will come up with ways to solve environmental damage and pollution, most people not willing to make sacrifices to protect the environment, and that we have responsibility to protect environment for future generations). Their level of agreement with six of the other statements is below two of the three other clusters. There is no variable for which the Neutral cluster has the highest mean level of agreement of the four clusters, although they have the second highest mean level of agreement for three of the statements (i.e., there is no urgent need to take measures to prevent climate change, do not have enough knowledge to make well-informed decisions on environmental issues, and personal actions do not have any significant effect on the environment).
#### National interest cluster
The National interest cluster is the smallest of the four with 239 respondents. This cluster agrees more strongly than any other cluster that US farmland should be used for food not fuel, and that increasing corn ethanol production will lead to higher food prices (Table 4). National security is of utmost importance to this cluster as they are most likely to agree that reducing our dependence on foreign oil is important and that it is more important than protecting the environment. Hence, they also feel most strongly about opening more US lands for oil drilling. In terms of climate change, this cluster is the least likely of all the clusters to agree that climate change is occurring and that it will lead to health and environmental problems around the world. The National interest cluster is also the most likely to disagree that there is an urgent need to take measures to prevent climate change, that they are concerned for the loss of the world's forests, and that they are concerned for the state of the environment both now and in the future. This cluster feels most strongly about their ability to make well-informed decisions on environmental issues, but they are also most likely to agree that personal actions do not have any significant effect on the quality of the environment. The National interest cluster is the most likely to agree that science and technology will develop solutions for environmental and pollution problems. They are the least likely out of the four clusters to agree that there is a responsibility to protect the environment for future generations.
The effects of cluster membership on WTP for emission reductions through use of E85 can be hypothesized based upon observed differences in the attitudes of the four clusters. Using membership in the Neutral cluster as the base case, membership in the Environmental cluster is expected to have a positive influence on WTP for emission reductions, as members of the Environmental cluster tend to have strong views about the importance of protecting the environment. Membership in the National interest cluster is expected to have a negative influence on WTP as these individuals are more concerned about national security and less concerned about the environment. WTP by the Potential activist cluster relative to that by the Neutral cluster is difficult to hypothesize, a priori, as the members of the Potential activist cluster are concerned about the environment, but feel that their personal actions have little effect while also believing that science and technology will solve environmental problems.
#### Estimated multinomial model of opinion clusters on demographics
As can be seen in Table 3, the coefficient on the Female variable for the National interest cluster in the multinomial logit model was negative and significant, implying that females were less likely to be members of the National interest cluster than of the Neutral cluster. Female was not significant for either of the other two clusters. The coefficient on Education was positive and significant for the each of the clusters. Thus, greater educational attainment increased the likelihood that the respondent would fall into an opinion cluster other than the Neutral cluster. Income was positively correlated with membership in the National interest cluster relative to the Neutral cluster. The coefficient on Age was positive and significant for all three clusters, suggesting that older respondents were more likely to have non-neutral opinions about the issues. The coefficient on the regional variables indicates that respondents residing in the South and the Midwest were more likely to fall in the National interest cluster. Respondents who leaned more toward being a Democrat were more likely to be a member of the Environmental cluster, but less likely to be a member of the National interest cluster. Relative to other races, respondents who were Black were less likely to fall into the Potential activists and the Environmental clusters. Hispanic respondents were more likely to be a member of the Potential activists cluster. A Hausman test revealed that the Independence of Irrelevant Alternatives assumption holds for the multinomial logit in this case.
#### Estimated models of WTP
Three different econometric analyses were performed on both the E0 and E10 survey versions to measure the effects of membership in the different clusters on WTP for emission reductions. These three analyses were a conditional logit and a RPL, in which the Potential activist, Environmental, and National interest cluster variables were interacted with the emissions reduction (Reduce) product attribute, and a RPL on the product attributes only. The base or omitted cluster for the analyses with interaction terms was the Neutral cluster. In order to identify whether conditional logits were sufficient or RPL needed to be employed, both the RPL models with E0 and E10 as bases were compared with their conditional logit counterparts. In both cases, the log-likelihood ratio test indicated that the RPL model was preferred (E0: LLR = 4559.17, 4df; E10: LLR = 3164.47, 4 df) at the 95% confidence level.f To measure whether the clusters as a group contributed to the model, log-likelihood ratio tests were also conducted using the RPL with fuel attributes only and the RPL with fuel attributes and the cluster interactions with Reduce. In both cases (E0 and E10), the tests indicated that the cluster interactions contributed significantly to the models (E0 79.449, 3 df; E10 81.6058, 3 df).
The results of the RPLs with the interaction terms for both the E0 and E10 cases are shown in Table 5. Both the E0 and E10 models were significant overall, as indicated by the LLR tests against an intercept only model. All of the coefficients on the non-emission characteristics were significantly different from zero and were of the expected sign. The coefficient on Reduce was significant in the E0 model, but not in the E10 model. The pattern of significance for the interaction of the cluster variables with emission reductions differed across the two models. The coefficient on Environmental*Reduce was positive and significant in both models, suggesting that WTP was higher among members of the Environmental cluster than among those in the Neutral cluster regardless of whether E0 or E10 was the base fuel. The patterns for the Potential activist and National interest interactions were mixed. The coefficient on Potential activist*Reduce was positive and significant in the E10 model, but insignificant in the E0 model, perhaps suggesting that Potential activists were more receptive to emission reductions when choosing between E85 and E10 than when choosing between E85 and E0. The coefficient on National interest*Reduce was negative and significant in the E0 model, but insignificant in the E10 model. This result could suggest that National interest respondents are less receptive to emission reductions when choosing between E85 and E0 than when choosing between E85 and E10. These two results together may reflect the reticence of certain market segments about moving away from existing gasoline technologies.
Table 5. Estimated random parameters logits for E85, with E0 and E10 as the base fuelsa
As can be seen in Table 6, for the E0 and E10 respondents, the estimated WTP for each of the non-emissions attributes was significantly different from zero and of the anticipated sign. The estimated WTP for emission reductions by the Environmentals cluster is positive and significantly different from zero in both the E0 and E10 models. The Neutrals’ WTP for emission reductions is positive and significant in the E0 model, but not significantly different from zero in the E10 model. The WTP estimates for the National Interests and Potential Activists clusters are insignificantly different from zero for both E0 and E10. Among the Environmentals, the estimate of WTP for each percentage point reduction in emissions is about 0.07 cents/km or about 0.63 cents/l given a 8.5 km/l vehicle for the E0 base and 0.08 cents/km or about 0.67 cents/l given a 8.5 km/l vehicle for the E10 base.
Table 6. Estimated willingness to pay for fuel emission reductions and other fuel attributesa,b,c
### Conclusions
This study segmented survey respondents into four distinct market clusters. The Potential activists are those who have environmental concerns, but who are also the least likely to feel that they have enough information to make well-informed decisions about environmental issues and tend not to believe that others will make sacrifices to protect the environment. The Environmentals have strong concerns about the environment and feel that we all have a responsibility to preserve the environment for future generations. Those in the Environmental cluster tend to be more educated and have more liberal political views. The members of the National interest cluster are more concerned about national security, placing a higher importance on it than the environment and believe most strongly in opening up additional lands for oil drilling. Members of this cluster are the greatest climate skeptics, being the least likely to agree that climate change is occurring. They also are the most likely to agree that land should be used for food and not fuel. Those in the National interest cluster tended to be more conservative in their political leanings, be males, and to have higher incomes. The Neutral cluster is generally neutral about environmental and national security issues, but were the least likely to believe that we should protect the environment for future generations.
These market opinion clusters play a significant role in estimates of WTP for emission reductions through purchases of E85. In particular, Environmentals is the only cluster which is consistently in willing to pay a premium for emission reductions. The Environmentals are willing to pay around 0.63 to 0.67 cents/l per percentage point of emission reduction. This result suggests that those who feel strongly about environmental issues may be the only consumers who are willing to pay a premium for E85 due to its potential to reduce GHG emission reductions. The Environmentals constituted just under 28% of the respondents to a national survey that was weighted to better represent the US population.
The results suggest that there is a potential niche market of consumers with strong environmental concerns who are willing to pay a premium for renewable fuels in order to reduce GHG emissions. While other consumers may not, in general, be willing to pay a premium for E85 in order to achieve emission reductions, they may be interested in other attributes of ethanol blends, such as the share that is produced domestically or availability of the fuel. Future research should focus on how the market opinion segments may impact WTP for these attributes. Policy makers may find this information useful as they seek to market E85 and facilitate the development of markets for alternative fuels more generally.
### Endnotes
aHoldout tasks are used as a means of assessing the validity of econometric models used to analyze responses to the choice tasks [51]. bStructured this way, the E0 or E10 alternative acts similar to the ‘none’ option that is commonly included in contingent choice tasks. cPerceived consumer effectiveness measures the extent to which an individual feels that his or her behavior has an impact on a given situation [52]. Berger and Corbin's study suggests that PCE is extremely influential as a representative of the environmental attitude/consumer behavior relationship [52]. dFaith in others represents a circumstance in which, rather than changing a personal action, an individual could choose to support policies, research, or groups to solve a particular problem. Bergin and Corbin's study suggests that an individual's level of FIO will influence the extent to which the individual supports others' actions in pursuing a solution to a problem [52]. , while . fThe log-likelihood ratio test is calculated as −2 (log likelihood restricted − log likelihood unrestricted).
### Competing interests
The authors declare that they have no competing interests.
### Authors' contributions
AM performed the analysis and was responsible for writing the manuscript. KJ, CC, BE, and DT all contributed by proofreading and editing the manuscripts as well as giving guidance and technical advice throughout the analytical and writing processes. All authors read and approved the final manuscript.
### Authors' information
AM and DT are former research associates of the Department of Agricultural & Resource Economics, University of Tennessee. CC is an associate professor, and KJ and BE are professors of the same department.
### Acknowledgments
This study was funded in part by a grant through the National Research Initiative Competitive Grants Program, USDA/CSREES.
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http://math.stackexchange.com/questions/58709/understanding-the-definition-of-dense-sets
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# Understanding the definition of dense sets
I am recently confused about the definition of dense sets. What I learned is as the following
In topology and related areas of mathematics, a subset $A$ of a topological space $X$ is called dense (in $X$) if any point $x$ in $X$ belongs to $A$ or is a limit point of $A$.
The point is that when we say "a set $A$ is dense in a topological space $X$" we should first have the fact that $A$ is a subset of $X$. However, there is a notion that "a set $E$ is dense in a ball $X$" as I mentioned in this question. In this notion, $E$ is not necessarily a subset of $X$.
[Edit: How should I understand the definition of dense sets?] Can anybody tell me a reference for the most general definition for the dense sets?
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It isn’t so much a matter of needing another definition as of getting the hang of how mathematical language evolves and is actually used ‘in the wild’. In the example in question, ‘$E$ is dense in the ball $B$’ can be thought of as verbal shorthand for ‘$E \cap B$ is a dense subset of the ball $B$’ $-$ which, when you think about it, is just about the only thing that it could reasonably mean.
How does such shorthand arise? Let’s say that you have the idea of a set $D$ in a topological space $X$ being dense in $X$ according to the definition that you gave. Any subset $Y$ of $X$ can be viewed as a space in its own right, with the subspace topology inherited from $X$, so you can certainly talk about a subset of $Y$ being dense in $Y$. But somewhere along the line you prove that $D$ is dense in $X$ iff $\operatorname{cl}D = X$; this characterization is far too useful to be omitted. What happens when you try to apply this definition to the subspace $Y$? It’s certainly true that a set $D \subseteq Y$ is dense in $Y$ iff $\operatorname{cl}_Y D = Y$, but if you’re thinking of $Y$ as a subset of $X$ rather than as a space in its own right, it’s more convenient to look at $\operatorname{cl}_X D$, which isn’t necessarily $Y$: it may be a proper superset of $Y$. (Take $X$ to be $E^1$, $Y$ to be $(0,1)$, and $D$ to be $\mathbb{Q} \cap (0,1)$.)
Thus, if we don’t want to bother with different closures in different sets, it’s much more convenient to say simply that a subset $D$ of a set $Y$ is dense in $Y$ iff $\operatorname{cl}D \supseteq Y$, where the closure operator is $\operatorname{cl}_X$, the closure in the whole space $X$. And once you get to that point, it’s sometimes convenient to separate the notion of dense in $Y$ from the notion of subset of $Y$ altogther. That is, we might as well say that $D$ is dense in $Y$ iff $\operatorname{cl}D \supseteq Y$, irrespective of whether $D \subseteq Y$. Then, for instance, we can say simply that the rationals are dense in $(0,1)$; we don’t have to say explicitly ‘the rationals in $(0,1)$’.
Many textbooks, including some very good ones (Munkres, Dugundji, Willard) define dense subset of a space but (so far as I can quickly tell) silently leave it to the reader to make the generalization to dense subset of a set in a space and the further generalization to dense in a set in a space, or to pick them up from context. Of course, one can define dense more generally. For example, John Greever’s Theory and Examples of Point-Set Topology gives this definition:
(2.14) Definition. If $(X,\mathscr{T})$ is a topological space and $A,B \subset X$, then $A$ is dense in $B$ if and only if $\overline{A} \supset B$.
Notice that he doesn’t require $A$ to be a subset of $B$: right from the start he’s using the most general of the three forms that I considered above. Had you learned the concept from Greever, you’d not have had a problem with the dense in a ball language. But whether with this concept or with another, you’re eventually going to encounter standard usages that require a little interpretation of or extrapolation from the ones that you’ve been taught.
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Dear Brian, I'm a bit confused by the assertion that cl $D \supseteq Y$ iff cl $D\cap Y \supseteq Y$. Couldn't $D \cap Y = \emptyset$, e.g. if $X = \mathbb R$, $D = \mathbb Q$, and $Y = \mathbb R\setminus \mathbb Q$? Or have I gotten things muddled? Best wishes, – Matt E Mar 11 '14 at 4:07
Brian, this is actually the same question as above. If we take the reals with the standard topology and put $Y=\{1\}$ and $D=(0,1)$, then $Y\subseteq\mathrm{cl}\,D$, yet $\mathrm{cl}\,(D\cap Y)=\emptyset$. – Mad Hatter Aug 17 '15 at 9:01
Indeed, if $Y\not\subset \overline{\operatorname{int}_X Y}$, then $Y\subset \overline{D}$ does not imply $Y\subset \overline{Y\cap D}$. – Daniel Fischer Aug 17 '15 at 14:56
In the second paragraph, $cl_Y(D)=cl_X(D)\cap Y$. Hence $cl_Y(D)=Y$ iff $cl_X(D)\cap Y=Y$ iff $cl_X(D)\supset Y$. I think this might be a reason why we don't need to bother with different closures in different sets. – Jack Sep 30 '15 at 14:36
@MadHatter: You and Matt E are quite right; fixed now. (I’m not sure how I missed yours before.) – Brian M. Scott Sep 30 '15 at 14:57
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https://tel.archives-ouvertes.fr/tel-01819086v4
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Long-Moody functors and stable homology of mapping class groups
Abstract : Among the linear representations of braid groups, Burau representations are recovered from a trivial representation using a construction introduced by Long in 1994, following a collaboration with Moody. This construction, called the Long-Moody construction, thus allows to construct more and more complex representations of braid groups. In this thesis, we have a functorial point of view on this construction, which allows find more easily some variants. Moreover, the degree of polynomiality of a functor measures its complexity. We thus show that the Long-Moody construction defines a functor LM, which increases the degree of polynomiality. Furthermore, we define analogous functors for other families of groups such as mapping class groups of surfaces and 3-manifolds, symmetric groups or automorphism groups of free groups. They satisfy similar properties on the polynomiality. Hence, Long-Moody functors provide twisted coefficients fitting into the framework of the homological stability results of Randal-Williams and Wahl for the afore mentioned families of groups. Finally, we give a comparison result for the stable homology with coefficient given by a functor F and the one with coefficient given by the functor LM(F), obtained applying a Long-Moody functor. This thesis has three chapters. The first one introduces Long-Moody functors for braid groups and deals with their effect on the polynomiality. The first one deals with the generalisation of Long-Moody functors for other families of groups. The last chapter touches on stable homology computations for mapping class group.
Keywords :
Document type :
Theses
Cited literature [76 references]
https://tel.archives-ouvertes.fr/tel-01819086
Contributor : Abes Star <>
Submitted on : Monday, May 6, 2019 - 10:39:06 AM
Last modification on : Thursday, August 29, 2019 - 2:43:16 PM
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Soulie_Arthur_ED269_2018_1.pdf
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• HAL Id : tel-01819086, version 4
Citation
Arthur Soulié. Long-Moody functors and stable homology of mapping class groups. Algebraic Topology [math.AT]. Université de Strasbourg, 2018. English. ⟨NNT : 2018STRAD016⟩. ⟨tel-01819086v4⟩
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http://tex.stackexchange.com/questions/127601/setting-the-size-of-an-image-using-tkz-fct
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# Setting the size of an image using tkz_fct
I'm working on our coding system which combines a number of software possibilities. Here is what I have thus far.
### TOPIC 1
\topic = Sullivan 10.2 easy: parabolas
|@|
### MODEL 1.1, QUESTION 1
\versions = 10
|@|
\code =
my $a = randint(-9,9,1,(0)); my$b = 4*$a; my$Xmin=-4*$a; my$Xmax=4*$a; my$Xstep=$a; my$Ymin=-4*$a; my$Ymax=4*$a; my$Ystep=$a; |@| \qutext=What is the focus of the parabola$x^2={#b}y? |@| \mode = point |@| \answer = (0,#a) |@| \soltext=Compare the equation $$x^2={#b}y$$ with the form $$x^2=4ay$$ and note that: \begin{align*} 4a&=#b\\ a&=#a \end{align*} The parabola having the formx^2=4ay$opens up or down, depending on the value of$a$. In this case,$a=#a$, so the focus is at the point$(0,#a)\$.
\begin{center}
\begin{tikzpicture}
\tkzInit[xmin=#Xmin,xmax=#Xmax,xstep=#Xstep,ymin=#Ymin,ymax=#Ymax,ystep=#Ystep]
\tkzGrid
\end{tikzpicture}
\end{center}
|@|
\endquestion|@|
As you can see near the bottom, I'm trying to use tkz_fct to draw a graph based on some of the perl settings in the \code section above. What I am having trouble with is the fact that the size of the final grid on screen will change with different values of a. I'd like to scale the picture so that it is 6cm by 6cm. Can you make any suggestions?
Thanks.
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Still working on this? Perhaps tex.stackexchange.com/questions/6388/… can be of help. – Torbjørn T. Jan 4 at 23:35
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https://phys.libretexts.org/Bookshelves/Relativity/Book%3A_General_Relativity_(Crowell)/10%3A_Appendices/10.02%3A_Appendix_A_(Part_2)
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$$\require{cancel}$$
# 10.2: Appendix A (Part 2)
## § 4. Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks
We envisage a rigid sphere26 of radius R, at rest relative to the moving system k, and with its centre at the origin of coordinates of k. The equation of the surface of this sphere moving relative to the system K with velocity v is
$\xi^{2} + \eta^{2} + \zeta^{2} = R^{2} \ldotp$
Note
That is, a body possessing spherical form when examined at rest.—AS
The equation of this surface expressed in x, y, z at the time t = 0 is
$\frac{x^{2}}{\left(\sqrt{1 - \dfrac{v^{2}}{c^{2}}} \right)^{2}} + y^{2} + z^{2} = R^{2} \ldotp$
A rigid body which, measured in a state of rest, has the form of a sphere, therefore has in a state of motion—viewed from the stationary system—the form of an ellipsoid of revolution with the axes
$R \sqrt{1 - \frac{v^{2}}{c^{2}}}, R, R \ldotp$
Thus, whereas the Y and Z dimensions of the sphere (and therefore of every rigid body of no matter what form) do not appear modified by the motion, the X dimension appears shortened in the ratio 1 : $$sqrt{1 − \frac{v^{2}}{c^{2}}}$$, i.e., the greater the value of v, the greater the shortening. For v = c all moving objects—viewed from the “stationary” system—shrivel up into plane figures.27 For velocities greater than that of light our deliberations become meaningless; we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.
Note
That is, a body possessing spherical form when examined at rest.—AS
It is clear that the same results hold good of bodies at rest in the “stationary” system, viewed from a system in uniform motion.
Further, we imagine one of the clocks which are qualified to mark the time t when at rest relative to the stationary system, and the time $$\tau$$ when at rest relative to the moving system, to be located at the origin of the coordinates of k, and so adjusted that it marks the time $$\tau$$. What is the rate of this clock, when viewed from the stationary system?
Between the quantities x, t, and $$\tau$$, which refer to the position of the clock, we have, evidently, x = vt and
$\tau = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} \left( t - \dfrac{vx}{c^{2}} \right) \ldotp$
Therefore,
$\tau = t \sqrt{1 - \frac{v^{2}}{c^{2}}} = t - \left( 1 - \sqrt{1 - \dfrac{v^{2}}{c^{2}}} \right) t$
whence it follows that the time marked by the clock (viewed in the stationary system) is slow by 1 − $$\sqrt{1 − \frac{v^{2}}{c^{2}}}$$ seconds per second, or—neglecting magnitudes of fourth and higher order—by $$\frac{1}{2} \frac{v^{2}}{c^{2}}$$.
From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by $$\frac{1}{2} \frac{tv^{2}}{c^{2}}$$ (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.
If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be $$\frac{1}{2} \frac{tv^{2}}{c^{2}}$$ second slow. Thence we conclude that a spring-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.28
Note
Einstein specifies a spring-clock (“unruhuhr”) because the effective gravitational field is weaker at the equator than at the poles, so a pendulum clock at the equator would run more slowly by about two parts per thousand than one at the north pole, for nonrelativistic reasons. This would completely mask any relativistic effect, which he expected to be on the order of $$\frac{v^{2}}{c^{2}}$$, or about 10−13. In any case, it later turned out that Einstein was mistaken about this example. There is also a gravitational time dilation that cancels the kinematic effect. See example 10. The two clocks would actually agree.—BC
## § 5. The Composition of Velocities
In the system k moving along the axis of X of the system K with velocity v, let a point move in accordance with the equations
$\xi = w_{\xi} \tau, \quad \eta = w_{\eta} \tau, \quad \zeta = 0,$
where $$w_{\xi}$$ and $$w_{\eta}$$ denote constants.
Required: the motion of the point relative to the system K. If with the help of the equations of transformation developed in § 3 we introduce the quantities x, y, z, t into the equations of motion of the point, we obtain
$\begin{split} x &= \frac{w_{\xi} + v}{1 + \frac{vw_{\xi}}{c^{2}}} t, \\ y &= \frac{\sqrt{1 - \frac{v^{2}}{c^{2}}}}{1 + \frac{vw_{\xi}}{c^{2}}} w_{\eta} t, \\ z &= 0 \ldotp \end{split}$
Thus the law of the parallelogram of velocities is valid according to our theory only to a first approximation. We set29
$\begin{split} V^{2} &= \left(\dfrac{dx}{dt} \right)^{2} + \left(\dfrac{dy}{dt} \right)^{2}, \\ w^{2} &= w^{2}_{\xi} + w^{2}_{\eta}, \\ a &= \tan^{-1} \frac{w_{\eta}}{w_{\xi}}, \end{split}$
a is then to be looked upon as the angle between the velocities v and w. After a simple calculation we obtain
$V = \frac{\sqrt{(v^{2} + w^{2} + 2vw \cos a) - (vw \sin \frac{a}{c})^{2}}}{1 + vw \cos \frac{a}{c^{2}}} \ldotp$
Note
This equation was incorrectly given in Einstein’s original paper and the 1923 English translation as a = tan−1 $$\frac{w_{y}}{w_{x}}$$.—JW
It is worthy of remark that v and w enter into the expression for the resultant velocity in a symmetrical manner. If w also has the direction of the axis of X, we get
$V = \frac{v + w}{1 + \frac{vw}{c^{2}}} \ldotp$
It follows from this equation that from a composition of two velocities which are less than c, there always results a velocity less than c. For if we set v = c − $$\kappa$$, w = c − $$\lambda$$, $$\kappa$$ and $$\lambda$$ being positive and less than c, then
$V = c \frac{2c - \kappa - \lambda}{2c - \kappa - \lambda + \frac{\kappa \lambda}{c}} < c \ldotp$
It follows, further, that the velocity of light c cannot be altered by composition with a velocity less than that of light. For this case we obtain
$V = \frac{c + w}{1 + \frac{w}{c}} = c \ldotp$
We might also have obtained the formula for V, for the case when v and w have the same direction, by compounding two transformations in accordance with § 3. If in addition to the systems K and k figuring in § 3 we introduce still another system of coordinates k' moving parallel to k, its initial point moving on the axis of $$\Xi$$30 with the velocity w, we obtain equations between the quantities x, y, z, t and the corresponding quantities of k', which differ from the equations found in § 3 only in that the place of “v” is taken by the quantity
$\frac{v + w}{1 + \frac{vw}{c^{2}}};$
from which we see that such parallel transformations—necessarily—form a group.
Note
“X” in the 1923 English translation.—JW
We have now deduced the requisite laws of the theory of kinematics corresponding to our two principles, and we proceed to show their application to electrodynamics.31
Note
The remainder of the paper is not given here, but can be obtained from John Walker’s web site at www.fourmilab.ch.—BC
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http://turbomachinery.asmedigitalcollection.asme.org/article.aspx?articleid=2618761
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0
Research Papers
# Mach Number Distribution and Profile Losses for Low-Pressure Turbine Profiles With High Diffusion Factors
[+] Author and Article Information
Roland Brachmanski
Institute of Jet Propulsion,
Universität der Bundeswehr München,
Neubiberg 85577, Germany
e-mail: [email protected]
Reinhard Niehuis
Institute of Jet Propulsion,
Universität der Bundeswehr München,
Neubiberg 85577, Germany
e-mail: [email protected]
1Corresponding author.
Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 7, 2016; final manuscript received March 5, 2017; published online May 9, 2017. Assoc. Editor: Guillermo Paniagua.
J. Turbomach 139(10), 101002 (May 09, 2017) (10 pages) Paper No: TURBO-16-1187; doi: 10.1115/1.4036436 History: Received August 07, 2016; Revised March 05, 2017
## Abstract
The results of this investigation come from two linear cascades at high diffusion factors (DFs). The measurements presented for each low-pressure turbine (LPT) profile were conducted at midspan under a range of Reynolds- and exit Mach numbers. The exit Mach number was varied in a range covering low subsonic up to values where a transonic flow regime on the suction side of the blade could be expected. This work focuses on two profiles with a diffusion factor in a range of $0.18≤DF≤0.22$, where values in this range are considered as a comparable for the two cascades. Profile A is a front-loaded design and has shown no obvious flow separation on the suction side of the blade. Compared to the design A, design B is a more aft-loaded profile which exhibits flow separation on the suction side for all Reynolds numbers investigated. The integral total pressure losses were evaluated by wake traverses downstream of the airfoil. To determine the isentropic Mach numbers and the character of the boundary layer along the suction side of the profile, the static pressure measurements and traverses with a flattened Pitot probe were carried out. A correlation between the position of maximum Mach number on the suction side and the integral total pressure losses has been successfully established. The results show that the optimum location of peak Mach number to minimize integral total pressure losses is significantly dependent on the Reynolds number. However, the correlation presented in this paper, which is based on the data of the integral total pressure losses of an attached boundary layer, is not able to predict the integral total pressure loss or the location of the maximum Mach number on the suction side of the blade when an open separation bubble occurs.
<>
## Figures
Fig. 1
Fig. 2
Schematic of the cascade co-ordinate system (geometry not to scale)
Fig. 3
Mach number distribution of profile B
Fig. 4
Mach number distribution of profile A
Fig. 5
Wake traverses of profile B
Fig. 6
Wake traverses of profile A
Fig. 7
Integral total pressure losses as a function of maximum Mach number location
Fig. 8
Derivatives of the parabola
Fig. 9
Integral total pressure losses as a function of maximumMach number location for high DF and variation of Tu intensities
Fig. 10
Mach number distribution of profile B at Re2th=125,000 and variation of Tu intensities
Fig. 11
Wake traverses of profile B at Re2th=125,000 for different Tu intensities
Fig. 12
Dynamic pressure distribution of design B at Re2th=125,000 and with variation of Tu intensities
Fig. 13
Trailing edge profiles of design B at Re2th=125,000 and with variation of Tu intensities
Fig. 14
Mach number distributions of the profile B at Re2th=125,000 at high Tu intensities
Fig. 15
Mach number distributions of the profile B at Re2th=125,000 at low Tu intensities
Fig. 16
Friction factors of design B at Re2th=125,000 and variation of Tu intensities
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https://www.ferpode.com/books/renewable-energy-systems/
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# Understanding Renewable Energy Systems
• Author : Volker Quaschning
• Publsiher : Routledge
• Release : 31 March 2016
• ISBN : 9781317669432
• Page : 406 pages
• Rating : 4/5 from 21 voters
Download or read online book entitled Understanding Renewable Energy Systems written by Volker Quaschning and published by Routledge. This book was released on 31 March 2016 with total page 406 pages. Available in PDF, EPUB and Kindle. Get best books that you want by click Get Book Button and Read as many books as you like. Book Excerpt : By mid-century, renewable energy must cover all of our energy supply if we are to phase out nuclear and successfully stop climate change. Now updated and expanded, the 2nd edition of this textbook covers the full range of renewable energy systems and now also includes such current trends as solar power storage, power-to-gas technologies, and the technology paths needed for a successful and complete energy transition. The topics are treated in a holistic manner, bringing together maths, engineering, climate studies and economics, and enabling readers to gain a broad understanding of renewable energy technologies and their potential.Numerous examples are provided for calculations, and graphics help visualize the various technologies and mathematical methodologies. Understanding Renewable Energy Systems is an ideal companion for students of renewable energy at universities or technical colleges on courses such as renewable energy, electrical engineering, engineering technology, physics, process engineering, building engineering, environment, applied mechanics and mechanical engineering, as well as scientists and engineers in research and industry.
### Understanding Renewable Energy Systems
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### Renewable Energy Systems in 90 Minutes
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http://en.wikipedia.org/wiki/Bohr_Effect
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# Bohr effect
(Redirected from Bohr Effect)
Hemoglobin Dissociation Curve. Dotted red line corresponds with shift to the right caused by Bohr effect
The Bohr effect is a physiological phenomenon first described in 1904 by the Danish physiologist Christian Bohr, stating that hemoglobin's oxygen binding affinity (see Oxygen–haemoglobin dissociation curve) is inversely related both to acidity and to the concentration of carbon dioxide.[1] That is to say, an increase in blood CO2 concentration which leads to a decrease in blood pH will result in hemoglobin proteins releasing their load of oxygen. Conversely, a decrease in carbon dioxide provokes an increase in pH, which results in hemoglobin picking up more oxygen. Since carbon dioxide reacts with water to form carbonic acid, an increase in CO2 results in a decrease in blood pH.
## Mechanism
In deoxyhemoglobin, the N-terminal amino groups of the α-subunits and the C-terminal histidine of the β-subunits participate in ion pairs. The formation of ion pairs causes them to decrease in acidity. Thus, deoxyhemoglobin binds one proton (H+) for every two O2 released. In oxyhemoglobin, these ion pairings are absent and these groups increase in acidity. Consequentially, a proton is released for every two O2 bound. Specifically, this reciprocal coupling of protons and oxygen is the Bohr effect.[2]
Additionally, carbon dioxide reacts with the N-terminal amino groups of α-subunits to form carbamates:[3]
R−NH2 + CO2 $\rightleftharpoons$ R−NH−COO- + H+
Deoxyhemoglobin binds to CO2 more readily to form a carbamate than oxyhemoglobin. When CO2 concentration is high (as in the capillaries), the protons released by carbamate formation further promotes oxygen release. Although the difference in CO2 binding between the oxy and deoxy states of hemoglobin accounts for only 5% of the total blood CO2, it is responsible for half of the CO2 transported by blood. This is because 10% of the total blood CO2 is lost through the lungs in each circulatory cycle.[4]
## Physiological role
This effect facilitates oxygen transport as hemoglobin binds to oxygen in the lungs, but then releases it in the tissues, particularly those tissues in most need of oxygen. When a tissue's metabolic rate increases, its carbon dioxide production increases. Carbon dioxide forms bicarbonate through the following reaction:
CO2 + H2O $\rightleftharpoons$ H2CO3 $\rightleftharpoons$ H+ + HCO3
Although the reaction usually proceeds very slowly, the enzyme family of carbonic anhydrase, which is present in red blood cells, accelerates the formation of bicarbonate and protons.[citation needed] This causes the pH of tissues to decrease, and so, promotes the dissociation of oxygen from hemoglobin to the tissue, allowing the tissue to obtain enough oxygen to meet its demands. Conversely, in the lungs, where oxygen concentration is high, binding of oxygen causes hemoglobin to release protons, which combine with bicarbonate to drive off carbon dioxide in exhalation. Since these two reactions are closely matched, there is little change in blood pH.
The dissociation curve shifts to the right when carbon dioxide or hydrogen ion concentration is increased. This facilitates increased oxygen dumping. This mechanism allows for the body to adapt the problem of supplying more oxygen to tissues that need it the most. When muscles are undergoing strenuous activity, they generate CO2 and lactic acid as products of cellular respiration and lactic acid fermentation. In fact, muscles generate lactic acid so quickly that pH of the blood passing through the muscles will drop to around 7.2. As lactic acid releases its protons, pH decreases, which causes hemoglobin to release ~10% more oxygen.[4]
## Effects of allostery
The Bohr effect is dependent on allosteric interactions between the hemes of the hemoglobin tetramer. This is evidenced by the fact that myoglobin, a monomer with no allostery, does not exhibit the Bohr effect. Hemoglobin mutants with weaker allostery may exhibit a reduced Bohr effect.
In the Hiroshima variant hemoglobinopathy, allostery in hemoglobin is reduced, and the Bohr effect is diminished. During periods of exercise, the mutant hemoglobin has a higher affinity for oxygen and tissue may suffer minor oxygen starvation.[5]
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https://stackabuse.com/understanding-pythons-yield-keyword/
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## Understanding Python's "yield" Keyword
The yield keyword in Python is used to create generators. A generator is a type of collection that produces items on-the-fly and can only be iterated once. By using generators you can improve your application's performance and consume less memory as compared to normal collections, so it provides a nice boost in performance.
In this article we'll explain how to use the yield keyword in Python and what it does exactly. But first, let's study the difference between a simple list collection and generator, and then we will see how yield can be used to create more complex generators.
### Differences Between a List and Generator
In the following script we will create both a list and a generator and will try to see where they differ. First we'll create a simple list and check its type:
# Creating a list using list comprehension
squared_list = [x**2 for x in range(5)]
# Check the type
type(squared_list)
When running this code you should see that the type displayed will be "list".
Now let's iterate over all the items in the squared_list.
# Iterate over items and print them
for number in squared_list:
print(number)
The above script will produce following results:
$python squared_list.py 0 1 4 9 16 Now let's create a generator and perform the same exact task: # Creating a generator squared_gen = (x**2 for x in range(5)) # Check the type type(squared_gen) To create a generator, you start exactly as you would with list comprehension, but instead you have to use parentheses instead of square brackets. The above script will display "generator" as the type for squared_gen variable. Now let's iterate over the generator using a for-loop. for number in squared_gen: print(number) The output will be: $ python squared_gen.py
0
1
4
9
16
The output is the same as that of the list. So what is the difference? One of the main differences lies in the way the list and generators store elements in the memory. Lists store all of the elements in memory at once, whereas generators "create" each item on-the-fly, displays it, and then moves to the next element, discarding the previous element from the memory.
One way to verify this is to check the length of both the list and generator that we just created. The len(squared_list) will return 5 while len(squared_gen) will throw an error that a generator has no length. Also, you can iterate over a list as many times as you want but you can iterate over a generator only once. To iterate again, you must create the generator again.
### Using the Yield Keyword
Now we know the difference between simple collections and generators, let us see how yield can help us define a generator.
In the previous examples, we created a generator implicitly using the list comprehension style. However in more complex scenarios we can instead create functions that return a generator. The yield keyword, unlike the return statement, is used to turn a regular Python function in to a generator. This is used as an alternative to returning an entire list at once. This will be again explained with the help of some simple examples.
Again, let's first see what our function returns if we do not use the yield keyword. Execute the following script:
def cube_numbers(nums):
cube_list =[]
for i in nums:
cube_list.append(i**3)
return cube_list
cubes = cube_numbers([1, 2, 3, 4, 5])
print(cubes)
In this script a function cube_numbers is created that accepts a list of numbers, take their cubes and returns the entire list to the caller. When this function is called, a list of cubes is returned and stored in the cubes variable. You can see from the output that the returned data is in-fact a full list:
$python cubes_list.py [1, 8, 27, 64, 125] Now, instead of returning a list, let's modify the above script so that it returns a generator. def cube_numbers(nums): for i in nums: yield(i**3) cubes = cube_numbers([1, 2, 3, 4, 5]) print(cubes) In the above script, the cube_numbers function returns a generator instead of list of cubed number. It's very simple to create a generator using the yield keyword. Here we do not need the temporary cube_list variable to store cubed number, so even our cube_numbers method is simpler. Also, no return statement is needed, but instead the yield keyword is used to return the cubed number inside of the for-loop. Now, when cube_number function is called, a generator is returned, which we can verify by running the code: $ python cubes_gen.py
<generator object cube_numbers at 0x1087f1230>
Even though we called the cube_numbers function, it doesn't actually execute at this point in time, and there are not yet any items stored in memory.
To get the function to execute, and therefore the next item from generator, we use the built-in next method. When you call the next iterator on the generator for the first time, the function is executed until the yield keyword is encountered. Once yield is found the value passed to it is returned to the calling function and the generator function is paused in its current state.
Here is how you get a value from your generator:
next(cubes)
The above function will return "1". Now when you call next again on the generator, the cube_numbers function will resume executing from where it stopped previously at yield. The function will continue to execute until it finds yield again. The next function will keep returning cubed value one by one until all the values in the list are iterated.
Once all the values are iterated the next function throws a StopIteration exception. It is important to mention that the cubes generator doesn't store any of these items in memory, rather the cubed values are computed at runtime, returned, and forgotten. The only extra memory used is the state data for the generator itself, which is usually much less than a large list. This makes generators ideal for memory-intensive tasks.
Instead of always having to use the next iterator, you can instead use a "for" loop to iterate over a generators values. When using a "for" loop, behind the scenes the next iterator is called until all the items in the generator are iterated over.
### Optimized Performance
As mentioned earlier, generators are very handy when it comes to memory-intensive tasks since they do not need to store all of the collection items in memory, rather they generate items on the fly and discards it as soon as the iterator moves to the next item.
In the previous examples the performance difference of a simple list and generator was not visible since the list sizes were so small. In this section we'll check out some examples where we can distinguish between the performance of lists and generators.
In the code below we will write a function that returns a list that contains 1 million dummy car objects. We will calculate the memory occupied by the process before and after calling the function (which creates the list).
Take a look at the following code:
import time
import random
import os
import psutil
car_names = ['Audi', 'Toyota', 'Renault', 'Nissan', 'Honda', 'Suzuki']
colors = ['Black', 'Blue', 'Red', 'White', 'Yellow']
def car_list(cars):
all_cars = []
for i in range (cars):
car = {
'id': i,
'name': random.choice(car_names),
'color': random.choice(colors)
}
all_cars.append(car)
return all_cars
# Get used memory
process = psutil.Process(os.getpid())
print('Memory before list is created: ' + str(process.memory_info().rss/1000000))
# Call the car_list function and time how long it takes
t1 = time.clock()
cars = car_list(1000000)
t2 = time.clock()
# Get used memory
process = psutil.Process(os.getpid())
print('Memory after list is created: ' + str(process.memory_info().rss/1000000))
print('Took {} seconds'.format(t2-t1))
Note: You may have to pip install psutil to get this code to work on your machine.
In the machine on which the code was run, following results were obtained (yours may look slightly different):
$python perf_list.py Memory before list is created: 8 Memory after list is created: 334 Took 1.584018 seconds Before the list was created the process memory was 8 MB, and after the creation of list with 1 million items, the occupied memory jumped to 334 MB. Also, the time it took to create the list was 1.58 seconds. Now, let's repeat the above process but replace the list with generator. Execute the following script: import time import random import os import psutil car_names = ['Audi', 'Toyota', 'Renault', 'Nissan', 'Honda', 'Suzuki'] colors = ['Black', 'Blue', 'Red', 'White', 'Yellow'] def car_list_gen(cars): for i in range (cars): car = { 'id':i, 'name':random.choice(car_names), 'color':random.choice(colors) } yield car # Get used memory process = psutil.Process(os.getpid()) print('Memory before list is created: ' + str(process.memory_info().rss/1000000)) # Call the car_list_gen function and time how long it takes t1 = time.clock() cars = car_list_gen(1000000) t2 = time.clock() # Get used memory process = psutil.Process(os.getpid()) print('Memory after list is created: ' + str(process.memory_info().rss/1000000)) print('Took {} seconds'.format(t2-t1)) Following results were obtained by executing the above script: $ python perf_gen.py
Memory before list is created: 8
Memory after list is created: 8
Took 3e-06 seconds
From the output, you can see that by using generators the memory difference is negligible (it remains at 8 MB) since the generators do not store the items in memory. Furthermore, the time taken to call the generator function was only 0.000003 seconds, which is also far less compared to time taken for list creation.
### Conclusion
Hopefully from this article you have a better understanding of the yield keyword, including how it's used, what it's used for, and why you'd want to use it. Python generators are a great way to improve the performance of your programs and they're very simple to use, but understanding when to use them is the challenge for many novice programmers.
|
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|
http://mathhelpforum.com/calculus/168481-attempt-solve-confusing-integral-x-3-e-x-2-dx-see-attached-scanned-paper.html
|
# Math Help - Attempt to solve confusing integral $x^3 *e^[x^2] * dx (See attached scanned paper) 1. ## Attempt to solve confusing integral$x^3 *e^[x^2] * dx (See attached scanned paper)
Here it is
2. Originally Posted by Riazy
Here it is
Put $\displaystyle{u = x^2\,; \;u'=2x\,,\,\,v'=xe^{x^2}\,;\;v=\frac{1}{2}e^{x^2} }$ , so integrating by parts:
$\displaystyle{\int x^3e^{x^2} dx=\int x^2(xe^{x^2})dx=\frac{1}{2}x^2e^{x^2}-\int xe^{x^2}dx=\frac{e^{x^2}}{2}\left(x^2-1)+C$ .
Tonio
3. $\displaystyle \int{x^3e^{x^2}\,dx} = \int{\frac{1}{2}x^2\cdot 2x\,e^{x^2}\,dx}$.
Now use integration by parts with $\displaystyle u = \frac{1}{2}x^2 \implies du = x\,dx$ and $\displaystyle dv = 2x\,e^{x^2}\,dx \implies v = e^{x^2}$ and the integral becomes
$\displaystyle \frac{1}{2}x^2e^{x^2} - \int{x\,e^{x^2}\,dx}$
$\displaystyle = \frac{1}{2}x^2e^{x^2} - \frac{1}{2}\int{2x\,e^{x^2}\,dx}$
$\displaystyle = \frac{1}{2}x^2e^{x^2} - \frac{1}{2}e^{x^2} + C$.
|
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|
http://gmatclub.com/forum/if-john-makes-a-contribution-to-a-charity-fund-at-school-th-89545.html
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# If john makes a contribution to a charity fund at school, th
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If john makes a contribution to a charity fund at school, th [#permalink] 22 Jan 2010, 10:16
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Difficulty:
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Question Stats:
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If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 5 other contributions made before john's, what is the size of his donation? A.$100
B. $150 C.$200
D. $250 E.$450
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Re: 700-800 level problem Statistics [#permalink] 22 Jan 2010, 10:20
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Cavg = average contribution before John
Cavg*1.5 = 75, therefore the average cont is $50 before John. If he needs to increase the average contribution by$25, he must put in $25 for each of the 5 people. so$125.
But, he also has to put in the average for himself (the sixth person), so add $75. So$200 is your answer.
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Re: 700-800 level problem Statistics [#permalink] 22 Jan 2010, 10:33
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yes 200 is the ans.
final avg = 75 = 1.5 of old
i.e old avg = 50 = total of five/5
total of five = 250
new avg = 75 = total of six/6
total of 6 = 450
so John's contribution = 450-250 =200
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Re: 700-800 level problem Statistics [#permalink] 22 Jan 2010, 10:35
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GMAT10 wrote:
If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person.If there were 5 other contributions made before john's,what is the size of his donation? a)$100
b)$150 c)$200
d)$250 e)$450
Let $$a$$ be the average contribution size before John makes his contribution.
Let $$c$$ be the total contribution size before John makes his contribution.
Let $$x$$ be John's contribution.
$$1.5a=75$$ --> $$a=50$$
$$a=50=\frac{c}{5}$$ --> $$c=250$$
$$\frac{c+x}{6}=75$$ --> $$\frac{250+x}{6}=75$$ --> $$x=200$$
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Re: Contribution to a charity Fund [#permalink] 17 Nov 2011, 16:25
If, after John's donation, the average was $75 per person then the total is$75(6) which comes to a total of 450 contributed dollars by all donees. If John's donation increases the total contributions by 50% then it is now 150% of what it was and John's contribution was 1/3 of that, which would be 1/3 of the $450. John contributed$150.
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Re: Contribution to a charity Fund [#permalink] 18 Nov 2011, 01:43
ok here is how I approached this question:
I, first, got the original average before the increase and without john's:
1.5x=75
x=50
then, I got the sum of the contributions of the 5 dominees without John:
5x/5=50
hence, 5x=250
after that, i set up the average equation with john's contribution:
250+x/6=75
250+x=75(6)
250+x=450
hence, x, which is John's amouts= 200
so the answer I got is C, hope this helps
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Last edited by manalq8 on 18 Nov 2011, 13:48, edited 1 time in total.
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Re: Contribution to a charity Fund [#permalink] 18 Nov 2011, 07:52
Thought I'd write my reasoning out in a more quantitative form.
J = {6($75)}/3, or J = [{1($75) +5($75)}/150]*50. The key, I think, is to realize that John's contribution was 1/3 of all the current contributions. Since we know the total contribution is 6($75)=$450, then we know his contribution was 1/3 of that. 1/3*450=$150.
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Re: Contribution to a charity Fund [#permalink] 20 Nov 2011, 00:07
1
KUDOS
Expert's post
enigma123 wrote:
If John makes a contribution to a charity fund at school, the average contribution size will increase by 50%, reaching $75 per person. If there were 5 other contributions made before John’s, what is the size of his donation? (A)$100
(B) $150 (C)$200
(D) $250 (E)$450
OA is not provided, but I have got C. Do you guys think C is the right answer?
Responding to a pm:
After John's contribution, the average size increases by 50% and reaches $75. What must have been the average size of contribution before John's donation? It must have been$50 since a 50% increase would lead us to $75.$50 was the average size for 5 donations. Total amount donated = $250$75 is the average size for 6 donations. Total amount donated = $450 John's contribution must have been 450 - 250 =$200
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Joined: 28 Jul 2011 Posts: 563 Location: United States Concentration: International Business, General Management GPA: 3.86 WE: Accounting (Commercial Banking) Followers: 2 Kudos [?]: 105 [0], given: 16 Re: Contribution to a charity Fund [#permalink] 20 Nov 2011, 00:12 Thanks VeritasPrepKarishma _________________ +1 Kudos If found helpful.. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5870 Location: Pune, India Followers: 1483 Kudos [?]: 7995 [1] , given: 190 Re: Contribution to a charity Fund [#permalink] 20 Nov 2011, 08:04 1 This post received KUDOS Expert's post Stoneface wrote: If, after John's donation, the average was$75 per person then the total is $75(6) which comes to a total of 450 contributed dollars by all donees. If John's donation increases the total contributions by 50% then it is now 150% of what it was and John's contribution was 1/3 of that, which would be 1/3 of the$450. John contributed $150. Answer B. Responding to a pm: We cannot say that John's contribution is a third. To increase the average by 50%, you need to invest more than a third of the total. The reason is that previous average is for 5 people. New average has another person so the total contribution needs to be higher. The total contribution now = 75*6 = 450 Out of this, if 150 were contributed by John, the previous total contribution must have been 300. With 5 people, that would mean an average of 60. We need 6 people to make the average 50 but before John made the contribution, there were only 5 people. That's where you made a mistake. Since a person increases, the contribution needs to be even higher than a third. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199
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Re: Contribution to a charity Fund [#permalink] 21 Nov 2011, 06:02
I do not understand at all, but thanks for your time. I think I'll spend a little extra time in the ol' GMAT book today.
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Re: If john makes a contribution to a charity fund at school, th [#permalink] 23 Sep 2013, 23:30
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Re: If john makes a contribution to a charity fund at school, th [#permalink] 23 Sep 2013, 23:30
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https://www.infoq.com/news/2019/01/c-sharp-targeted-type-new/
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InfoQ Homepage News C# 8: Type Inference for the New Keyword
# C# 8: Type Inference for the New Keyword
In many situations, there is only one possible type allowed in a given place. And yet C# still requires you to explicitly list the type. If the Target-typed new expression proposal is adopted, such boilerplate code will no longer be necessary.
Superficially, this feature looks like the reverse of the var keyword. But instead of inferring the variables type from an expression, it infers the expression’s type from a variable. Here is an example from the proposal using the current and proposed syntax.
Dictionary<string, List<int>> field = new Dictionary<string, List<int>>();
Dictionary<string, List<int>> field = new();
As you can see, it simply removes the need to specify the type when it can be inferred from the context. With local variables this isn’t too interesting, but where it can come in handy is short-lived arguments.
XmlReader.Create(reader, new XmlReaderSettings() { IgnoreWhitespace = true });
In the above code, the XmlReaderSettings class isn’t very interesting. It is merely a holder for options values to be passed to the XmlReader. One could even argue the type name XmlReaderSettings distracts from the important information.
Another place where this feature is useful is fields and properties where the var keyword is not an option. For example,
private readonly static object s_syncObj = new();
According to the proposal, there are four exceptions to its use.
• Enum types: not all enum types contain the constant zero, so it should be desirable to use the explicit enum member.
• Interface types: this is a niche feature and it should be preferable to explicitly mention the type.
• Array types: arrays need a special syntax to provide the length.
• Struct default constructor: this rules out all primitive types and most value types. If you wanted to use the default value of such types you could write default instead.
Status
Currently type inference for the new keyword is listed on the C# 8 roadmap with the status “Prototype”. The feature test plan is available on GitHub.
Style
## Hello stranger!
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Get the most out of the InfoQ experience.
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• ##### Long overdue
by wakin imgen /
• ##### Re: Long overdue
by Cameron Purdy /
• ##### Re: Long overdue
by Jonathan Allen /
• ##### Re: Long overdue
by wakin imgen /
• ##### Re: Long overdue
by wakin imgen /
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by Jonathan Allen /
• ##### Copy+Paste error
by Mark Rendle /
• ##### Long overdue
by wakin imgen /
Your message is awaiting moderation. Thank you for participating in the discussion.
I forget how many times I think to myself when I declare Dictionary<TKey, TValue> in a class that this is so stupid that I have to type the stuff twice. Now finally it's being fixed. This kind of annoyance is really annoying.
• ##### Re: Long overdue
Your message is awaiting moderation. Thank you for participating in the discussion.
That you "have to type the stuff twice" is not something that I have experienced, but then again, I use IntelliJ.
However, this unbounded fascination with reducing typing as a proxy for actual language improvements is ultimately self-defeating. For example, efficiency improvements in typing code pale to efficiency improvements in the readability of code.
• ##### Re: Long overdue
Your message is awaiting moderation. Thank you for participating in the discussion.
In the XmlReader.Create example, the goal is to improve readability. The idea is to remove the boilerplate (XmlReaderSettings) in order to bring the important information (IgnoreWhitespace = true) to the forefront.
Whether or not it actually improves readability is a matter of opinion. I'm just relating the thought process behind it.
• ##### Re: Long overdue
by wakin imgen /
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I don't think
Dictionary<int, int> _dict = new ();
Dictionary<int, int> _dict = new Dictionary<string, int>();
• ##### Re: Long overdue
by wakin imgen /
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Somehow the formatting is hard to do in the comments. Why don't InfoQ adopt Markdown?
• ##### Re: Long overdue
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When InfoQ was created, Markdown wasn't widely used for forum/comment systems. Changing it now would be difficult, but I'll bring it up with management as I do agree it would be nicer.
• ##### Copy+Paste error
by Mark Rendle /
Your message is awaiting moderation. Thank you for participating in the discussion.
The Status note at the bottom of the article references the Caller Expression Attribute, not the new() type inference feature.
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https://hal-insu.archives-ouvertes.fr/insu-01182158
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# Discovery of a Spin-down State Change in the LMC Pulsar B0540-69
Abstract : We report the discovery of a large, sudden, and persistent increase in the spin-down rate of B0540-69, a young pulsar in the Large Magellanic Cloud, using observations from the Swift and RXTE satellites. The relative increase in the spin-down rate $\dot{\nu }$ of 36% is unprecedented for B0540-69. No accompanying change in the spin rate is seen, and no change is seen in the pulsed X-ray emission from B0540-69 following the change in the spin-down rate. Such large relative changes in the spin-down rate are seen in the recently discovered class of "intermittent pulsars," and we compare the properties of B0540-69 to such pulsars. We consider possible changes in the magnetosphere of the pulsar that could cause such a large change in the spin-down rate.
Document type :
Journal articles
Cited literature [15 references]
https://hal-insu.archives-ouvertes.fr/insu-01182158
Contributor : Nathalie Pothier <>
Submitted on : Thursday, June 9, 2016 - 2:09:33 PM
Last modification on : Thursday, October 15, 2020 - 4:06:49 AM
### File
apjl_807_2_L27.pdf
Publisher files allowed on an open archive
### Citation
F. E. Marshall, Lucas Guillemot, A. K. Harding, P. Martin, D. A. Smith. Discovery of a Spin-down State Change in the LMC Pulsar B0540-69. The Astrophysical journal letters, Bristol : IOP Publishing, 2015, 807 (2), pp.L27. ⟨10.1088/2041-8205/807/2/L27⟩. ⟨insu-01182158⟩
Record views
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https://chem.libretexts.org/Courses/Case_Western_Reserve_University/CHEM_121%3A_Concepts_for_a_Molecular_View_of_Biology_II_(Cunningham)/1%3A_Organic_Chemistry_Basics/1.12%3A_Physical_Properties_of_Alkenes
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# 1.12: Physical Properties of Alkenes
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
Learning Objectives
• To identify the physical properties of alkenes and describe trends in these properties.
The physical properties of alkenes are similar to those of the alkanes. The table at the start of the chapter shows that the boiling points of straight-chain alkenes increase with increasing molar mass, just as with alkanes. For molecules with the same number of carbon atoms and the same general shape, the boiling points usually differ only slightly, just as we would expect for substances whose molar mass differs by only 2 u (equivalent to two hydrogen atoms). Like other hydrocarbons, the alkenes are insoluble in water but soluble in organic solvents.
## Looking Closer: Environmental Note
Alkenes occur widely in nature. Ripening fruits and vegetables give off ethylene, which triggers further ripening. Fruit processors artificially introduce ethylene to hasten the ripening process; exposure to as little as 0.1 mg of ethylene for 24 h can ripen 1 kg of tomatoes. Unfortunately, this process does not exactly duplicate the ripening process, and tomatoes picked green and treated this way don’t taste much like vine-ripened tomatoes fresh from the garden.
The bright red color of tomatoes is due to lycopene—a polyene.
Other alkenes that occur in nature include 1-octene, a constituent of lemon oil, and octadecene (C18H36) found in fish liver. Dienes (two double bonds) and polyenes (three or more double bonds) are also common. Butadiene (CH2=CHCH=CH2) is found in coffee. Lycopene and the carotenes are isomeric polyenes (C40H56) that give the attractive red, orange, and yellow colors to watermelons, tomatoes, carrots, and other fruits and vegetables. Vitamin A, essential to good vision, is derived from a carotene. The world would be a much less colorful place without alkenes.
## Concept Review Exercises
1. Briefly describe the physical properties of alkenes. How do these properties compare to those of the alkanes?
2. Without consulting tables, arrange the following alkenes in order of increasing boiling point: 1-butene, ethene, 1-hexene, and propene.
1. Alkenes have physical properties (low boiling points, insoluble in water) quite similar to those of their corresponding alkanes.
2. ethene < propene < 1-butene < 1-hexene
## Key Takeaway
• The physical properties of alkenes are much like those of the alkanes: their boiling points increase with increasing molar mass, and they are insoluble in water.
## Exercises
1. Without referring to a table or other reference, predict which member of each pair has the higher boiling point.
1. 1-pentene or 1-butene
2. 3-heptene or 3-nonene
2. Which is a good solvent for cyclohexene, pentane or water?
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http://math.stackexchange.com/questions/45074/finding-sets-that-do-not-intersect-approximation-algorithm
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# Finding sets that do not intersect. Approximation algorithm
I am trying to solve the following problem. Let $S$ be a set and $F \subset {S \choose k}$ that is $F$ is a subset of the set of all $k$-sets of $S$.
A set $M \subset F$ such that no two elements of $M$ intersect is called a solution for the problem.
I am looking for an algorithm $A$ that finds a solution to the above problem such that if the given solution is a set $M$ and the largest set that is a solution for the same instance is $M^*$ then
$$\frac{|M|}{|M^*|} \geq \frac1{k}\qquad (1)$$
The only algorithm I can see for the above problem is to pick an element $P$ from $F$, remove all the elements in $F$ that intersect with $P$ and continue.
However I am not able to analyze the above procedure to obtain the given bound (if even attainable).
Any hints on this problem?
-
This problem is usually called the unweighted set-packing problem. As a side-note, this problem is NP-complete; in fact, as I came to know only today (thanks, OP!), it is one of Karp's gang of 21!
Here's a simple proof that the heuristic sketched in the question gives a set $M$ that is at most a factor $k$ from the optimum, call this $M^*$. Create a bipartite graph with the sets in $M$ as the left vertices, and the sets in $M^*$ as the right vertices. Add an edge between $A \in M$ and $B \in M^*$ iff $A$ intersects $B$. Here are some basic observations:
• Every right vertex has at least one left neighbor. Otherwise, we could add this set safely to $M$ to get a bigger family, contradicting the maximality of $M$.
• Every left vertex has at most $k$ right neighbors. Otherwise two of the right neighbors will be forced to "share" a common element, contradicting the assumption that $M^*$ is a disjoint family of sets.
Putting these two together, you should be able to deduce that $|M^*| \leq |M|/k$. (Note that we do not have strict inequality.) Btw, the set-packing problem for the case $k=2$ is the well-known maximum matching problem. If you have seen matchings before, I encourage you to work out the proof for this specific case; it's quite illuminating.
This bound is tight, as seen from the following example: let $S$ be the set of $k^2$ points arranged as a $k \times k$ grid. Define $M$ to be just the leftmost column. Define $M^*$ to be the family of $k$ rows, each of which contains $k$ points. Take $F$ to be $M \cup M^*$. Clearly $|M| =1$ and $|M^*|=k$.
Better heuristics. Apparently, better local-heuristics heuristics are known for this problem, achieving a factor $k/2+\epsilon$ approximation. See e.g.: "Approximating Discrete Collections via Local Improvements" by Halldorsson.
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What is wrong with partitioning $S$ into $k$ element disjoint sets?
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Ross, that doesn't work since the $k$-sets in $M$ are required to be picked from $F$. – Srivatsan Jul 23 '11 at 23:19
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http://sci-gems.math.bas.bg/jspui/browse?type=author&sort_by=1&order=ASC&rpp=20&etal=-1&value=Liu%2C+F.&starts_with=N
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## Browsing by Author "Liu, F."
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Issue DateTitleAuthor(s)Publisher
2005 Numerical Approximation of a Fractional-In-Space Diffusion Equation, IIlic, M.; Liu, F.; Turner, I.; Anh, V.Institute of Mathematics and Informatics Bulgarian Academy of Sciences
2006 Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary ConditionsIlic, M.; Liu, F.; Turner, I.; Anh, V.Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Showing results 1 to 2 of 2
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http://mathoverflow.net/questions/847/is-any-representation-of-a-finite-group-defined-over-the-algebraic-integers/882
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# Is any representation of a finite group defined over the algebraic integers?
Apologies in advance if this is obvious.
-
I'm pretty sure it's not obvious...my guess is there isn't, but I can't think of any counterexamples right off the bat. – Ben Webster Oct 17 '09 at 14:51
So you are asking if there exist a basis for every GIVEN finite subgroup, not one basis that works for every finite subgroup, right? Coz then the answer is no. – shenghao Oct 17 '09 at 19:55
Yes, any particular subgroup. – Qiaochu Yuan Oct 17 '09 at 21:39
The subset of GL_n(\bar{Q}) consisting of matrices such that the matrix AND its inverse have algebraic integer entries is a subgroup, and obviously a group representation with algebraic integer entries would have to land there. – Ben Webster Oct 18 '09 at 1:54
Somewhat related: groupprops.subwiki.org/wiki/… Unfortunately, not every ring of algebraic integers (or even cyclotomic integers) is a PID. – Vipul Naik Apr 26 '11 at 20:12
This is not really an answer, but is too long for a comment. The proof given by Moonface above is given in more or less that form in the 1962 book of Curtis and Reiner. As far as I know, it is still open whether all irreducible representations of a finite group $G$ can be realized over $\mathbb{Z}[\omega]$, where $\omega$ is a complex primitive $|G|$-th roots of unity, though I think the paper of Cliff,Ritter and Weiss settles the questions for finite solvable groups. The paper of Serre ( the three letters to Feit) give counterexamples to a slightly different question: they show (among other things) that a representation of a finite group can be realised over some number fields, but might not be able to be realised over the ring of algebraic integers of that field. Brauer's characterization of characters/Brauer's induction theorem show that all representations of the finite group $G$ may be realised over $\mathbb{Q}[\omega]$ for $\omega$ as above ( $|G|$ can be replaced by the exponent of $G$ if desired). As I said, realizability over $\mathbb{Z}[\omega]$ is a different matter.
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http://alexanderpruss.blogspot.com/2012/08/are-infinite-and-infinitesimal-sizes.html
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Tuesday, August 28, 2012
Are infinite and infinitesimal sizes relational?
Suppose that Leibniz is right, and in addition us (call us "macros") there are infinitesimal embodied beings ("micros") and infinite embodied beings ("megas"). Suppose we are teaching English to one of the micros. Should we tell her to say:
1. The micros are infinitesimal, the macros are finite and non-infinitesimal, and the megas are infinite,
as we do, or should she say:
1. The micros are finite and non-infinitesimal, the macros are infinite, and the megas are infinitely many times bigger than the infinite macros?
I am inclined to think she should say (2), and so infinite and infinitesimal sizes are merely relational or indexical.
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http://ssconlineexam.com/onlinetest/SSC-CGL-Tier-1/Quantitative-Aptitude/QA-Test-13
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SSC CGL Tier 1 :: QA Test 13
Home » SSC CGL Tier 1 » QA Test 13 » General Questions
# SSC CGL Tier 1 Quantitative Aptitude Questions and Answers Free Online Mock Test 13
ssc cgl tier 1 free quantitative aptitude questions and answers free online test previous questions online tests mock tests quiz sample questions ssc cgl online quiz ssc online test ssc practice test free
Exercise
"Love is like a war, Easy to begin Hard to end." - (Proverb)
1 . A tank can be f ill ed by t wo pipes in 20 minutes and 30 minutes respectively. When the tank was empty, the two pipes were opened. After some time, the first pipe was stopped and the tank was filled in 18 minutes. After how much time of the start was the first pipe stopped ?
5 minutes 8 minutes 10 minutes 12 minutes
2 . A hare sees a dog 100 metres away from her and scuds off in the opposite direction at a speed of 12 km per hr. A minute later the dog perceives her and chases her at a speed of 16 km per hr. At what distance from the spot dog will overtake the hare when the hare took flight ?
900 metre 950 metre 1000 metre 1100 metre
3 . A train met with an accident 3 hours after starting, which detains it for one hour, after which it proceeds at 75% of its original speed. It arrives at the destination 4 hours late. Had the accident taken place 150 km further along the railway line, the train would have arrived only 3$1\over2$ 2 hours late. Find the length of the trip and the original speed of the train
1100 km and 100 kmph 1200 km and 100 kmph 1200 km and 90 kmph 1600 km and 90 kmph
4 . A motorboat in still water travels at a speed of 36 kmph. It goes 56 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be –
2 hours 25 minutes 3 hours 1 hour 24 minutes 2 hours 21 minutes
5 .
a b c d
6 .
32 8 1 0
7 . the value of $1\over20$+$1\over30$+$1\over42$+$1\over56$+$1\over72$+$1\over90$ is ---
A.$31\over10$
B.$3\over5$
C.$3\over20$
D.$7\over20$
a b c d
8 . (x+$1\over x$)(x-$1\over x$)($x^2$ + $1\over x^2$ -1)($x^2$ + $1\over x^2$ +1) is equal to --
A.$x^6$ + $1\over x^6$
B.$x^8$ + $1\over x^8$
C.$x^8$ - $1\over x^8$
D.$x^6$ - $1\over x^6$
a b c d
$(a-b)^2\over (b-c)(c-a)$+ $(b-c)^2\over (b-c)(c-a)$+ $(c-a)^2\over (b-c)(c-a)$ is --
0 3 $1\over2$ 2
10 . If a+ b+ c= 2s, then $(s-a)^2+(s-b)^2+(s-c)^2+(s-d)^2+d^2\over a^2+b^2+c^2$ is equal to –
$a^2+b^2+c^2$ 0 1 2
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http://www.mathcaptain.com/statistics/mean.html
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Even though mean refers to one of the measures of average in statistics, it is the most commonly used measure of central tendency, because it is based on all the data values and least affected by fluctuations in sampling. Mean is of three types based on the method of computation:
1. Arithmetic Mean
2. Geometric Mean
3. Harmonic Mean
## Definition of Mean in Statistics
Mean is a central measure which is used in describing a data distribution.
Indeed a data set is described by mean along with a measure of dispersion like range or variance.
Mean in statistics is also called Expectation or expected value when computed for random variables associated with probability experiments. In such cases the mean is essential to compute the probabilities of the variable assuming a specific discrete value or a range of values in an interval.
## Arithmetic Mean
The arithmetic mean of a data set is often referred to as mean of the data set. It is the mathematical average of the data values.
The arithmetic mean of n observations x1, x2, .......xn is given by
x = $\frac{x_{1}+x_{2}+......x_{n}}{n}$ or using sigma notation = $\frac{\sum_{i=1}^{n}x_{i}}{n}$
When the data is represented by a frequency distribution where f1, f2,......fn are the corresponding frequencies of data values x1, x2, xn, then the arithmetic mean is computed using the formula
x = $\frac{\sum_{i=1}^{n}x_{i}f_{i}}{N}$ where N = f1 + f2 + .........+ fn.
While x denotes the mean of sample data the letter μ is used to represent the population mean.
The value of arithmetic mean is also used in other computations of statistic measures like variance.
Even though the arithmetic mean is easy to compute and based on all data values, it's value is influenced by outliers or extreme values in the data set and hence lead to misinterpretations.
Example: The AM (x ) of the given five numbers $10,12,8,14,2$ is
$\frac{10+12+8+14+2}{5}$ = $9.2$
## Geometric Mean
Geometric Mean of n data values is the nth root of their product.
The formula for finding the geometric mean of n values x1 , x2, .......xn is given by
GM = $(x_{1}x_{2}......x_{n})$$^{\frac{1}{n}} which can be written using Pi notation as (\Pi_{i=1}^{n} x_{i})$$^{\frac{1}{n}}$
If f1, f2,....fn are the corresponding frequencies associated with the above data values the GM is given by,
GM = $(x_{1}^{f_{1}}x_{2}^{f_{2}}....x_{n}^{f_{n}})$$^{\frac{1}{N}} where N = f1 + f2 + .........+ fn. Example: The GM of the given five numbers 10, 12, 8, 14, 2 is (10\times 12\times 8\times 14\times 2)$$^{\frac{1}{5}}$ = $7.689$
## Harmonic Mean
Harmonic mean of n observations x1 , x2, .......xn is defined by
HM = $n(\Pi_{i=1}^{n}$$\frac{1}{x_{i}}$)$^{-1}$ = $\frac{n}{\frac{1}{x_{1}}+\frac{1}{x_{2}}+......+\frac{1}{x_{n}}}$
Harmonic mean formula for a frequency distribution is as follows:
HM = $\frac{N}{\frac{f_{1}}{x_{1}}+\frac{f_{2}}{x_{2}}+......\frac{f_{n}}{x_{n}}}$
where N = f1 + f2 + .........+ fn.
Example: The HM of the given five numbers $10, 12, 8, 14, 2$ is
$\frac{5}{\frac{1}{10}+\frac{1}{12}+\frac{1}{8}+\frac{1}{14}+\frac{1}{2}}$ = $\frac{5}{0.8797}$ = $5.68335$
### Median
Arithmetic Mean Geometric Mean Harmonic Mean
Arithmetic Means Geometrical Mean Harmonic Means Integration Meaning Intercept Meaning Mean Proportion Meaning of Quadrant parabola meaning A Negative Correlation Means that Binomial Distribution Mean Calculus Mean Value Theorem Central Tendency Mean
Calculator Mean Calculate Mean Deviation Calculate Sample Mean
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https://informesia.com/3571/a-particle-moves-in-x-y-plane-according-to-the-equations-x-4-t-2-5-t-16-and-y-5-t-where-x-y-are-in-metre-and-t-is-in-second-the-acceleration-of-the-particle-is
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34 views
A particle moves in $x-y$ plane according to the equations $x=4 t^{2}+5 t+16$ and $y=5 t$ where $x, y$ are in metre and $t$ is in second. The acceleration of the particle is
(a) $8 \mathrm{~m} \mathrm{~s}^{-2}$
(b) $12 \mathrm{~m} \mathrm{~s}^{-2}$
(c) $14 \mathrm{n} \mathrm{s}^{-2}$
(d) $16 \mathrm{~m} \mathrm{~s}^{-2}$
The correct option of this question will be (a).
Solution —
As $x=4 t^{2}+5 t+16$ and $y=5 t$
$\therefore \quad v_{x} =\frac{d x}{d t}=\frac{d}{d t}\left(4 t^{2}+5 t+16\right)=8 t+5$
$v_{y} =\frac{d y}{d t}=\frac{d}{d t}(5 t)=5$
$a_{x} =\frac{d v_{x}}{d t}=\frac{d}{d t}(8 t+5)=8$
$\text { and } a_{y} =\frac{d v_{y}}{d t}=\frac{d}{d t}(5)=0$
The acceleration of the particle is
$\vec{a}=a_{x} \hat{i}+a_{y} \hat{j}=8 \hat{i}+0 \hat{j}=8 \hat{i}$
or $a=\sqrt{8^{2}}=8 ms ^{-2}$
by
4.4k Points
23 views
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1 Vote
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https://www.physicsforums.com/threads/conceptual-question-on-angular-momentum.870998/
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# Conceptual Question on Angular Momentum.
• #1
65
15
## Homework Statement
A Person sitting firmly over a rotating stool has his arms stretched. If he fold his arms, his angular momentum about the axis of rotation :
A.) Increases
B.) Decreases
C.) Remains Unchanged
D.) doubles
## Homework Equations
[/B]Conservation of Angular Momentum
## The Attempt at a Solution
Since External Torque =0
Then final angular momentum = initial angular momentum
=> (C.)
But I wanted to further ask that in the Equation L=I*(omega)
since L has to be constant(if external torque = 0) then:
If I increases then omega decreases to keep L constant
or if omega increases then I decreases to keep constant
Will folding his arms increase I( Moment of Inertia ) or decrease it??
• #2
963
214
But I wanted to further ask that in the Equation L=I*(omega)
since L has to be constant(if external torque = 0) then:
If I increases then omega decreases to keep L constant
or if omega increases then I decreases to keep constant
by folding his arms the new moment of inertia of the system will increase /decrease?
how moment of inertia depends on mass distribution? if a mass is farther from axis of rotation its moment of inertia should be larger as I= m.r^2
L= I . angular velocity therefore a decrease/increase in I should result in the angular velocity to increse/decrease
Likes Sahil Kukreja
• #3
65
15
by folding his arms the new moment of inertia of the system will increase /decrease?
how moment of inertia depends on mass distribution? if a mass is farther from axis of rotation its moment of inertia should be larger as I= m.r^2
L= I . angular velocity therefore a decrease/increase in I should result in the angular velocity to increse/decrease
Ok. Thanks! so if the mass is extremely close and external torque=0, then angular velocity will reach very high.
• #4
963
214
Ok. Thanks! so if the mass is extremely close and external torque=0, then angular velocity will reach very high.
the example is ice-skating sport -there the rotation speed of skaters is increased or decreased by them using their arms folded or spreading out.
Likes Sahil Kukreja
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http://www.gradesaver.com/textbooks/science/physics/physics-for-scientists-and-engineers-a-strategic-approach-with-modern-physics-3rd-edition/chapter-10-energy-exercises-and-problems-page-271/1
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## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)
We first find the kinetic energy of the bullet; $KE = \frac{1}{2}mv^2$ $KE = \frac{1}{2}(0.010~kg)(500~m/s)^2$ $KE = 1250~joules$ We then find the kinetic energy of the bowling ball; $KE = \frac{1}{2}mv^2$ $KE = \frac{1}{2}(10~kg)(10~m/s)^2$ $KE = 500~joules$ The bullet has the larger kinetic energy.
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http://users.dune-project.org/projects/main-wiki/wiki/Guides_bug_reporting
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# Guidelines for bug reporting¶
This is meant as a collection for how to make a useful bug report, either to the bug tracker or to the mailing lists. Bug report is meant in a wide sense: the information we request here is often also useful when you just want to ask a question. Also note that these are guidelines: for instance, when you report a problem with the webpage you don't have to tell us the version of your compiler.
When you are unable to obtain some piece of information requested here, or it would require much work, please tell us so. Often, this already gives us some leads about your original problem, and at other times we may know a better way to obtain that information.
A usual bug report should observe the following points:
• Keep the discussion on the list
• Provide a problem description
• Provide unabbreviated log files
• Provide the version of your compiler
• Provide the versions of your Dune-modules
This guide may list more points, but generally the above should be a good start.
## Keep the discussion on the list¶
Often other people have problems similar to yours, or other developers on the list may have a better idea of how to solve your problem then the guy you have been communicating with all the time. There are exceptions of course: if we request some data that is either too big or too confidential to send to the list, you can send it privately to whoever requested it, but please send a note to the list that you did so, so the others are not kept totally in the dark.
The same applies to the bug-tracker, of course.
## Provide a problem description¶
"Dune does not compile" does not give us many clues as to what the problem is. We need to know exactly how you tried to compile, that means for instance
• the command, e.g. "dune-control --module=dune-foo all" or "make all", and the directory you were in when you executed the command
• if you used an options file for dunecontrol, the contents of that file
• if you just clicked a button in your IDE, what IDE you used and which button it was
We need to know exactly what went wrong:
• If there was an error message, give us the full error message
• If there was no error message, tell us so, and also tell us how you noticed that something was wrong
## Provide unabbreviated log files¶
If something went wrong, there is often some output that can help to determine the exact problem. If you run a compilation command like "dunecontrol" or "make", provide us with the complete output of that command. Yes, it is a lot of information, but it often contains some clues that we recognize. It is OK (and often even preferable) to give this logfile as an attachment. If you are nice, you can even compress it, but please use gzip or bzip2, if possible.
If you must, you can remove confidential information from those logfiles, but please replace it by something like "[CENSORED]" and explain what you removed ("I replaced all password by [CENSORED]") so we know what is missing.
## Provide the version of your compiler¶
If you don't know which compiler is being used, look at the output that is generated during compilation. It will probably contain lines that have the name of compiler somewhere in the beginning. Common compiler names include:
• cc
• gcc
• c++
• CC
• g++
• icc
• clang++
• xlc
• Any of the above with a version number appended, e.g. g++-4.3
• Any of the above with a path prepended, e.g. /opt/gcc/bin/g++
Once you have figured out what is probably your compiler, ask it for the exact version: open a terminal and type "g++ --version" (substitude the name of your compiler for g++). Send us the output of that command.
## Provide the versions of your Dune-modules¶
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Repository Root: https://svn.dune-project.org/svn/dune-common
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Last Changed Date: 2010-11-28 02:39:13 +0100 (So, 28 Nov 2010)
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Please give us the versions of all relevant dune modules, not just the one where the problem occurred. Please also give us similar information for external libraries you have compiled dune with, e.g. UG, ALUGrid, Alberta.
## config.log¶
One of the steps when the buildsystem is generated is to run the shell-script configure in the top of each modules directory tree. configure checks the system for the presence or absence of different features and generates all those lines beginning with "Checking for " or "Checking whether " in the compilation output. It also write a logfile "config.log" in the directory where it was run (usually the top of each module).
When there is a problem with configure, we usually want to see this logfile in addition to the output generated when compiling. Please observe the point about unabbreviated logfiles.
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http://math.stackexchange.com/questions/147190/birational-map-between-product-of-projective-varieties
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# Birational map between product of projective varieties
What is an example of a birational morphism between $\mathbb{P}^{n} \times \mathbb{P}^{m} \rightarrow \mathbb{P}^{n+m}$?
-
The subset $\mathbb A^n\times \mathbb A^m$ is open dense in $\mathbb P^n\times \mathbb P^m$ and the subset $\mathbb A^{n+m}$ is open dense in $\mathbb P^n\times \mathbb P^m$.
Hence the isomorphism $\mathbb A^n\times \mathbb A^m\stackrel {\cong}{\to} \mathbb A^{n+m}$ is the required birational isomorphism.
why $\mathbb{A}^{n} \times \mathbb{A}^{m}$ and $\mathbb{A}^{n+m}$ are open in $\mathbb{P}^{n} \times \mathbb{P}^{m}$? Can you please explain more this part? – user31509 May 19 '12 at 23:34
Dear user, $\mathbb A^N=\mathbb P^N \setminus H$ where $H$ is the hyperplane $z_0=0$ ( $\mathbb P^N$ has coordinates $[z_0:z_1:...:z_N]$). Since $z_0$ is a homogeneous polynomial (of degree one) , $H$ is closed and its complement $\mathbb A^N$ is open. For your first question use this result plus the fact that the product of two open sets is open : the Zariski topology for $\mathbb P^n\times \mathbb P^m$ is finer than the product topology. – Georges Elencwajg May 19 '12 at 23:49
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https://www.edaboard.com/threads/g-antenna-specifications.272679/
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# \$G antenna specifications
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4G antenna specifications
Hi friends
I'm going to design an MIMO antenna for cellphone that is suitable for 4G cellular systems. But I have some vague that I looked for a lot and found nothing. Would you please give me a clue for following issues:
1. What is the frequency and frequency range for UL and DL in LTE-Advanced (4G). I found that the spectrum flexibility for LTE release 10 are:
• 450–470 MHz band
• 698–862 MHz band
• 790–862 MHz band
• 2.3–2.4 GHz band
• 3.4–4.2 GHz band
• 4.4–4.99 GHz band
So what does that mean? Should we design an antenna in one of the aferomentioned frequency ranges or it should cover all ?
2. How much is the required bandwidth for LTE-Advanced in designing the antenna. As I found the minimum is 40 MHz and the maximum limit is 100 MHz. But some articles mentioned this bandwidth will provide by Carrier Aggregation of 2 up to 5, 20 MHz contiguous spectrum. So how much bandwidth should we consider in our design? 20 MHz (same before?) or 40 MHz ?
3. As some articles mentioned it required at most 8$\times$8 MIMO. Locating 8 antennas on cellphone is impossible. I need to know that is it possible to locate 2 antennas on cellphone and support the required bit rate in 4G or we need at least 4 antennas?
So appreciated.
#### Roger Miller
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Well not a very technical guy I am but I am using LTE technology in mobile. Long Term Evolution (LTE) is new revolutionary concept in mobile internet.
I think it should cover all because different service providers uses different frequencies to provide services of 4G like AT&T uses 700 Band 17, 1700/2100 MHz, Verizon uses 700, 1700/2100 MHz etc.
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https://www.groundai.com/project/trisections-of-4-manifolds-via-lefschetz-fibrations/2
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Trisections of 4-manifolds via Lefschetz fibrations
# Trisections of 4-manifolds via Lefschetz fibrations
Nickolas A. Castro and Burak Ozbagci Department of Mathematics, UC Davis, Davis, CA 95616 Department of Mathematics, UCLA, Los Angeles, CA 90095 and Department of Mathematics, Koç University, 34450, Istanbul, Turkey
###### Abstract.
We develop a technique for gluing relative trisection diagrams of -manifolds with nonempty connected boundary to obtain trisection diagrams for closed -manifolds. As an application, we describe a trisection of any closed -manifold which admits a Lefschetz fibration over equipped with a section of square , by an explicit diagram determined by the vanishing cycles of the Lefschetz fibration. In particular, we obtain a trisection diagram for some simply connected minimal complex surface of general type. As a consequence, we obtain explicit trisection diagrams for a pair of closed -manifolds which are homeomorphic but not diffeomorphic. Moreover, we describe a trisection for any oriented -bundle over any closed surface and in particular we draw the corresponding diagrams for and using our gluing technique. Furthermore, we provide an alternate proof of a recent result of Gay and Kirby which says that every closed -manifold admits a trisection. The key feature of our proof is that Cerf theory takes a back seat to contact geometry.
###### 2000 Mathematics Subject Classification:
The second author was partially supported by a research grant of the Scientific and Technological Research Council of Turkey.
## 1. Introduction
Recently, Gay and Kirby [12] proved that every smooth, closed, oriented, connected -manifold admits a trisection, meaning that for every , there exist non-negative integers such that is diffeomorphic to the union of three copies of the -dimensional -handlebody , intersecting pairwise in -dimensional handlebodies, with triple intersection a closed, oriented, connected -dimensional surface of genus . Such a decomposition of is called a -trisection or simply a genus trisection, since is determined by using the fact that , where denotes the Euler characteristic of .
Moreover, they showed that the trisection data can be encoded as a -tuple , which is called a -trisection diagram, such that each triple , , and is a genus Heegaard diagram for . Furthermore, they proved that trisection of (and its diagram) is unique up to a natural stabilization operation.
On the other hand, various flavors of Lefschetz fibrations have been studied extensively in the last two decades to understand the topology of smooth -manifolds. Suppose that a closed -manifold admits a Lefschetz fibration over , whose regular fiber is a smooth, closed, oriented, connected surface of genus . The fibration induces a handle decomposition of , where the essential data can be encoded by a finite set of ordered simple closed curves (the vanishing cycles) on a surface diffeomorphic to . The only condition imposed on the set curves is that the product of right-handed Dehn twists along these curves is isotopic to the identity diffeomorphism of .
In addition, every -manifold with nonempty boundary has a relative trisection and under favorable circumstances also admits an achiral Lefschetz fibration over with bounded fibers. The common feature shared by these structures is that each induces a natural open book on . To exploit this feature in the present paper, we develop a technique to obtain trisection diagrams for closed -manifolds by gluing relative trisection diagrams of -manifolds with nonempty connected boundary. The precise result is stated in Proposition 2.12, which is too technical to include in the introduction. Nevertheless, our gluing technique has several applications — one of which is the following result.
Theorem 3.7. Suppose that is a smooth, closed, oriented, connected -manifold which admits a genus Lefschetz fibration over with singular fibers, equipped with a section of square . Then, an explicit -trisection of can be described by a corresponding trisection diagram, which is determined by the vanishing cycles of the Lefschetz fibration. Moreover, if denotes the -manifold obtained from by blowing down the section of square , then we also obtain a -trisection of along with a corresponding diagram.
In particular, Theorem 3.7 provides a description of a -trisection diagram of the Horikawa surface (see [14, page 269] for its definition and properties), a simply connected complex surface of general type which admits a genus Lefschetz fibration over with singular fibers, equipped with a section of square . This section is the unique sphere in with self-intersection so that by blowing it down, we obtain a trisection diagram for the simply connected minimal complex surface of general type.
To the best of our knowledge, none of the existing methods in the literature can be effectively utilized to obtain explicit trisection diagrams for complex surfaces of general type. For example, Gay and Kirby describe trisections of , , , closed -manifolds admitting locally trivial fibrations over or (including of course , and ) and arbitrary connected sums of these in [12].
Note that, by Freedman’s celebrated theorem, the Horikawa surface is homeomorphic to (and also to the elliptic surface ), since it is simply connected, nonspin and its Euler characteristic is , while its signature is . On the other hand, since is a simply connected complex surface (hence Kähler) with , it has non-vanishing Seiberg-Witten invariants, while has vanishing Seiberg-Witten invariants which follows from the fact that . Hence, we conclude that is certainly not diffeomorphic to .
As a consequence, we obtain explicit -trisection diagrams for a pair of closed -manifolds, the Horikawa surface and , which are homeomorphic but not diffeomorphic. Note that has a natural -trisection diagram (obtained by the connected sum of the standard -trisection diagrams of and ), which can be stabilized four times to yield a -trisection diagram.
More generally, Theorem 3.7 can be applied to a large class of -manifolds. A fundamental result of Donaldson [6] says that every closed symplectic -manifold admits a Lefschetz pencil over . By blowing up its base locus the Lefschetz pencil can be turned into a Lefschetz fibration over , so that each exceptional sphere becomes a (symplectic) section of square . Conversely, any -manifold satisfying the hypothesis of Theorem 3.7 must carry a symplectic structure where the section of square can be assumed to be symplectically embedded. Therefore, is necessarily a nonminimal symplectic -manifold.
In [11, Theorem 3], Gay describes a trisection for any closed -manifold admitting a Lefschetz pencil, although he does not formulate the trisection of in terms of the vanishing cycles of the pencil (see [11, Remark 9]). He also points out that his technique does not extend to cover the case of Lefschetz fibrations on closed -manifolds [11, Remark 8].
We would like to point out that Theorem 3.7 holds true for any achiral Lefschetz fibration equipped with a section of square . In this case, is not necessarily symplectic. We opted to state our result only for Lefschetz fibrations to emphasize their connection to symplectic geometry.
Next we turn our attention to another natural application of our gluing technique where we find trisections of doubles of -manifolds with nonempty connected boundary. It is well-known (see, for example, [14, Example 4.6.5]) that there are two oriented -bundles over a closed, oriented, connected surface of genus : the trivial bundle and the twisted bundle . The former is the double of any -bundle over with even Euler number, while the latter is the double of any -bundle over with odd Euler number. We obtain trisections of these -bundles by doubling the relative trisections of the appropriate -bundles. In particular, we draw the corresponding -trisection diagram for and the -trisection diagram for using our gluing technique.
For any , the twisted bundle is not covered by the examples in [12], while our trisection for has smaller genus compared to that of given in [12]. We discuss the case of oriented -bundles over nonorientable surfaces in Section 4.5.
Finally, we provide a simple alternate proof of the following result due to Gay and Kirby.
Theorem 5.1. Every smooth, closed, oriented, connected -manifold admits a trisection.
Our proof is genuinely different from the two original proofs due to Gay and Kirby [12], one with Morse -functions and one with ordinary Morse functions, since not only contact geometry plays a crucial role in our proof, but we also employ a technique for gluing relative trisections.
After the completion of our work, we learned that Baykur and Saeki [3] gave yet another proof of Theorem 5.1, setting up a correspondence between broken Lefschetz fibrations and trisections on -manifolds, using a method which is very different from ours. In particular, they prove the existence of a -trisection on a 4-manifold which admits a genus Lefschetz fibration over with Lefschetz singularities — generalizing the first assertion in our Theorem 3.7, but without providing the corresponding explicit diagram for the trisection. They also give examples of trisections (without diagrams) on a pair of closed -manifolds (different from ours) which are homeomorphic but not diffeomorphic. In addition, for any , they give small genus trisections (again without the diagrams) for .
Conventions: All -manifolds are assumed to be smooth, compact, oriented and connected throughout the paper. The corners which appear in gluing manifolds are smoothed in a canonical way.
## 2. Gluing relative trisections
We first review some basic results about trisections and their diagrams (cf. [12]). Let denote the standard genus Heegaard splitting of obtained by stabilizing the standard genus Heegaard splitting times.
###### Definition 2.1.
A -trisection of a closed -manifold is a decomposition such that for each ,
1. there is a diffeomorphism and
2. taking indices mod , and .
It follows that is a closed surface of genus . Also note that and determine each other, since the Euler characteristic is equal to , which can be easily derived by gluing and first and then gluing .
Suppose that each of and is a collection of disjoint simple closed curves on some compact surface . We say that two such triples and are diffeomorphism and handleslide equivalent if there exists a diffeomorphism such that is related to by a sequence of handleslides and is related to by a sequence of handleslides.
###### Definition 2.2.
A -trisection diagram is an ordered -tuple such that
1. is a closed genus surface,
2. each of , and is a non-separating collection of disjoint, simple closed curves on ,
3. each triple , and is diffeomorphism and handleslide equivalent to the standard genus Heegaard diagram of depicted in Figure 1.
According to Gay and Kirby [12], every closed -manifold admits a trisection, which in turn, can be encoded by a diagram. Conversely, every trisection diagram determines a trisected closed -manifold, uniquely up to diffeomorphism.
Next we recall the analogous definitions of relative trisections and their diagrams for -manifolds with nonempty connected boundary (cf. [12, 5]).
Suppose that is a -manifold with nonempty connected boundary . We would like to find a decomposition , such that each is diffeomorphic to for some fixed . Since , it would be natural to require that part of each contribute to . Hence, we need a particular decomposition of to specify a submanifold of to be embedded in . With this goal in mind, we proceed as follows to develop the language we will use throughout the paper.
Suppose that are non-negative integers satisfying and
g+p+b−1≥k≥2p+b−1.
Let and for , and , .
We denote by a fixed genus surface with boundary components. Let
D={reiθ∈C|r∈[0,1]and−π/3≤θ≤π/3}
be a third of the unit disk in the complex plane whose boundary is decomposed as , where
∂−D ={reiθ∈∂D|θ=−π/3} ∂0D ={eiθ∈∂D} ∂+D ={reiθ∈∂D|θ=π/3}
The somewhat unusual choice of the disk will be justified by the construction below. We set , which is indeed diffeomorphic to . Then, inherits a decomposition , where and .
Let be the standard genus one Heegaard splitting of . For any , let , where the boundary connected sum is taken in neighborhoods of the Heegaard surfaces, inducing the standard genus Heegaard splitting of . Stabilizing this Heegaard splitting times we obtain a genus Heegaard splitting of .
We set and . Note that we can identify , where the boundary connected sum again takes place along the neighborhoods of points in the Heegaard surfaces. We now have a decomposition of as follows:
∂Zk=Yk=Y+g,k;p,b∪Y0g,k;p,b∪Y−g,k;p,b,
where and
###### Definition 2.3.
A -relative trisection of a -manifold with non-empty connected boundary is a decomposition such that for each ,
1. there is a diffeomorphism and
2. taking indices mod , and
As a consequence, is diffeomorphic to , which is a genus surface with boundary components. Note that the Euler characteristic is equal to , which can be calculated directly from the definition of a relative trisection. We also give alternate method to calculate in Corollary 2.10.
According to [12], every -manifold with nonempty connected boundary admits a trisection. Moreover, there is a natural open book induced on , whose page is diffeomorphic to , which is an essential ingredient in our definition of .
Informally, the contribution of each to is one third of an open book. This is because the part of each that contributes to is diffeomorphic to
Y0g,k;p,b=∂0U=(P×∂0D)∪(∂P×D),
where is one third of the truncated pages, while is one third of the neighborhood of the binding. In other words, not only we trisect the -manifold , but we also trisect its boundary . Conversely, if an open book is fixed on , then admits a trisection whose induced open book coincides with the given one.
###### Definition 2.4.
A -relative trisection diagram is an ordered -tuple such that
1. is a genus surface with boundary components,
2. each of and is a collection of disjoint, essential, simple closed curves,
3. each triple , and is diffeomorphism and handleslide equivalent to the diagram depicted in Figure 2.
It was shown in [5] that every relative trisection diagram determines uniquely, up to diffeomorphism, (i) a relatively trisected -manifold with nonempty connected boundary and (ii) the open book on induced by the trisection. Moreover, the page and the monodromy of the open book on is determined completely by the relative trisection diagram by an explicit algorithm, which we spell out below.
Suppose that is a -relative trisection diagram, which represents a relative trisection of a -manifold with nonempty connected boundary. The page of the induced open book on is given by , which is the genus surface with boundary components obtained from by performing surgery along the curves. This means that to obtain , we cut open along each curve and glue in disks to cap off the resulting boundaries.
Now that we have a fixed identification of the page of as , we use Alexander’s trick to describe the monodromy of . Namely, we cut into a single disk via two distinct ordered collections of arcs, so that for each arc in one collection there is an arc in the other collection with the same endpoints. As a result, we get a self-diffeomorphism of that takes one collection of arcs to the other respecting the ordering of the arcs, and equals to the identity otherwise. This diffeomorphism uniquely extends to a self-diffeomorphism of the disk, up to isotopy. Therefore, we get a self-diffeomorphism of fixing pointwise, which is uniquely determined up to isotopy. Next, we provide some more details (see [5, Theorem 5]) about how to obtain the aforementioned collection of arcs.
Let be any ordered collection of disjoint, properly embedded arcs in disjoint from , such that the image of in cuts into a disk. We choose a collection of arcs , and a collection of simple closed curves disjoint from in such that is handleslide equivalent to , and is handleslide equivalent to . This means that arcs are obtained by sliding arcs over curves, and is obtained by sliding curves over curves. Next we choose a collection of arcs , and a collection of simple closed curves disjoint from in such that is handleslide equivalent to , and is handleslide equivalent to . This means that arcs are obtained by sliding arcs over curves, and is obtained by sliding curves over curves. Finally, we choose a collection of arcs , and a collection of simple closed curves disjoint from in such that is handleslide equivalent to , and is handleslide equivalent to . This means that arcs are obtained by sliding arcs over curves, and is obtained by sliding curves over curves. It follows that is handleslide equivalent to for some collection of arcs disjoint from in .
###### Definition 2.5.
We call the triple a cut system of arcs associated to the diagram .
Now we have two ordered collections of arcs and in , such that each of their images in cuts into a disk. Then, as we explained above, there is a unique diffeomorphism , up to isotopy, which fixes pointwise such that .
###### Remark 2.6.
It is shown in [5] that, up to isotopy, the monodromy of the resulting open book is independent of the choices in the above algorithm.
Next, we give a very simple version of the general gluing theorem [4] for relatively trisected -manifolds. Here we present a different proof — where we use the definition of a relative trisection as given in [5] instead of [12] — for the case of a single boundary component.
###### Lemma 2.7.
Suppose that and are -manifolds such that and are both nonempty and connected. Let and be - and -relative trisections with induced open books and on and , respectively. If is an orientation-reversing diffeomorphism which takes to (and hence and ), then the relative trisections on and can be glued together to yield a -trisection of the closed -manifold , where and .
###### Proof.
Since there is an orientation-reversing diffeomorphism which takes the open book to the open book , we have and . Let and be - and -relative trisections, respectively. Then, by Definition 2.3, there are diffeomorphisms and for .
Let and be the bindings of and , where and are the projection maps of these open books, respectively. Since the gluing diffeomorphism takes to by our assumption, we have , for all Moreover, we may assume that
fi=φ′i∘f∘φ−1i:Y0g,k;p,b→Y0g′,k′;p,b
is a diffeomorphism for each . Informally, we identify each third of on with the appropriate third of on via the gluing map . This allows us to define
Xi=Wi∪fW′i=Wi∪W′i/∼
where if and , where .
We claim that is a -trisection, where
G=g+g′+b−1andK=k+k′−(2p+b−1).
In order to prove our claim, we first need to describe, for each , a diffeomorphism . The diffeomorphism is essentially obtained by gluing the diffeomorphisms and using the diffeomorphism , as we describe below.
To construct the desired diffeomorphism , it suffices to describe how to glue with to obtain by identifying with using the gluing map .
By definition, , and similarly , where and . Note that is diffeomorphic to via . To glue to we identify with via the diffeomorphism . Next, we observe that by gluing and along the aforementioned parts of their boundaries using , we get , where .
To see this, we view as , and similarly as , where . We glue with and then take its product with . To glue with we identify with using . The result of this identification is diffeomorphic to . However, to complete the identification dictated by , we have to take the quotient of by the relation for all . Note that we suppressed here since we have already identified with via . The result is still diffeomorphic to the handlebody . Therefore, the gluing of and is diffeomorphic to , since it is a thickening of by taking its product with .
As a consequence, the result of gluing to is diffeomorphic to
(♮lS1×B3)♮Vn♮Vn′≅♮l+n+n′S1×B3≅♮KS1×B3≅ZK,
since .
To finish the proof of the lemma, we need to show that taking indices mod ,
Φi(Xi∩Xi+1)=Y+G,KandΦi(Xi∩Xi−1)=Y−G,K,
where is the standard genus Heegaard splitting of .
We observe that
Φi(Xi∩Xi+1)=φi(Wi∩Wi+1)∪fiφ′i(W′i∩W′i+1)=((Y+g,k;p,b∪Y+g′,k′;p,b)/∼)⊂YK
where if and .
Note that by definition, and similarly . Since the boundary connected sums are taken along the interior of Heegaard surfaces, the identification does not interact with and and hence
But we see that is diffeomorphic to , by exactly the same argument used above when we discussed the gluing of with . Therefore, we have
(Y+g,k;p,b∪Y+g′,k′;p,b)/∼ ≅((∂+U∪∂+U′)/∼)♮(∂+sVn♮∂+s′Vn′) ≅(♮lS1×B2)♮(∂+sVn♮∂+s′Vn′) ≅(♮lS1×B2)♮s+n+s′+n′S1×B2 ≅♮GS1×B2
since . Similarly, we have
Φi(Xi∩Xi−1)=φi(Wi∩Wi−1)∪fiφ′i(W′i∩W′i−1)=(Y−g,k;p,b∪Y−g′,k′;p,b)/∼)⊂YK
where if and . Thus we obtain . Moreover,
Therefore, and gives the standard genus Heegaard splitting of , as desired.
To summarize, we showed that there is a diffeomorphism , for each , and moreover, taking indices mod , and . Therefore, we conclude that is a -trisection. ∎
Here is an immediate corollary of Lemma 2.7.
###### Corollary 2.8.
Suppose that is a -relative trisection of a -manifold with nonempty connected boundary. Let denote the double of obtained by gluing and (meaning with the opposite orientation) by the identity map of the boundary . Then admits a -trisection.
###### Proof.
If is a -relative trisection of with the induced open book on , then is a -relative trisection of with the induced open book on , where is obtained from by reversing the orientation of the pages. Since the identity map from to is an orientation-reversing diffeomorphism which takes to , we obtain the desired result about by Lemma 2.7. ∎
The point of Corollary 2.8 is that one does not need to know the monodromy of the open book on to describe a trisection on .
###### Example 2.9.
Let denote the -bundle over with Euler number . In [5], there is a description of a -relative trisection of for , and a -relative trisection of . Since the double of is or depending on modulo , we get a -trisection of (resp. ) for any even (resp. odd) nonzero integer , by Corollary 2.8.
In particular, by doubling the -relative trisection of , we obtain a -trisection of which is smaller compared to the -trisection presented in [12], provided that . Similarly, by setting , we obtain a -trisection for , which is not covered by the examples in [12], except for . Note that there is also a -relative trisection of given in [5] for each . Since the double of is or depending on modulo , we get infinitely many -trisections of and .
###### Corollary 2.10.
If is a -relative trisection of a -manifold with nonempty connected boundary, then the Euler characteristic is equal to
###### Proof.
Using Corollary 2.8, we compute
χ(W)=12χ(DW)=12(2+2g+b−1−3(2k−2p−b+1)))=g−3k+3p+2b−1.
One can of course derive the same formula directly from the definition of a relative trisection. ∎
Since every relatively trisected -manifold with connected boundary is determined by some relative trisection diagram, it would be desirable to have a version of Lemma 2.7, where one “glues” the relative trisection diagrams corresponding to and to get a diagram corresponding to the trisection . This is the content of Proposition 2.12, but first we develop some language to be used in its statement.
Let and be - and -relative trisection diagrams corresponding to the relative trisections and , with induced open books and on and
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https://homework.zookal.com/questions-and-answers/1-which-of-the-followings-are-true-a-h2o-contains-642666057
|
1. Science
2. Chemistry
3. 1 which of the followings are true a h2o contains...
# Question: 1 which of the followings are true a h2o contains...
###### Question details
1. Which of the followings are true:
A. H2O contains polar covalent bonds B. H2O can disrupt other hydrogen bonds in aqueous solutions C. Non-polar molecules can not have polar covalent bonds D. H2O has a higher boiling point than methane primarily due to the hydrogen bond formation E. Usually hydrogen bonds are weaker than covalent bonds
* The answer A, D, E is incorrect
|
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http://mathhelpforum.com/calculus/136855-newtons-method-finding-solutions.html
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1. ## newtons method(finding solutions)
we first used newtons method to find the approximate value of 200^(1/7) and got it equal to the awnser in the caclulator which is = 2.131663117
i need some help in the right direction on how to solve the question after solving the above equation using newtons method!
Question:
the fundamental theorem of algebra guarantees that the equation x^7-200 = 0 must have 7 solutions. You have just found one of these. Are there any more real solutions? Use your tools of calculus to sustain your awnser.
2. Do you know Descartes rule of sign?
3. ## k
ok so in other words using decartes rule states that
x^(7)-200=0
has only 1 possible positive real zero? the other 6 are imaginary/complex values?
4. Yes because we obtain 1 (+), 0 (-), so the last solutions are 3 pairs of complex congujates
5. ## y
thx
6. I don't think you need DesCarte's rule of signs. Just observe that the derivative of $x^7- 200$, $7x^6$ is always non-negative so it is a "one to one" function on the real numbers.
7. Originally Posted by dwsmith
Yes because we obtain 1 (+), 0 (-), so the last solutions are 3 pairs of complex congujates
Descartes rule of signs tells you there is exactly one positive solution. Substitute $u=-x$ and you get $-u^7-1$ and then Descartes rule of signs tells you there are no positive solutions for $u$ and so no negative solutions for $x$ to the original equation. Hence there is exactly 1 real solution to $x^7-1=0$.
But the question requires that you use HallsofIvy's method not the rule of signs.
CB
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https://sunfluidh.limsi.fr/sunfluidh:spaceaveragedsnapshots_dataset_namelist
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# Documentation du code de simulation numérique SUNFLUIDH
## Web LIMSI
sunfluidh:spaceaveragedsnapshots_dataset_namelist
## Namelist "SpaceAveragedSnapshots_Dataset"
This data set is used to get the space-averaged fields of physical quantities in a specific direction at un given time. The recording rate is specified in the namelist “Simulation_Management”.
### Full data set of the namelist
&SpaceAveragedSnapshots_Dataset SpaceAverageDirection="J-DIRECTION", Field_Number=3, List_of_Fields="U","V","W"/
### SpaceAverageDirection
• Type : Character string
• Set the the direction in which the space average is performed : “I-DIRECTION”, “J-DIRECTION” or “K-DIRECTION”
### Field_number
• Type : Integer value
• Set the number of fields for which the space average will be computed.
### List_of_Fields
• Type : Character string.
• Set the name of physical quantities for which the space average will be computed (6 characters max.). See the namelist Namelist "Instantaneous_Fields_Listing" in order to get the list of available physical quantities.
sunfluidh/spaceaveragedsnapshots_dataset_namelist.txt · Dernière modification: 2019/12/25 15:01 de yann
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https://spindynamics.org/wiki/index.php?title=Ngce.m&oldid=4287
|
# ngce.m
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Numerical integral route to the Redfield relaxation superoperator.
## Syntax
R=ngce(spin_system,H,dt)
## Arguments
H0 - static laboratory frame Hamiltonian commutation su-
peroperator acting in the background
H1 - stochastic part of the laboratory frame Hamiltonian
commutation superoperator with a zero average, as a
K by N cell array with the following topology:
{H(0) H(dt) H(2dt) ... H(Ndt); % MD trajectory 1
H(0) H(dt) H(2dt) ... H(Ndt); % MD trajectory 2
............................
H(0) H(dt) H(2dt) ... H(Ndt)}; % MD trajectory K
i.e. the rows are made of individual MD trajectories.
dt - time step of the MD trajectory, seconds
## Outputs
R - laboratory frame relaxation superoperator
## Examples
A test against the analytical relaxation superoperator is provided in examples/relaxation_theory/ngce_test.m file.
## Notes
Enough trajectory points must be present to converge each integral, and enough trajectories must be present to converge the average.
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https://docs.mesastar.org/en/latest/test_suite/1.3M_ms_high_Z.html
|
# 1.3M_ms_high_Z¶
The test checks the evolution of metal-rich low-mass stars by evolving a 1.3 Msun, metal-rich Z=0.04 model from the pre-main sequence to core hydrogen depletion.
This test case has two parts.
• Part 1 (inlist_zams) creates the pre-main-sequence model and stops near zams.
• Part 2 (inlist_1.3M_ms_high_Z) evolves the model from zams to when the luminosity reaches log10(L/Lsun) = 0.7.
The final model, click on the image for a larger version, shows
The left plot shows the HR diagram. The yellow curve is a precalculated HR track loaded from HR_OPAL.dat, while the green curve is the model calculated. The right plot shows a profile of the metal mass fraction. The curve rises above the background metallicity as hydrogen burns to helium and goes below the background metallicity as core hydrogen depletes.
pgstar commands used for the plots above:
&pgstar
pgstar_interval = 10
! device
file_white_on_black_flag = .true. ! white_on_black flags -- true means white foreground color on black background
file_device = 'png' ! png
file_extension = 'png'
!file_device = 'vcps' ! postscript
!file_extension = 'ps'
! build grid
Grid1_title = '1.3M_ms_high_Z'
Grid1_win_flag = .true.
Grid1_win_width = 15
Grid1_win_aspect_ratio = 0.4 ! aspect_ratio = height/width
Grid1_xleft = 0.05 ! fraction of full window width for margin on left
Grid1_xright = 0.95 ! fraction of full window width for margin on right
Grid1_ybot = 0.08 ! fraction of full window width for margin on bottom
Grid1_ytop = 0.92 ! fraction of full window width for margin on top
Grid1_num_cols = 5 ! divide plotting region into this many equal width cols
Grid1_num_rows = 1 ! divide plotting region into this many equal height rows
Grid1_num_plots = 2 ! <= 10
Grid1_plot_name(1) = 'HR'
Grid1_plot_row(1) = 1 ! number from 1 at top
Grid1_plot_rowspan(1) = 1 ! plot spans this number of rows
Grid1_plot_col(1) = 1 ! number from 1 at left
Grid1_plot_colspan(1) = 2 ! plot spans this number of columns
Grid1_plot_pad_left(1) = 0.025 ! fraction of full window width for padding on left
Grid1_plot_pad_right(1) = 0.05 ! fraction of full window width for padding on right
Grid1_plot_pad_top(1) = 0.05 ! fraction of full window height for padding at top
Grid1_plot_pad_bot(1) = 0.05 ! fraction of full window height for padding at bottom
Grid1_txt_scale_factor(1) = 1.0 ! multiply txt_scale for subplot by this
Grid1_plot_name(2) = 'Profile_Panels1'
Grid1_plot_row(2) = 1 ! number from 1 at top
Grid1_plot_rowspan(2) = 1 ! plot spans this number of rows
Grid1_plot_col(2) = 3 ! number from 1 at left
Grid1_plot_colspan(2) = 3 ! plot spans this number of columns
Grid1_plot_pad_left(2) = 0.05 ! fraction of full window width for padding on left
Grid1_plot_pad_right(2) = 0.025 ! fraction of full window width for padding on right
Grid1_plot_pad_top(2) = 0.05 ! fraction of full window height for padding at top
Grid1_plot_pad_bot(2) = 0.05 ! fraction of full window height for padding at bottom
Grid1_txt_scale_factor(2) = 1.0 ! multiply txt_scale for subplot by this
! file output
Grid1_file_flag = .true.
Grid1_file_dir = 'png'
Grid1_file_prefix = 'grid1'
Grid1_file_interval = 1000000 ! output when mod(model_number,Grid1_file_interval)==0
Grid1_file_width = 15 ! negative means use same value as for window
Grid1_file_aspect_ratio = -1 ! negative means use same value as for window
pgstar_model_scale = 1.4
pgstar_model_disp = 1.5
pgstar_model_coord = 0.98
pgstar_model_fjust = 1.0
pgstar_age_scale = 1.4
pgstar_age_disp = 1.5
pgstar_age_coord = -0.04
pgstar_age_fjust = 0.0
! HR diagram
HR_win_flag = .false.
HR_win_aspect_ratio = 1.0
! set static plot bounds
HR_logT_min = 3.55
HR_logT_max = 3.85
HR_logL_min = 0.1
HR_logL_max = 1.0
! show OPAL results
HR_fname = 'HR_OPAL.dat' ! file name for extra HR data
! profile
Profile_Panels1_win_flag = .false.
Profile_Panels1_num_panels = 1
Profile_Panels1_xaxis_name = 'mass'
Profile_Panels1_xmin = -101d0 ! only used if /= -101d0
Profile_Panels1_xmax = -101d0 ! only used if /= -101d0
Profile_Panels1_yaxis_name(1) = 'z_mass_fraction_metals'
Profile_Panels1_ymin(1) = 0.038 ! only used if /= -101d0
Profile_Panels1_ymax(1) = 0.042 ! only used if /= -101d0
Profile_Panels1_other_yaxis_name(:) = ''
/ ! end of pgstar namelist
Last-Updated: 27May2021 (MESA ebecc10) by fxt
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|
https://meangreenmath.com/tag/microsoft-excel/
|
# Exponential growth and decay (Part 9): Amortization tables
This post is inspired by one of the questions that I pose to our future high school math teachers during our Friday question-and-answer sessions. In these sessions, I play the role of a middle- or high-school student who’s asking a tricky question to his math teacher. Here’s the question:
A student asks, “My father bought a house for $200,000 at 12% interest. He told me that by the time he fi nishes paying for the house, it will have cost him more than$500,000. How is that possible? 12% of $200,000 is only$24,000.”
Without fail, these future teachers don’t have a good response to this question. Indeed, my experience is that most young adults (including college students) have never used an amortization table, which is the subject of today’s post.
In the past few posts, we have considered the solution of the following recurrence relation, which is often used to model the payment of a mortgage or of credit-card debt:
$A_{n+1} = r A_n - k$
With this difference equation, the rate at which the principal is reduced can be simply computed using Microsoft Excel. This tool is called an amortization schedule or an amortization table; see E-How for the instructions of how to build one. Here’s a sample Excel spreadsheet that I’ll be illustrating below: Amortization schedule. My personal experience is that many math majors have never seen such a spreadsheet, even though they are familiar with compound interest problems and certainly have the mathematical tools to understand this spreadsheet.
Here’s a screen capture from the spreadsheet:
The terms of the loan are typed into Cells B1 (length of loan, in years), B2 (annual percentage rate), and B3 (initial principal). Cell B4 is computed from this information using the Microsoft Excel command $\hbox{PMT}$:
$=\hbox{PMT}(\hbox{B2}/12,\hbox{B1}*12,-\hbox{B3})$
This is the amount that must be paid every month in order to pay off the loan in the prescribed number of years. Of course, there is a formula for this:
$M = \displaystyle \frac{Pr}{12 \displaystyle \left[1 - \left( 1 + \frac{r}{12} \right)^{-12t} \right]}$
I won’t go into the derivation of this formula here, as it’s a bit complicated. Notice that this formula does not include escrow, points, closing costs, etc. This is strictly the amount of money that’s needed to pay down the principal.
The table, beginning in Row 8 of the above picture, shows how quickly the principal will be paid off. In row 8, the interest that’s paid for that month is computed by
$=\hbox{B8} * \ \hbox{B}\\hbox{2}/12$
Therefore, the amount of the monthly payment that actually goes toward paying down the principal will be
$= \\hbox{B}\\hbox{4} - \hbox{C8}$
Column E provides an opportunity to pay something extra each month; more on this later. So, after taking into account the payments in columns D and E, the amount remaining on the loan is recorded in Cell F8:
$= \hbox{B8} - \hbox{D8} - \hbox{E8}$
This amount is then copied into Cell B9, and then the pattern can be filled down.
The yellow graph shows how quickly the balance of the loan is paid off over the length of the loan. A picture is worth a thousand words: in the initial years of the loan, most of the payments are gobbled up by the interest, and so the principal is paid off slowly. Only in the latter years of the loan is the principal paid off quickly.
So, it stands to reason that any extra payments in the initial months and years of the loan can do wonders for paying off the loan quickly. For example, here’s a screenshot of what happens if an extra $200/month is paid only in the first 12 months of the loan: A definite bend in the graph is evident in the initial 12 months until the normal payment is resumed in month 13. As a result of those extra payments, the curve now intersects the horizontal axis around 340. In other words, 20 fewer months are required to pay off the loan. Stated another way, the extra payments in the first year cost an extra $\200 \times 12 = \2400$. However, in the long run, those payments saved about $\536.82 \times 20 \approx \10,700$! # Exponential growth and decay (Part 8): Paying off credit-card debt via recurrence relations The following problem in differential equations has a very practical application for anyone who has either (1) taken out a loan to buy a house or a car or (2) is trying to pay off credit card debt. To my surprise, most math majors haven’t thought through the obvious applications of exponential functions as a means of engaging their future students, even though it is directly pertinent to their lives (both the students’ and the teachers’). You have a balance of$2,000 on your credit card. Interest is compounded continuously with a rate of growth of 25% per year. If you pay the minimum amount of $50 per month (or$600 per year), how long will it take for the balance to be paid?
In previous posts, I approached this problem using differential equations. There’s another way to approach this problem that avoids using calculus that, hypothetically, is within the grasp of talented Precalculus students. Instead of treating this problem as a differential equation, we instead treat it as a first-order difference equation (also called a recurrence relation):
$A_{n+1} = r A_n - k$
The idea is that the amount owed is multiplied by a factor $r$ (which is greater than 1), and from this product the amount paid is deducted. With this approach — and unlike the approach using calculus — the payment period would be each month and not per year. Therefore, we can write
$A_{n+1} = \displaystyle \left( 1 + \frac{0.25}{12} \right) A_n - 50$
Notice that the meaning of the 25% has changed somewhat… it’s no longer the relative rate of growth, as the 25% has been equally divided for the 12 months. The solution of this difference equation is
$A_n = r^n P - k \left( \displaystyle \frac{1 - r^n}{1-r} \right)$
A great advantage of using a difference equation to solve this problem is that the solution can be easily checked with a simple spreadsheet. (Indeed, pedagogically, I would recommend showing a spreadsheet like this before doing any of the calculations of the previous few posts, so that students can begin to wrap their heads around the notion of a difference equation before the solution is presented.)
To start the spreadsheet, I wrote “Step” in Cell A1 and “Amount” in Cell B1. Then I entered the initial conditions: $0$ in Cell A2 and $2000$ in Cell B2. (In the screenshot below, I changed the format of column B to show dollars and cents.) Next, I entered $=\hbox{A2}+1$ in Cell A3 and
$=\hbox{B2}*(1+0.25/12)-50$
in Cell B3. Finally, I copied the pattern in Cells A3 and B3 downward. Here’s the result:
After the formula the algebraic solution of the difference equation has been found, this can be added to the spreadsheet in a different column. For example, I added the header “Predicted Amount” in Cell D1. In Cell D2, I typed the formula
$=2000*\hbox{POWER}(1+0.25/12,\hbox{A2})-50*(1-\hbox{POWER}(1+0.25/12,\hbox{A2}))/(1-(1+0.25/12))$
Finally, I copied this pattern down the Column D. Here’s the result:
Invariably, when I perform a demonstration like this in class, I elicit a reaction of “Whoa…. it actually works!” Even for a class of math majors. Naturally, I tease them about this… they didn’t believe me when I used algebra, but now it has to be true because the computer says so.
Here’s the spreadsheet that I used to make the above pictures: CreditCardDebt.
# Day One of my Calculus I class: Part 5
In this series of posts, I’d like to describe what I tell my students on the very first day of Calculus I. On this first day, I try to set the table for the topics that will be discussed throughout the semester. I should emphasize that I don’t hold students immediately responsible for the content of this lecture. Instead, this introduction, which usually takes 30-45 minutes, depending on the questions I get, is meant to help my students see the forest for all of the trees. For example, when we start discussing somewhat dry topics like the definition of a continuous function and the Mean Value Theorem, I can always refer back to this initial lecture for why these concepts are ultimately important.
I’ve told students that the topics in Calculus I build upon each other (unlike the topics of Precalculus), but that there are going to be two themes that run throughout the course:
1. Approximating curved things by straight things, and
2. Passing to limits
We are now trying to answer the following problem.
Problem #2. Find the area under the parabola $f(x) = x^2$ between $x=0$ and $x=1$.
Using five rectangles with right endpoints, we find the approximate answer of $0.44$. With ten rectangles, the approximation is $0.385$. With one hundred rectangles (and Microsoft Excel), the approximation is $0.33835$. This last expression was found by evaluating
$0.01[ (0.01)^2 + (0.02)^2 + \dots + (0.99)^2 + 1^2]$
At this juncture, what I’ll do depends on my students’ background. For many years, I had the same group of students for both Precalculus and Calculus I, and so I knew full well that they had seen the formula for $\displaystyle \sum_{k=1}^n k^2$. And so I’d feel comfortable showing my students the contents of this post. However, if I didn’t know for sure that my students had at least seen this formula, I probably would just ask them to guess the limiting answer without doing any of the algebra to follow.
Assuming students have the necessary prerequisite knowledge, I’ll ask, “What happens if we have $n$ rectangles?” Without much difficulty, they’ll see that the rectangles have a common width of $1/n$. The heights of the rectangles take a little more work to determine. I’ll usually work left to right. The left-most rectangle has right-most $x-$coordinate of $1/n$, and so the height of the leftmost rectangle is $(1/n)^2$. The next rectangle has a height of $(2/n)^2$, and so we must evaluate
$\displaystyle \frac{1}{n} \left[ \frac{1^2}{n^2} + \frac{2^2}{n^2} + \dots + \frac{n^2}{n^2} \right]$, or
$\displaystyle \frac{1}{n^3} \left[ 1^2 + 2^2 + \dots + n^2 \right]$
I then ask my class, what’s the formula for this sum? Invariably, they’ve forgotten the formula in the five or six weeks between the end of Precalculus and the start of Calculus I, and I’ll tease them about this a bit. Eventually, I’ll give them the answer (or someone volunteers an answer that’s either correct or partially correct):
$\displaystyle \frac{1}{n^3} \times \frac{n(n+1)(2n+1)}{6}$, or $\frac{(n+1)(2n+1)}{6n^2}$.
I’ll then directly verify that our previous numerical work matches this expression by plugging in $n=5$, $n= 10$, and $n = 100$.
I then ask, “What limit do we need to take this time?” Occasionally, I’ll get the incorrect answer of sending $n$ to zero, as students sometimes get mixed up thinking about the width of the rectangles instead of the number of rectangles. Eventually, the class will agree that we should send $n$ to plus infinity. Fortunately, the answer $\displaystyle \frac{(n+1)(2n+1)}{6n^2}$ is an example of a rational function, and so the horizontal asymptote can be immediately determined by dividing the leading coefficients of the numerator and denominator (since both have degree 2). We conclude that the limit is $2/6 = 1/3$, and so that’s the area under the parabola.
# Reminding students about Taylor series (Part 4)
I’m in the middle of a series of posts describing how I remind students about Taylor series. In the previous posts, I described how I lead students to the definition of the Maclaurin series
$f(x) = \displaystyle \sum_{k=0}^{\infty} \frac{f^{(k)}(0)}{k!} x^k$,
which converges to $f(x)$ within some radius of convergence for all functions that commonly appear in the secondary mathematics curriculum.
Step 4. Let’s now get some practice with Maclaurin series. Let’s start with $f(x) = e^x$.
What’s $f(0)$? That’s easy: $f(0) = e^0 = 1$.
Next, to find $f'(0)$, we first find $f'(x)$. What is it? Well, that’s also easy: $f'(x) = \frac{d}{dx} (e^x) = e^x$. So $f'(0)$ is also equal to $1$.
How about $f''(0)$? Yep, it’s also $1$. In fact, it’s clear that $f^{(n)}(0) = 1$ for all $n$, though we’ll skip the formal proof by induction.
Plugging into the above formula, we find that
$e^x = \displaystyle \sum_{k=0}^{\infty} \frac{1}{k!} x^k = \sum_{k=0}^{\infty} \frac{x^k}{k!} = 1 + x + \frac{x^2}{2} + \frac{x^3}{3} + \dots$
It turns out that the radius of convergence for this power series is $\infty$. In other words, the series on the right converges for all values of $x$. So we’ll skip this for review purposes, this can be formally checked by using the Ratio Test.
At this point, students generally feel confident about the mechanics of finding a Taylor series expansion, and that’s a good thing. However, in my experience, their command of Taylor series is still somewhat artificial. They can go through the motions of taking derivatives and finding the Taylor series, but this complicated symbol in $\displaystyle \sum$ notation still doesn’t have much meaning.
So I shift gears somewhat to discuss the rate of convergence. My hope is to deepen students’ knowledge by getting them to believe that $f(x)$ really can be approximated to high precision with only a few terms. Perhaps not surprisingly, it converges quicker for small values of $x$ than for big values of $x$.
Pedagogically, I like to use a spreadsheet like Microsoft Excel to demonstrate the rate of convergence. A calculator could be used, but students can see quickly with Excel how quickly (or slowly) the terms get smaller. I usually construct the spreadsheet in class on the fly (the fill down feature is really helpful for doing this quickly), with the end product looking something like this:
In this way, students can immediately see that the Taylor series is accurate to four significant digits by going up to the $x^4$ term and that about ten or eleven terms are needed to get a figure that is as accurate as the precision of the computer will allow. In other words, for all practical purposes, an infinite number of terms are not necessary.
In short, this is how a calculator computes $e^x$: adding up the first few terms of a Taylor series. Back in high school, when students hit the $e^x$ button on their calculators, they’ve trusted the result but the mechanics of how the calculator gets the result was shrouded in mystery. No longer.
Then I shift gears by trying a larger value of $x$:
I ask my students the obvious question: What went wrong? They’re usually able to volunteer a few ideas:
• The convergence is slower for larger values of $x$.
• The series will converge, but more terms are needed (and I’ll later use the fill down feature to get enough terms so that it does converge as accurate as double precision will allow).
• The individual terms get bigger until $k=11$ and then start getting smaller. I’ll ask my students why this happens, and I’ll eventually get an explanation like
$\displaystyle \frac{(11.5)^6}{6!} < \frac{(11.5)^6}{6!} \times \frac{11.5}{7} = \frac{(11.5)^7}{7!}$
but
$\displaystyle \frac{(11.5)^{11}}{11!} < \frac{(11.5)^{11}}{11!} \times \frac{11.5}{12} = \frac{(11.5)^{12}}{12!}$
At this point, I’ll mention that calculators use some tricks to speed up convergence. For example, the calculator can simply store a few values of $e^x$ in memory, like $e^{16}$, $e^{8}$, $e^{4}$, $e^{2}$, and $e^{1} = e$. I then ask my class how these could be used to find $e^{11.5}$. After some thought, they will volunteer that
$e^{11.5} = e^8 \cdot e^2 \cdot e \cdot e^{0.5}$.
The first three values don’t need to be computed — they’ve already been stored in memory — while the last value can be computed via Taylor series. Also, since $0.5 < 1$, the series for $e^{0.5}$ will converge pretty quickly. (Some students may volunteer that the above product is logically equivalent to turning $11$ into binary.)
At this point — after doing these explicit numerical examples — I’ll show graphs of $e^x$ and graphs of the Taylor polynomials of $e^x$, observing that the polynomials get closer and closer to the graph of $e^x$ as more terms are added. (For example, see the graphs on the Wikipedia page for Taylor series, though I prefer to use Mathematica for in-class purposes.) In my opinion, the convergence of the graphs only becomes meaningful to students only after doing some numerical examples, as done above.
At this point, I hope my students are familiar with the definition of Taylor (Maclaurin) series, can apply the definition to $e^x$, and have some intuition meaning that the nasty Taylor series expression practically means add a bunch of terms together until you’re satisfied with the convergence.
In the next post, we’ll consider another Taylor series which ought to be (but usually isn’t) really familiar to students: an infinite geometric series.
P.S. Here’s the Excel spreadsheet that I used to make the above figures: Taylor.
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http://math.stackexchange.com/questions/32938/does-anyone-know-of-any-good-ways-to-get-good-at-algebra-without-as-muchgrind?answertab=active
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Does anyone know of any good ways to get good at algebra without as much“grind” as doing hundreds of questions a night
I'm coming to a point in college where I can't avoid my math classes any longer. I need to get better at algebra so I don't flunk out of the class when I take it, however I've never been able to get good at doing it without taking forever on one problem. The main problem I always seem to have is just memorizing the rules for various things such as inequalities. Does anyone know of any good methods to learn and get better at remembering the rules of these equations without having to do hundreds of questions a night. Please note that I know homework will involve doing hundreds of problems a night, and I can deal with that, however my main issue is that I want to at least get to a point over the summer so that I can get good enough to not take ten minutes on one question while not taking all day for multiple days a week doing math questions.
Also, if anyone can provide me with ideas that involve computer programming in the process, that would make it more fun for me, as I do enjoy computer programming, and it would make learning how to do the equations more fun.
Thanks, Flyboy
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You have to make the effort to understand how the steps you carry out in the algebra really make sense. Your previous "method" of learning (memorizing rules instead of understanding rules) is analogous to someone who memorizes passages from text in a foreign language and can parrot it back without realizing that those foreign words actually mean something. I'm not saying you have to understand something about mathematical rigor, but if you memorize rules without realizing why the rules make sense, you're not going to learn algebra well at all. – KCd Apr 14 '11 at 7:06
Well, practice is indeed key; "there is no royal road" and all that. I would say you might try having formula crutches along for the first few times you practice; it might happen that constant use will have you remembering the formulae you need. – Ｊ. Ｍ. Apr 14 '11 at 7:39
If it's doing things at night you have a problem with, here's a little advice: do it all day long at moments you have nothing to do. You get up in the morning, a couple during breakfast, you have to take a poo, do a couple of exercises while you're at it. You're taking public transportation or somebody is driving you, exercises, you have lunch, exercises, you have a break, exercises, etc... The more you're busy with it, the better you'll get at it. It will become like breathing. – Raskolnikov Apr 14 '11 at 9:20
if you want to write code, you can do something like write a program that generates random problems (say random quadratic expressions) and code the answer (completeing the square, quadratic formula, factoring into product of linear factors) which you can then solve and compare. this will be limited by what you code but will provide you with endless practice problems of the type you make and provide abstract insight in the process, as you code algorithms to solve the problems in the generality required. – yoyo Apr 14 '11 at 11:13
What a lot of people don't realize is, when you're doing the problems related to a certain chapter or section, look at a problem, and if the way to do it is not immediate, go back to the chapter, skim it, look for similar problems and examples. People just read the chapter then try to do the problems. It has to be done simultaneously to be able to understand. Don't memorize, use references. You will end up knowing the formulas anyway. – Jon Beardsley Apr 14 '11 at 16:04
A certain amount of repetition is necessary for proficiency. It seems to me that it is better to have a good understanding of how to solve a few problems of a given type rather than to mindlessly solve billions and billions of problems. By this I mean: How does each step in the solution help you get closer to a solution for the problem? Is there a reason the steps are done in this order or could they be done in some other order?
It does not matter so much how long the first problem of a given type take. This supposes we are talking about minutes, not years. What matters is that once you start on a new type of problem you have the means to get proficient in a reasonable length of time.
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Thanks, this seems like the best bet. I've always had a problem with the fact that it seemed to me like the repetition was just excessive and not really productive in my case, but this seems to make sense. It's better to repeat a few problems (rather than do the entire book) in order to understand the concept, rather than to grind thousands of problems without actually learning that much. – th3flyboy May 16 '11 at 7:40
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Sorry but I must object to your suggestion: what good will it make to watch these (excellent) videos except delaying still more the moment when th3flyboy will start actually doing some maths, in the sense of solving exercises, realizing some parts of the lesson are useful to find the solutions, learning these parts, going back to the exercises, and so on? You know, in the end maths is not a spectator's sport. – Did May 15 '11 at 8:20
@Anyone:$~$ Are there any remarks in this direction when it comes to higher algebra such as Abstract Algebra or Commutative Algebra. Thanks. – night owl Jul 10 '11 at 22:59
@night owl: The harvard video lectures here are good: extension.harvard.edu/open-learning-initiative/abstract-algebra – Nick Alger Nov 30 '11 at 22:07
Nick: Thanks for that! I will definitely look at them. :) – night owl Dec 1 '11 at 4:15
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https://brilliant.org/problems/is-it-really-correct/
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# Is it really correct?
Algebra Level 2
A polynomial $$g(x) = x^3 + ax^2 + bx + c$$ has $$3$$ distinct roots and each root of $$g(x) = 0$$ is also a root of $$f(x) = x^4 + x^3 + bx^2 + 100x + c$$.
Then find the value of $$f(1)$$.
×
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http://www.physicsforums.com/showthread.php?t=385204
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# Negative acceleration and instantaneous velocity on an object.
by CaptFormal
Tags: acceleration, instantaneous, negative, object, velocity
P: 33 1. The problem statement, all variables and given/known data The position of an object along a straight tunnel as a function of time is plotted below: 1. Are there any time intervals in which the object has a negative acceleration? If so, list them and explain how you know. 2. Calculate the instantaneous velocity at t=20s and t-45s. 2. Relevant equations N/A 3. The attempt at a solution So, for the first question I stated that at 30s to 37s the object's velocity is decreasing, thus the acceleration is negative. However, I was told that this is only part of the interval. What am I missing? For the second question I did the following calculations: at 20s = (6 m)/(20s) = 0.3 m/s at 45s = (16m)/(45s) = 0.36 m/s I did get the instantaneous velocity at 20s correct but not the instantaneous velocity at 45 s. Where am I going wrong? Thanks for your assistance.
P: 1,877 I would say that the velocity is decreasing from about 27 seconds (at the inflection point) to about 46s (at the other inflection point). Draw tangent lines to the graph, and note the parts where those slopes are getting smaller and smaller (the slope of the slopes). I think you must be close for the one at 45 seconds. It should be around what you got, I'd say more around .43m/s though it's an estimate when you are using a graph rather than the function.
HW Helper
P: 2,324
Quote by CaptFormal 1. The problem statement, all variables and given/known data So, for the first question I stated that at 30s to 37s the object's velocity is decreasing, thus the acceleration is negative. However, I was told that this is only part of the interval. What am I missing?
The velocity is decreasing up until 45 s. Remember that velocity can be negative, so if velocity goes from -1 m/s to -2 m/s, it's decreasing.
For the second question I did the following calculations: at 20s = (6 m)/(20s) = 0.3 m/s at 45s = (16m)/(45s) = 0.36 m/s I did get the instantaneous velocity at 20s correct but not the instantaneous velocity at 45 s. Where am I going wrong?
The velocity should be negative, not positive. Also, you're calculating average velocity. The question is looking for instantaneous velocity, which is the slope of the tangent of the graph.
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https://nuclearengineering.asmedigitalcollection.asme.org/turbomachinery/article-abstract/123/4/766/464269/An-Experimental-Study-of-Impingement-on-Roughened?redirectedFrom=fulltext
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Airfoil leading-edge surfaces in state-of-the-art gas turbines, being exposed to very high gas temperatures, are often life-limiting locations and require complex cooling schemes for robust designs. A combination of convection and film cooling is used in conventional designs to maintain leading-edge metal temperatures at levels consistent with airfoil life requirements. Compatible with the external contour of the airfoil at the leading edge, the leading-edge cooling cavities often have complex cross-sectional shapes. Furthermore, to enhance the heat transfer coefficient in these cavities, they are often roughened on three walls with ribs of different geometries. The cooling flow for these geometries usually enters the cavity from the airfoil root and flows radially to the airfoil tip or, in the more advanced designs, enters the leading edge cavity from the adjacent cavity through a series of crossover holes in the wall separating the two cavities. In the latter case, the crossover jets impinge on a smooth leading-edge wall and exit through the showerhead film holes, gill film holes on the pressure and suction sides, and, in some cases, form a crossflow in the leading-edge cavity, which is ejected through the airfoil tip hole. The main objective of this investigation was to study the effects that film holes on the target surface have on the impingement heat transfer coefficient. Available data in the open literature are mostly for impingement on a flat smooth surface with no representation of the film holes. This investigation involved two new features used in airfoil leading-edge cooling, those being a curved and roughened target surface in conjunction with leading-edge row of film holes. Results of the crossover jets impinging on these leading-edge surface geometries with no film holes were reported by these authors previously. This paper reports experimental results of crossover jets impinging on those same geometries in the presence of film holes. The investigated surface geometries were smooth, roughened with large and small conical bumps as well as tapered radial ribs. A range of flow arrangements and jet Reynolds numbers were investigated, and the results were compared to those of the previous study where no film holes were present. It was concluded that the presence of leading-edge film holes along the leading edge enhances the internal impingement heat transfer coefficients significantly. The smaller conical bump geometry in this investigation produced impingement heat transfer coefficients up to 35 percent higher than those of the smooth target surface. When the contribution of the increased area in the overall heat transfer is taken into consideration, this same geometry for all flow cases as well as jet impingement distances $Z/djet$ provides an increase in the heat removal from the target surface by as much as 95 percent when compared with the smooth target surface.
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https://www.physicsforums.com/threads/a-physics-question.268489/
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# Homework Help: A Physics Question
1. Oct 31, 2008
### unstoppable
1. The problem statement, all variables and given/known data
2) A researcher claims that she can convert a circularly polarized plane wave in air into a linearly polarized one by simply reflecting it from a suitably chosen lossless nonmagnetic dieletric. Assume the dielectric she will use has refractive index n. Is this feat possible for normail incidence, as she claims? Calculate the reflected wave to justify your answer. If she is right, is there a mininum value of n for this to work? If she is wrong; briefly explain why, based on your calculation.
2. Relevant equations
3. The attempt at a solution
2. Nov 1, 2008
### malawi_glenn
attempt to solution?
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https://openclimb.io/practice/p3/q11/
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Let $I_n=\int_{-\pi/2}^{\pi/2} \cos^n\!x \,dx$ for any non-negative integer $n.$ $\;(i)$ Find a recursive expression for $I_n.$ $(ii)$ Find the simplest non-recursive expression for $I_{2n}$ that contains $\binom{2n}{n},$ where $\binom{n}{k}=\frac{n!}{k!(n-k)!}.$
1. Evaluate $\int_{-\pi}^{\pi}x^2\,dx.$
2. Find $\int\ln x \,dx.$
3. A geometric sequence starts with $\frac{1}{5}, \frac{2}{15}, \frac{4}{45} \ldots.$ Find a recursive formula for the sequence and solve it to get the closed form.
Try to split $\cos^n x$ into some terms, one of which you can integrate easily.
Have you tried integrating by parts?
Integrate and simplify $I_n$ as much as you can.
Try to rewrite $I_n$ as a recurrence relation.
… you may find a trigonometric identity helpful.
Which initial term can you find to help solve the recurrence for $I_{2n}?$
Try writing out and unwinding $I_{2n}.$
… remembering that your expression should contain $\frac{(2n)!}{(n!)^2}.$
Writing $\cos^n x = \cos x \cdot \cos^{n-1} x$ allows us to use integration by parts to get $I_n = [\sin x \cdot \cos^{n-1} x]_{-\pi/2}^{\pi/2} + \int_{-\pi/2}^{\pi/2} (n-1) \sin^2\!x \cos^{n-2}\!x \,dx.$ Simplifying using a trigonometric identity yields $I_n = (n-1) \int_{-\pi/2}^{\pi/2} (\cos^{n-2} x-\cos^{n} x) \,dx,$ so $I_n = (n-1)(I_{n-2}-I_{n}).$ Rearranging gives $I_{n} = \frac{n-1}{n} I_{n-2}.$
To solve this recurrence relation for $I_{2n},$ we first find $I_0=\int_{-\pi/2}^{\pi/2}dx=\pi.$ Unwinding the recursion we get $I_{2n} = \frac{2n-1}{2n}\cdot\frac{2n-3}{2n-2}\cdot\frac{2n-5}{2n-4}\cdots\frac{1}{2}\cdot\pi$ which has the product of all odd terms in the numerator and the product of all even terms in the denominator. To get $(2n)!$ in the numerator, we need to fill in the even terms, so we multiply both the numerator and denominator with the denominator, which yields $I_{2n} = \pi \cdot \frac{(2n)!}{2^2 4^2 6^2 \cdots (2n)^2}.$ Factorising $2^2$ from each term in the denominator gives $I_{2n}=\pi \cdot \frac{(2n)!}{2^{2n} (n!)^2}=\binom{2n}{n}\frac{\pi}{4^n}.$
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https://crypto.stackexchange.com/questions/39956/aes-cbc-authentication-and-password-validation
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# AES-CBC authentication and password validation
Let's say, Alice uses AES256-CBC to encrypt some data. The key for encryption is derived using PBKDF2, where password is some passphrase Alice and Bob agreed on (using DH) and salt is random generated (using /dev/urandom for now)*. The IV for the CBC is generated the same way as the salt.
Now Bob receives the cipher and would like to authenticate it, so he can tell for sure, that the message really came from Alice (or anyone else who knows the passphrase). Should Alice encrypt the data first, use the derived key as password, the cipher as message and append/prepend the result to the cipher? Or she ought to use the derived key as password, the plain text as message, prepend the HMAC to the plain text and encrypt?
(There is a lot of related questions and answers, I am just confused what to use when and what are the pros and cons)
Another problem I'm struggling with is, how will Bob get the IV and the salt which were randomly generated at encryption time?
Last problem I'm trying to solve is, when Bob will decrypt the cipher, how can he know the password he entered is correct, without decrypting all of the data?
*Is /dev/urandom secure enough to generate random salt and IV?
Just to clarify, I don't intend to use this implementation in real world situation, this is purely for educational purpose
Now Bob receives the cipher and would like to authenticate it, so he can tell for sure, that the message really came from Alice (or anyone else who knows the passphrase).
Bob should be using an AEAD mode of AES, full-stop. GCM is the go-to candidate for this, rolling your own CBC+HMAC mode is also possible, but should be used as a last resort and only if you emphatically know what you're doing.
Another problem I'm struggling with is, how will Bob get the IV and the salt which were randomly generated at encryption time?
IVs and salts are not secret. Send them with the ciphertext.
Besides your direct question, it looks like you're trying to wire together your own transport encryption protocol. I strongly recommend you just use TLS instead. Barring that, I'd recommend using libsodium's out-of-the-box AEAD modes instead of rolling your own.
• As I said, I do that just for educational purpose and don't intend to use this implementation in real world situation. My question about the authentication might seem a little bit unclear. I do want to implement my own CBC+HMAC, I just don't know which way. This part of question is strongly related to my other question, how can I tell if the password is incorrect when decrypting, without decrypting all of the data? And is that even right approach? Thanks for clearing out the Salt and IV, I thought it must be kept in secret.. – ProXicT Sep 14 '16 at 8:24
• Sorry, I missed the part where this was for educational purposes. My link should have more information on how to roll your own CBC+HMAC. The entire point of the HMAC (or authenticated modes in general) is that you can validate the authenticity of all the inputs before decrypting, which answers the other part of your question. – Stephen Touset Sep 14 '16 at 19:04
• Thank you very much! The last sentence was really important for me, can you add that to your answer so it is more visible? Have a great day! – ProXicT Sep 15 '16 at 0:15
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https://aquila.usm.edu/theses_dissertations/2385/
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## Dissertation Archive
#### Title
An Analysis of the Humoral Immune System of Three Species of Cetaceans: The Atlantic Bottlenose Dolphin (Tursiops truncatus), Beluga Whale (Delphinapterus leucas), and Pacific White-Sided Dolphin (Lagenorhynchus obliquidens)
1998
Dissertation
#### Degree Name
Doctor of Philosophy (PhD)
#### Department
Biological Sciences
Bobby L. Middlebrooks
Very little information is available concerning the immune systems, especially humoral immune system, of cetaceans. In a preliminary study of how a cetacean's humoral immune system responds to an immunogen, four Tursiops truncatus (Atlantic bottlenose dolphin) were employed in two immunization protocols using bovine serum albumin (BSA) as the immunogen. The primary and secondary immune responses in these animals were monitored by a double-indirect enzyme linked immunosorbent assay (ELISA) to measure the antibodies produced against the BSA. The results from the ELISA clearly showed that the immunization protocol with multiple injections was more effective at producing an immune response in these animals than the one using a single injection. However, no antibodies were detectable after six months with either of the immunization protocols. Qualitative characterization of the primary and secondary immune response was not possible because of the limitations of the anti-T. Truncatus antibodies used in the ELISA; for such characterization it was necessary to produce antibodies specific for individual immunoglobulin classes of each cetacean species to be studied. In order to provide these antibodies, the focus of the study shifted to the development of immunochemical techniques to isolate and purify the three major immunoglobulin isotypes involved in humoral immunity (IgG, IgA, and IgM) from the serum of T. truncatus, Delphinapterus leucas (beluga whale), and Lagenorhynchus obliquidens (Pacific white-sided dolphin). It was determined that IgG could be purified using a Protein G Sepharose$\sp{\circler}$ 4 Fast Flow affinity chromatography column, that IgA could be purified using an Immobilized Jacalin affinity chromatography column, and that IgM could be purified using a Sephacryl$\sp{\circler}$ S400-HR gel filtration chromatography column. IgM has only been purified from T. truncatus thus far due to limited sources of sera for the other two cetacean species. These purified immunoglobulin isotypes were partially characterized, and antisera were produced against several of the isotypes. To date antisera have been produced against (1) T. truncatus whole serum, precipitated serum, whole IgG, and gamma ($\gamma$) heavy chains; (2) D. leucas precipitated serum and $\gamma$ heavy chains; and (3) L. obliquidens precipitated serum and $\gamma$ heavy chains.
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https://rd.springer.com/article/10.1007/JHEP04%282015%29036
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# Higgs boson decay into b-quarks at NNLO accuracy
• Vittorio Del Duca
• Claude Duhr
• Gábor Somogyi
• Francesco Tramontano
• Zoltán Trócsányi
Open Access
Regular Article - Theoretical Physics
## Abstract
We compute the fully differential decay rate of the Standard Model Higgs boson into b-quarks at next-to-next-to-leading order (NNLO) accuracy in αs. We employ a general subtraction scheme developed for the calculation of higher order perturbative corrections to QCD jet cross sections, which is based on the universal infrared factorization properties of QCD squared matrix elements. We show that the subtractions render the various contributions to the NNLO correction finite. In particular, we demonstrate analytically that the sum of integrated subtraction terms correctly reproduces the infrared poles of the two-loop double virtual contribution to this process. We present illustrative differential distributions obtained by implementing the method in a parton level Monte Carlo program. The basic ingredients of our subtraction scheme, used here for the first time to compute a physical observable, are universal and can be employed for the computation of more involved processes.
### Keywords
QCD Phenomenology Jets
## Notes
### References
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## Authors and Affiliations
• Vittorio Del Duca
• 1
• Claude Duhr
• 2
• 3
• Gábor Somogyi
• 4
• Francesco Tramontano
• 5
• Zoltán Trócsányi
• 4
1. 1.Istituto Nazionale di Fisica NucleareLaboratori Nazionali di FrascatiFrascatiItaly
2. 2.PH Department, TH Unit, CERNGeneva 23Switzerland
3. 3.Center for Cosmology, Particle Physics and Phenomenology (CP3)Université Catholique de Louvain, Chemin du Cyclotron 2Louvain-La-Neuve,Belgium
4. 4.University of Debrecen and MTA-DE Particle Physics Research GroupDebrecenHungary
5. 5.Dipartimento di FisicaUniversità degli studi di Napoli and INFN — Sezione di NapoliNapoliItaly
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https://dirkmittler.homeip.net/blog/archives/tag/fluids
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## What Is A Plasma?
The fact that blood plasma exists in Medicine, should not be confused with the fact that Plasmas exist, that are defined in Physics, and which all matter can be converted to. In short, a Plasma is what becomes of a gas, when its temperature is too hot, for it to be a gas.
The long form of the answer is a bit more complex. In Elementary School, Students are taught that there exist three familiar phases of a given substance: Solid, Liquid and Gas. But according to slightly more advanced knowledge in Physics, there is no real guarantee, that there will always be these three phases. A gas first results when the thermal agitation between molecules becomes stronger – i.e. their temperature hotter – than the force that holds individual molecules together. At that point, the molecules separate and a gas results, the physical behavior of which is approximately what one would obtain, if a swarm of particles was to exist through collisions but through few other interactions.
Similarly, Liquids will form, when the molecules are forced from occupying fixed positions, but when they still don’t expand.
Well, as the degree of thermal agitation (of a Gas) is increased further, first, molecules become separated into atoms, and then, the electrons get separated from their nuclei, as a result of ordinary collisions with other atoms. This results in the negative particles – electrons – following different trajectories than the positive particles – the nuclei. And the result of that is that the collective behavior of the fluid changes, from that of a gas.
When a charged particle crosses the lines of force, of a magnetic field, a force is generated which is perpendicular to both the velocity vector and the magnetic field vector. As a result, the particles can travel without restriction along the lines of magnetic force, but their motion at right angles to it is deflected, and becomes helical. Not only that, but the direction in which the paths of the particles becomes curved, is opposite for the negative and positive particles.
For this reason, Plasmas can be confined by magnetic fields, except along the lines of the magnetic field. Increasing the strength of an applied field will also cause a Plasma to become compressed, as these helices become narrower.
A good natural example of this type of Plasma, is what becomes of the substance of the Sun. Its temperatures are easily hot enough to cause the transition from Gas to Plasma, especially since the temperature inside the Sun is much higher, than the temperatures which are observed at its surface. At 5000K, gasses are still possible. But at hundreds of thousands Kelvin, or at a Million degrees Kelvin, the bulk of the Sun’s substance becomes a Plasma.
Now, if the reader is a skeptic, who has trouble believing that ‘other phases’ can exist, than Solid, Liquid and Gas, there is an example that takes place at lower temperatures, and that involves Oxygen, namely, O2. We’re aware of gaseous O2 as well as liquid O2 that gets used in rocketry. But as the O2 is cooled further, to 54.36K at 1 atmosphere, it solidifies. Thus, it has already demonstrated the 3 phases which we’re taught about in Elementary School. But, if we cool already-solid O2 below an even lower temperature, 43.8K at 1 atmosphere, its phase changes again, into yet another phase, which is also a solid one. It’s currently understood that solid O2 has 6 phases. (:1)
At the same time, many fluids are known to exhibit Supercritical Behavior, which is most commonly, a behavior of a fluid which is normally differentiated between Liquid and Gaseous, losing this differentiation, due to its critical pressure being exceeded, but at temperatures at which fluids are commonly boiled. This has nothing to do with Plasmas, but without any distinction between Liquid and Gaseous, a substance which is ordinarily though to have three phases – such as water – ends up demonstrating only two: Fluid and Non-Fluid.
So there is no ultimate reason for which matter needs to be in one out of three phases.
(Updated 10/14/2018, 10h25 … )
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https://gamedev.stackexchange.com/questions/18418/state-of-the-art-in-image-compression
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# State of the art in image compression?
I'm looking for good algorithms for compressing textures offline (ie decompressing them at install or load time, I know about using DXT/3DC to save runtime video memory, but these create awful visual artifacts while often being larger in disk than a lossless format like JPEG-LS, even after using LZMA or something for entropy). Since the data will only need to be read by my program, I don't need a portable format like JPEG, which means I'm open to more experimental algorithms. To be clear, I'm concerned with reducing the download size of my game; I will be using them uncompressed on the video card.
I'm looking for formats that support different features... For example, 10 bits-per-channel color (HDR) for higher color fidelity under dynamic lighting conditions, normal map formats(16 bits in X and Y), alpha channels, etc, etc...
NOTE: My particular use case is for 2.5D backgrounds. In their uncompressed format, they are 10 bytes per pixel stored in 3 textures:
4 bytes - color - D3DFMT_A2R10G10B10
4 bytes - normal - D3DFMT_G16R16F
2 bytes - depth - D3DFMT_R16F
I store these in 1024x1024 tiles, and since every area has a different background, these can get really large really fast. However, I think knowing more about image codecs in general will help with finding an efficient method to compress these.
• Is this related to gamedev? – Daniel Pendergast Oct 11 '11 at 23:11
• @Dan - yes; this is for a game... are you saying this is the wrong place for the question? Images in games have different requirements than other images (ie JPEG would be unsuitable) and a good normal map compressor would take into account the particular format of the data. – Robert Fraser Oct 11 '11 at 23:37
• You are dealing with sprites. I'm not really sure what it is you're trying to do with sprites that would need, "10 bits-per-channel color (HDR) for higher color fidelity under dynamic lighting conditions, normal map formats(16 bits in X and Y), alpha channels". It'd be a lot easier to just make and animate an actual model; it'd probably act as a more effective form of image compression than anything you might find or create. – Nicol Bolas Oct 12 '11 at 1:21
• @Nicol Bolas - I updated the question with my specific use case. – Robert Fraser Oct 12 '11 at 2:30
• If I understand correctly, your whole question could be rephrased to: "What's the best losslessly compressed image format". – Jari Komppa Oct 12 '11 at 9:26
I'm looking for good algorithms for compressing textures offline
What is your purpose in compressing these images? There are generally two reasons to compress a texture:
1. You want to make the texture smaller so that it takes up less memory on the GPU.
2. You want to make the texture smaller so that it takes less time to load/requires less harddrive space, resulting in a smaller download.
The most important thing you can understand is this: you cannot satisfy both of these at once. You must pick one: smaller GPU memory, or smaller disk space/load time.
So let's look at both cases.
## Case 1
Your possibilities here are the various "Block Compressed" types, using the D3D 10 language for them.
I'll assume you know what BC1-3 are, since they are formerly known as DXT1, DXT3, and DXT5, respectively. BC4 and BC5 are for 1 and 2-channel formats respectively. These two can be either unsigned or signed normalized.
BC5, 2-channel compressed, can be used for storing tangent-space normal maps, with the third coordinate (Z) reconstructed in your shader. It does a reasonably good job.
BC6H and BC7 are quite new. BC6H is a compressed, floating-point format. BC7 is a more accurate way to compressed RGBA color data. You can only get BC6H and BC7 support from DX11-class hardware.
The OpenGL internal formats for these are as follows:
1. BC1: GL_COMPRESSED_RGB_S3TC_DXT1_EXT and GL_COMPRESSED_RGBA_S3TC_DXT1_EXT
2. BC2: GL_COMPRESSED_RGBA_S3TC_DXT3_EXT
3. BC3: GL_COMPRESSED_RGBA_S3TC_DXT5_EXT
4. BC4: GL_COMPRESSED_RED_RGTC1 and GL_COMPRESSED_SIGNED_RED_RGTC1
5. BC5: GL_COMPRESSED_RG_RGTC2 and GL_COMPRESSED_SIGNED_RG_RGTC2
6. BC6H: GL_COMPRESSED_RGB_BPTC_SIGNED_FLOAT_ARB and GL_COMPRESSED_RGB_BPTC_UNSIGNED_FLOAT_ARB
7. BC7: GL_COMPRESSED_RGBA_BPTC_UNORM_ARB
The BC1-3 and BC7 formats can also be in the sRGB colorspace. OpenGL provides similar sRGB variants and GL_COMPRESSED_SRGB_ALPHA_BPTC_UNORM_ARB.
Obviously, none of these are lossless.
As I understand it, BC6H and BC7 are not widely supported in tools, though I seem to recall that NVIDIA's texture tools do support them.
## Case 2
If you're talking about normal 8-bit-per-channel images, you already know your options. But for more exotic texture types, like floating-point, 10-bit-per-channel, and normal maps, you're out of luck.
The simple fact is that most general image compression software is intended for regular old images. Most people who deal with floating-point textures don't really care enough about loading speed or disk space to bother with compressing them. They're big, but they've accepted that. And it's really hard to losslessly compress floating-point values.
So really, just stick with known paths for regular images, and use zlib or 7z or some other general compression method for the others. That's generally about the best you can do.
Do note that any lossless image compression technique can be made to work on any pixel data, so long as that data can fit. So you can always put a normal map in a PNG, even if it is a 2-component normal map (the third component is 0). It may not compress well, but it will probably beat out pure-zip.
4 bytes - color - D3DFMT_A2R10G10B10
If you're storing a color, a normal, and a depth, then I can only assume that you are doing some form of deferred rendering-type thing here. That is, the color is the diffuse reflectance, not the light radiating from the background.
Given that, 10-bit colors are pretty much overkill. You don't need that level of color accuracy for a diffuse reflectance value; you can get the same level of accuracy from an sRGB color value. HDR is all about the lighting; you can do HDR just fine with lower color-depth.
Once you're dealing with regular sRGB colors, you can start using standard image compression techniques.
4 bytes - normal - D3DFMT_G16R16F
There's no reason you can't take that down to G8B8 using signed-normalised values. Games do this all the time, and normals are not sensitive enough to need 16 bits worth of accuracy. And they're normals, so even using floating-point is way overkill.
Whether you can live with the artifacts produced by feeding it through BC5 compression is up to you. But you can at least go down from 32-bpp to 16-bpp with no detectable loss of fidelity.
Ultimately, everything is a tradeoff. You need to decide how much image quality you are willing to give up to get your game's data size under control. And since it's a tradeoff, you need to run actual tests to see where you are willing to draw that line.
• Thanks for the detailed answer - yes, I'm mostly interested in case 2 and it saddens me that there's not more research in this area :-(. – Robert Fraser Oct 12 '11 at 2:29
• Wow; thanks for the upate! I will see how it looks with 8-bit normals... As for the colors, the idea is to bring out detail under different lighting conditions. If a very bright light shines on a dark area, you don't just want gray. The difference was noticeable when I implemented it, but perhaps not enough to justify the increased texture size. – Robert Fraser Oct 12 '11 at 19:59
• @RobertFraser: One more thing: the depth should also not be floating-point. Since it's on the range [0, 1], you're wasting bits by using a 16-bit float over a 16-bit unsigned normalized integer value. – Nicol Bolas Oct 12 '11 at 20:03
There's WebP which Google have been suggesting as an improvement over JPEG.
For 2D images where compression artefacts are unacceptable, I'd go with some form of lossless compression like PNG.
Also note that DXT compressed images will usually shrink significantly when zlib or other lossless compression is applied to them.
For more exotic formats like HDR and 16-bit normals you could try OpenEXR. I've not used it myself though.
• Thanks. Yes, I'm aware of PNG, but if I wanted true lossless for a 24bpp color image, I'd use something like JPEG-2000 or JPEG-LS. I'm looking for more exotic things here -- most codecs for web are 10+ years old and are unsuitable for many data formats used in textures. – Robert Fraser Oct 12 '11 at 0:45
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http://physics.stackexchange.com/questions/35658/how-can-we-define-bf-theory-on-a-general-4-manifold/38356
|
How can we define BF theory on a general 4-manifold?
(I have rewritten the question some, with new understanding)
4d BF theory is classically presented as the TFT arising from the Lagrangian
$B\wedge F$,
where $B$ is an abelian 2-connection (locally a real 2-form) and $F$ is the curvature of a connection $A$. People often throw about this theory on general 4-manifolds, but it seems the naive definition from the Lagrangian above is anomalous for most situations. If one restricts to the simpler case of $A$ and $B$ being globally defined forms (not considering them as connections) the phase space is $H^1(\Sigma_4,\mathbb{R}) + H^2(\Sigma_4,\mathbb{R})$ with $A$ as the first coordinate and $B$ as the second. $A$ and $B$ are conjugate from the point of view of the above Lagrangian, but this has no chance of being symplectic if the first and second Betti numbers are not equal. If $A$ and $B$ are connections, however, the only solution to the equations of motion (which not only set $dA=dB=0$ but also their holonomies) is the trivial one, and it is not a problem
However, what I'd really like to consider is $nB\wedge F$. With $A$ and $B$ full-fledged connections. Let us first integrate out $B$. $B$ is a (2-)connection, so $dB$ can be any integral 3-form. We can thus write it as $d\beta + \sum_k m^k \lambda_k$, where $\beta$ is an ordinary real 2-form, and $\lambda_k$ form a basis of integral harmonic 3-forms. Then the action becomes $dA \wedge \beta + \sum_k n m^k A\wedge\lambda_k$. The first term sets $dA=0$ after integrating over $\beta$ and the second term sets the holonomies of $A$ to be nth roots of unity. If our 4-manifold doesn't have torsion, there are precisely $n^{b_1}$ such $A$s.
If we do the same thing, integrating out $A$ instead, we get Dirac deltas setting $dB=0$ and the holonomies of $B$ to be nth roots of unity. Again, if we have no torsion, there are $n^{b_2}$ such $B$s.
It looks like the determinants for these Dirac deltas are all 1, so from the naive calculation above, $Z_n = n^{b_1}$ but also $Z_n = n^{b_2}$. This is a problem on a general 4-manifold, but like the simpler situation above, there is no issue in quantizing on something of the form $\Sigma_3 \times \mathbb{R}$. What I think must be happening is that when I am integrating out $A$ or $B$, I am really only integrating out the non-flat parts. There should still be some more factors that correct the discrepancy above. I think I should be more careful in defining the above integral. Perhaps it is possible to define it sensibly on 4-manifolds which bound a 5-manifold a la Chern-Simons theory.
How does one define this theory on general 4-manifolds?
Thanks.
-
BF theory secretly has another name - $Z_n$ gauge theory in the deconfined limit. The parameter $n$ is what appears in front of the $BF$ action. $Z_n$ gauge theory can be defined on any manifold you want - just introduce a lattice approximation of the manifold and compute the lattice gauge theory partition function. By taking the extreme deconfined limit of the lattice gauge theory one can verify that this construction is independent of the way you approximated the manifold.
Basic examples
In the deconfined limit the $Z_n$ flux through every plaquette of the lattice gauge theory is zero. (This is like the constraint imposed by integrating out $B$.) We have a residual freedom to specify the holonomy around all non-contractible loops. Hence $Z_n(M) = Z_n(S^4) n^{b_1(M)}$ where $Z_n(S^4)$ is a normalization constant. Requiring that $Z_n(S^3 \times S^1) =1$ gives $Z_n(S^4) = 1/n$. This condition, $Z_n(S^3 \times S^1) = 1$, is the statement that the theory has one unique ground state on $S^3$. In general, $Z_n(\Sigma^3 \times S^1)$ is $\text{tr}(e^{-\beta H})$, but since $H=0$ we are simply counting ground states.
As a quick check, $Z_n(S^2 \times S^1 \times S^1) = n$, which is the number of ground states on $S^2 \times S^1$, and $Z_n(T^3\times S^1) = n^3$, which is the number of ground states on $T^3 = (S^1)^3$.
Further relations
Another check on the value of $Z_n(S^4)$: this is the renormalized topological entanglement entropy of a ball in the $3+1$d topological phase described by deconfined $Z_n$ gauge theory. More precisely, the topological entanglement entropy of a ball is $-\ln{Z_n(S^4)}$ which gives $-\log{n}$ in agreement with explicit wavefunction calculations.
We can also consider defects. The $BF$ action is $\frac{n}{2\pi} \int B \wedge d A$. Pointlike particles (spacetime worldlines) that minimally couple to $A$ carry $Z_n$ charge of $1$. Similarly, string excitations (spacetime worldsheets) that minimally couple to $B$ act like flux tubes carry $Z_n$ flux of $2\pi/n$. Now when a minimal particle encircles a minimal flux, we get a phase of $2 \pi/n$ (AB phase), but this also follows from the $BF$ action. Without getting into two many details, the term in the action like $B_{12} \partial_t A_3$ fixes the commutator of $A_3$ and $B_{12}$ to be $[A_3(x),B_{12}(y)] = \frac{2\pi i}{n} \delta^3(x-y)$ (flat space). The Wilson-line like operators given by $W_A = e^{i \int dx^3 A_3}$ and $W_B = e^{i \int dx^1 dx^2 B_{12}}$ thus satisfy $W_A W_B = W_B W_A e^{2 \pi i /n}$ which is an expression of the braiding flux above that arises since the particle worldline pierced the flux string worldsheet.
Conservative thoughts
If I understand you correctly, what you want to do is sort of argue directly from the continuum path integral and show how the asymmetry you mentioned arises. I haven't done this calculation, so I can't be of direct help on this point right now. I'll ponder it though.
That being said, it's not at all clear to me that treating the action as $\int A dB$ leads one to just counting 2-cycles. Of course, I agree that 2-cycles are how you get non-trivial configurations of $B$, but in a conservative spirit, it's not at all clear to me, after gauge fixing and adding ghosts and whatever else you need to do, that the path integral simply counts these.
The way that I know the path integral counts 1-cycles is that I have an alternative formulation, the lattice gauge theory, that is easy to define and unambiguously does the counting. However, I don't know how it works for the other formulation. I suppose a naive guess would be to look at lattice 2-gauge theory for $B$, but this doesn't seem to work.
Ground states
One thing I can address is the issue of ground states. In fact, I favor this approach because one doesn't have to worry about so many path integral subtleties. All you really needs is the commutator.
Take the example you raise, $S^2 \times S^1$. There are two non-trivial operators in this case, a $W_B$ for the $S^2$ and a $W_A$ for the $S^1$. Furthermore, these two operators don't commute, which is why there are only $n$ ground states. If we define $|0\rangle$ by $W_A |0 \rangle = |0\rangle$, then the $n$ states $\{|0\rangle, W_B |0\rangle, ..., W_B^{n-1} | 0 \rangle\}$ span the ground state space and are distinguished by their $W_A$ eigenvalue. Importantly, you can also label states by $W_B$ eigenvalue, but you still only get $n$ states. Poincare duality assures you that this counting of states will always work out no matter how you do it.
Furthermore, the operator $W_B$ has a beautiful interpretation in terms of tunneling flux into the non-contractible loop measured by $W_A$. It's easier to visualize the analogous process in 3d, but it still works here.
You can also see the difference between the theory in 4d and 4d. Since both $B$ and $A$ are 1-forms you have different possibilities. The analogue of $S^2 \times S^1$ might be $S^1 \times S^1$ and this space does have $n^2$ states. However, that is because both $A$ and $B$ can wrap both cycles.
The remarkable thing is that the $Z_n$ gauge theory formulation always gets it right. You simply count the number of one-cycles and that's it.
Getting at other spaces
The state counting approach gets you everything of the form $Z_n(\Sigma^3 \times S^1)$, but even spaces like $S^2 \times S^2$ can be accessed. You can either do the direct euclidean gauge theory computation, or you can regard $Z_n(S^2 \times S^2) = |Z(S^2 \times D^2)|^2$ i.e. the inner product of a state on $S^2 \times S^1 = \partial (S^2 \times D^2)$ generated by imaginary time evolution.
-
Thanks, Physics Monkey. This is a good answer so far, but it does not address the inconsistency that I'm talking about. If one takes the other polarization ($B$ as coordinates, integrating out $A$), the theory is [ $U(1)$-n->$U(1)$ ] 2-gauge theory (roughly speaking, instead of holonomies around 1-cycles, we have holonomies around 2-cycles, also in $\mathbb{Z}_n$). This interpretation gives the calculation $Z_n = n^{b_2}$. – Ryan Thorngren Sep 5 '12 at 19:52
Let me be more particular with my complaint. The number of ground states on $S^2 \times S^1$ in my mind should be $n^2$. Once you pick two elements of $\mathbb{Z}_n$ this uniquely defines for you a flat 2-connection $B$ (that is, a global 2-form with $dB=0$) and a flat 1-connection $A$ each with the prescribed holonomies around the sphere and circle factor, respectively. That is to say, $dB=0$ does not imply that $B$ has null periods. I guess this really comes down to what we choose our gauge transformations to be. – Ryan Thorngren Sep 5 '12 at 19:56
Here's what I mean by my last comment. The theory is symmetric under $B\rightarrow B+\beta$ and $A\rightarrow A+\alpha$ for a flat 2-connection $\beta$ and a flat 1-connection $\alpha$. There is a unique ground state up to these gauge transformations. – Ryan Thorngren Sep 5 '12 at 19:59
Ok, I think I understand more what you're getting at. I'll edit my answer above. – Physics Monkey Sep 7 '12 at 1:09
Thanks for the updated answer. I certainly see what you mean for $S^2 \times S^1$ and agree with you now (also, my third comment is wrong, those are not actually symmetries). The $A$ and $B$ coordinates are conjugate is another way to look at why $W_A$ and $W_B$ must not commute (indeed, the linking number prescription is like a topological Heisenberg algebra). I am continuing to think about more general 4-manifolds. I will get back to you hopefully soon with some resolution or maybe more questions. – Ryan Thorngren Sep 7 '12 at 3:38
I figured this out a little while ago, so as not to leave any of you hanging, here is a (almost complete) resolution.
First, there is a lattice formulation of the 2-gauge theory that agrees with the 1-gauge theory up to the topological factor $n^{\chi(\Sigma_4)}$. One has a $\mathbb{Z}_n$ variable for each 2-cell, gauge transformations on 1-cells, and importantly, 2-gauge transformations (gauge transformations between gauge transformations) on 0-cells. The number of configurations is $n^{b_2}$. Then we divide by the volume of the gauge group, which is the number of gauge transformations divided by the number of 2-gauge transformations. So the partition function of this lattice theory is $n^{b_2-b_1+b_0}$. This gives the same answer as the $A$-theory on any 4-manifold fibered over $S^1$, in particular the 4-torus @Physics Monkey and I were discussing.
To get this answer from the path integral, I gauge fix $B$ using the Lorentz gauge $d*B=0$, introducing a Lagrange multiplier term $\langle \pi_1, \delta B\rangle$ as well as some ghost terms not involving $B$ or $\pi_1$. $\pi_1$ has gauge symmetries, being a 1-form, which I also fix, introducing a term $\langle E_0, \delta \pi_1\rangle$ and some more ghost terms which do not involve $B$, $\pi_1$, or $E_0$. Now I scale $B\rightarrow B/n$, $\pi_1 \rightarrow n\pi_1$, and $E_0\rightarrow E_0/n$ to reduce the integrand to the case with $n=1$ (that integral can be shown to be 1).
I just need to find how the path integral measure scales under these transformations. $DB$ will scale by $n$ to the power of the dimension of the $B$s being integrated over. It's important to notice that the zero modes of the integrand are precisely the harmonic 2-forms, a space of dimension $b_2$. Then if $B_2$ is the (infinite) dimension of all 2-forms, $DB$ scales by $n^{b_2-B_2}$. Terms like $n^{B_k}$ can all be removed by some suitable regularization a la Witten's paper on abelian S-duality. What we are left with is the answer above, $n^{b_2-b_1+b_0}$.
Maybe there is some way to understand the topological factor that appears?
-
Excuse me, is the k-cycle used in your context is the same as this definition? i.e. The length of a cycle, is the number of elements of its orbit of non-fixed elements. A cycle of length k is also called a k-cycle. – mysteriousness Jan 10 at 20:43
I mean cycle in the homology sense. Let me know if you have more questions. I understand this topic quite a bit more now that it's been over a year. :) – Ryan Thorngren Jan 12 at 5:48
How do you understand the $B$ as a n-form field in terms of $\mathbb{Z}_N$ gauge group? In the sense of group cohomology, a 1-form field $A$ can be realize as a group element $a \in \mathbb{Z}_N$. The derivative of 1-form $A$ as $dA$ can be realize as $(a+b)-[a+b]$mod$\mathbb{Z}_N$. Is that $B$ as n-form field still realize as $b \in \mathbb{Z}_N$? or something more? – mysteriousness Jan 21 at 1:55
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https://www.albert.io/ie/combinatorics/infrequent-math-jokes
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Free Version
Moderate
# Infrequent Math Jokes
COMBIN-E4YLNQ
A math professor tells $4$ different jokes to her combinatorics class each semester.
What is the size of a smallest set of jokes so that she never needs o repeat the same quadruple of jokes over a period of $8$ semesters?
A
$6$
B
$5$
C
$4$
D
$8$
E
$9$
F
$10$
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https://learnzillion.com/lesson_plans/3259-8-solve-multi-step-division-problems-fp
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Lesson plan
# 8. Solve multi-step division problems (FP)
teaches Common Core State Standards CCSS.Math.Content.4.NBT.B.6 http://corestandards.org/Math/Content/4/NBT/B/6
teaches Common Core State Standards CCSS.Math.Content.4.OA.A.3 http://corestandards.org/Math/Content/4/OA/A/3
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8
## You have saved this lesson plan!
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Card of
Lesson objective: Solve multi-step division word problems using various strategies.
This lesson helps to build fluency with multi-digit whole number division using various strategies. The area model and partial quotients are used here because they support the development of other strategies and the standard algorithm. This work develops students' understanding that regardless of the strategy used, the relationships between the numbers and the solution remain the same.
Students engage in Mathematical Practice #1, make sense of problems and persevere in solving them as they analyze the problem and determine a strategy for solving it. Students engage in Mathematical Practice #8, look for and express regularity in repeated reasoning as they examine similarities and differences between strategies.
Key vocabulary:
• area model
• decompose
• distributive property
• partial quotients
• place value
• properties of operations
• relationship
Related content
Appears in
• 8. Solve multi-step division problems (FP)
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https://tex.stackexchange.com/questions/279782/latex-xstring-strcut-with-macros/279785
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# LaTeX xstring \StrCut with macros
I've been trying to give some formatted input to \StrCut from the xstring package in a very complex code, and I've been getting an error.
Here is a MWE :
\documentclass[a4paper]{article}
\usepackage{xstring}
\begin{document}
\newcommand{\test}{\emph{First} part:Second part}
\StrCut{\test}{:}\firstpart\secondpart%
\firstpart --- \secondpart%
\end{document}
I get this error :
! Use of \@xs@StrCut@@ doesn't match its definition.
\text@command #1->\def \reserved@a {
#1}\ifx \reserved@a \@empty \let \check@...
l.7 \StrCut{\test}{:}
\firstpart\secondpart%
Any tip ?
EDIT :
With this MWE :
\documentclass[a4paper]{article}
\usepackage{xstring}
\begin{document}
\newcommand{\test}{\emph{First} part:Second part}
\newcommand{\testbis}{\test}
\expandarg\StrCut{\testbis}{:}\firstpart\secondpart%
\firstpart --- \secondpart%
\end{document}
I don't get any error, but the output is not what I expect, since \test isn't cut.
• Welcome to TeX.SX! You have to expand the argument here, i.e. \expandarg\StrCut etc. – user31729 Nov 24 '15 at 17:27
• Thank you a lot ! It cuts the mistake, but it does not solve completely my problem, because my issue was with a macro inside a macro, see my second MWE in Edit. – mberthet Nov 24 '15 at 20:19
• Sorry, this is not ok -- you change the question and leaves my solution useless! – user31729 Nov 24 '15 at 21:00
• Sorry then, this is my first question here, I don't know what I should do. Your answer is totally fine for my first question, and does not work for my second question. Should I open another thread for my second question ? – mberthet Nov 24 '15 at 21:13
• No, I'll try. I suspect that it's not possible to use it the way you've done – user31729 Nov 24 '15 at 21:15
You don't need \StrCut for this application. There are two problems with your code:
1. You seem to want an arbitrary layer of macros above macros
2. You want to use “dangerous” commands such as \emph, that don't survive full expansion.
You can use \protected@edef in order to overcome the two issues:
\documentclass{article}
\makeatletter
\newcommand{\splitatcolon}[3]{%
\protected@edef\split@temp{#1}%
\expandafter\split@colon\split@temp:\@nil{#2}{#3}%
}
\def\split@colon#1:#2\@nil#3#4{%
\def#3{#1}%
\if\relax\detokenize{#2}\relax
% no colon
\let#4\@empty
\else
\split@eatcolon#2\@nil{#4}%
\fi
}
\def\split@eatcolon#1:\@nil#2{\def#2{#1}}
\makeatother
\begin{document}
\newcommand{\test}{\emph{First} part:Second part}
\newcommand{\testbis}{\test}
\splitatcolon{\emph{First} part:Second part}\firstpart\secondpart
\firstpart\ --- \secondpart
\splitatcolon{\test}\firstpart\secondpart
\firstpart\ --- \secondpart
\splitatcolon{\testbis}\firstpart\secondpart
\firstpart\ --- \secondpart
\splitatcolon{\emph{First} part:Second part:Third part}\firstpart\secondpart
\firstpart\ --- \secondpart
\splitatcolon{\secondpart}\secondpart\thirdpart
\firstpart\ --- \secondpart\ --- \thirdpart
\end{document}
The same idea with xstring:
\documentclass{article}
\usepackage{xstring}
\makeatletter
\newcommand{\splitatcolon}[3]{%
\protected@edef\split@temp{#1}%
\saveexpandmode
\expandarg\StrCut{\split@temp}{:}#2#3%
\restoreexpandmode
}
\makeatother
\begin{document}
\newcommand{\test}{\emph{First} part:Second part}
\newcommand{\testbis}{\test}
\splitatcolon{\emph{First} part:Second part}\firstpart\secondpart
\firstpart\ --- \secondpart
\splitatcolon{\test}\firstpart\secondpart
\firstpart\ --- \secondpart
\splitatcolon{\testbis}\firstpart\secondpart
\firstpart\ --- \secondpart
\splitatcolon{\emph{First} part:Second part:Third part}\firstpart\secondpart
\firstpart\ --- \secondpart
\splitatcolon{\secondpart}\secondpart\thirdpart
\firstpart\ --- \secondpart\ --- \thirdpart
\end{document}
• Thank you a lot, this seems perfect. I will try it out ASAP. – mberthet Nov 24 '15 at 23:52
• Your code definitely works fine. Sadly in some conditions I couldn't get \splitatcolon working fine. I had a lot of trouble finding out what was the problem, and I've finally understood that it comes from the babel package with the french option. If you add \usepackage[french]{babel} in your code above, it stops working. Any idea why, and how could I cope with this issue ? – mberthet Nov 27 '15 at 1:15
• Well, it works fine if I replace : by * as a splitter. No idea why though. – mberthet Nov 27 '15 at 1:19
• @mberthet Judging from your nickname, you're French. With babel-french, the colon becomes a special character. – egreg Nov 27 '15 at 9:34
The cutting fails most likely due to \emph, so expand the arguments:
\documentclass[a4paper]{article}
\usepackage{xstring}
\begin{document}
\newcommand{\test}{\emph{First} part:Second part}
\expandarg\StrCut{\test}{:}{\firstpart}{\secondpart}%
\firstpart\ --- \secondpart%
\end{document}
Update
\documentclass[a4paper]{article}
%\usepackage{xstring}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\StrCutNew}{mmmm}{%
\tl_set:Nx \l_tmpa_tl {#1}%
\seq_set_split:NnV \l_tmpa_seq {#2} {\l_tmpa_tl}
\expandafter\DeclareDocumentCommand\csname #3\endcsname{}{\seq_item:Nn \l_tmpa_seq{1}}
\expandafter\DeclareDocumentCommand\csname #4\endcsname{}{\seq_item:Nn \l_tmpa_seq{2}}
}
\ExplSyntaxOff
\begin{document}
\newcommand{\test}{First part:Second part}
\newcommand{\testbis}{\test}
\StrCutNew{\test}{:}{firstpart}{secondpart}
\firstpart\ --- \secondpart
\StrCutNew{\test}{:}{firstpart}{secondpart}
\firstpart\ --- \secondpart
\end{document}
• Thank you for helping me. I've just tried your updated code, it crashes for me when I use \emph{...} in the \test command. I got a good result using \StrExpand[3]{\testbis}{\testbisexp} and then feeding \testbisexp to StrCut. But it does not suit me since it depends on the level of expand necessary of \testbis, and I do not know it, it can vary. – mberthet Nov 24 '15 at 21:48
I found something which seems to be working well for the Edit :
\documentclass[a4paper]{article}
\usepackage{xstring}
\begin{document}
\newcommand{\test}{\emph{First} part:Second part}
\newcommand{\testbis}{\test}
\StrExpand[2]{\test}{\toto}
\StrExpand[2]{\testbis}{\totobis}
\expandarg\StrCut{\emph{First} part:Second part}{:}\firstpart\secondpart%
\firstpart --- \secondpart%
\expandarg\StrCut{\test}{:}\firstpart\secondpart%
\firstpart --- \secondpart%
\expandarg\StrCut{\testbis}{:}\firstpart\secondpart%
\firstpart --- \secondpart%
\expandarg\StrCut{\toto}{:}\firstpart\secondpart%
\firstpart --- \secondpart%
\expandarg\StrCut{\totobis}{:}\firstpart\secondpart%
\firstpart --- \secondpart%
\end{document}
It still doesn't solve the issue in my complex code, but I can't get a MWE to reproduce the issue. I'll come back :D
Thank you Christian Hupfer for your help.
|
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|
http://arnotgallery.comfaq.tug.org/pipermail/tex-live/2008-May/015846.html
|
# [tex-live] Bug#483019: texlive-xetex: xelatex fails to display included PDF graphics
Jonathan Kew jonathan_kew at sil.org
Wed May 28 17:34:43 CEST 2008
Hi again,
The OOo file is "tagged PDF" (whatever that means), which was not
supported by DVIPDFMx or (hence) xdvipdfmx until very recently. You'd
that xetex uses by default.
So the solution is to persuade OOo to refrain from writing tagged
PDF, or update to TL2008; the xdvipdfmx there will support this (to
the extent of ignoring the tagging but including the image anyway).
JK
On 28 May 2008, at 4:09 pm, Norbert Preining wrote:
> Hi Jonathan,
>
> after including the patch2 into the Debian packages we got a bug
> report
> which says that with the changes an included pdf file stopped being
> shown.
>
> To exclude any possible problems with the patching of xetex for
> poppler
> we did in Debian I also tried the binary of xetex as currently in the
> TeX Live subversion repository with the same result.
>
> Jonathan, do you have any idea what could have happened?
>
> A really minimal tex file is in the forwarded message below and the
> location of the to be included pdf file is at the end of the message
> below.
>
> Thanks a lot and all the best
>
> Norbert
>
>
> On Mo, 26 Mai 2008, Michael Ritzert wrote:
>> Package: texlive-xetex
>> Version: 2007.dfsg.1-3+b1
>> Severity: important
>>
>> When I try to include PDF graphics generated by OOo in my document
>> processed by xelatex, I get an output file where the space for the
>> graphic is reserved, but the graphic itself is not shown.
>>
>> In this example, I get an empty rectangle of the correct size when
>> processing it with xelatex 2007.dfsg.1-3+b1. With 2007.dfst.1-2, the
>> included file is shown inside the rectangle.
>>
>> I ONLY see this bahaviour when the PDF graphic has been generated by
>> OpenOffice.org. PDF graphics generated by epstopdf are correctly
>> displays in the output document.
>>
>> (Note: I sometimes see messages stating that the included file
>> generated
>> by OOo "had errors that were repaired or ignored." This message
>> does not
>> show up with the minmal PDF I'm using to reproduce the behaviour.)
>>
>>
>> ##################################
>> minimal input file
>>
>> \documentclass{article}
>>
>> \usepackage{graphics}
>>
>> \begin{document}
>> \framebox{\includegraphics{test.pdf}}
>> \{document}
>>
>>
>> Run xelatex x.tex.
>>
>>
>> ##################################
>> other files
>>
>> Any PDF generated by OpenOffice.org (oodraw) as test.pdf.
>> See http://sussrv01.ti.uni-mannheim.de/~ritzert/test.pdf if you don't
>> succeed in creating a file that fails to display.
>
> ----------------------------------------------------------------------
> ---------
> Dr. Norbert Preining <preining at logic.at> Vienna University
> of Technology
> Debian Developer <preining at debian.org>
> Debian TeX Group
> gpg DSA: 0x09C5B094 fp: 14DF 2E6C 0307 BE6D AD76 A9C0 D2BF
> 4AA3 09C5 B094
> ----------------------------------------------------------------------
> ---------
> DORRIDGE (n.)
> Technical term for one of the lame excuses written in very small print
> on the side of packets of food or washing powder to explain why
> there's hardly anything inside. Examples include 'Contents may have
> settled in transit' and 'To keep each biscuit fresh they have been
> individually wrapped in silver paper and cellophane and separated with
> corrugated lining, a cardboard flap, and heavy industrial tyres'.
> --- Douglas Adams, The Meaning of Liff
|
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|
http://link.springer.com/article/10.1007/s10967-005-0820-8
|
, Volume 265, Issue 2, pp 273-281
# Sources of uncertainties in prompt gamma activation analysis
Rent the article at a discount
Rent now
* Final gross prices may vary according to local VAT.
|
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|
https://lazyprogrammer.me/category/data-science/
|
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Remember, these links will self-destruct on April 29 (5 days). Act NOW!
P.S. As you know, I’m ALWAYS updating my courses based on feedback and adding new material. Sometimes, even stuff that has been only recently invented!
Here are a list of recent updates:
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– Recurrent Neural Networks (Deep Learning pt 5) and Deep NLP (Deep Learning pt 6): All language-modeling code can now train on the Brown corpus, which you can import directly from NLTK! No need to download and process Wikipedia data dumps anymore! This will make running the code much easier!
– Deep Learning pt 2: Added code samples for grid search and random search, as well as a simple intuitive example of how dropout “emulates” an ensemble (which, by the way, you can gain even FURTHER insight into by taking my Ensemble Machine Learning course!)
And coming very soon (next couple days):
– Deep Learning pt 1: Using SKLearn so using a neural network is just 3 lines of code!
– Recurrent Neural Networks (Deep Learning pt 5) and Deep NLP (Deep Learning pt 6): More discussion about why Tensorflow isn’t appropriate here, but at the same time, adding more Tensorflow examples!
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As usual, I’m providing $10 coupons for all my courses in the links below. Please use these links and share them with your friends! The$10 promo doesn’t come around often, so make sure you pick up everything you are interested in, or could become interested in later this year. The promo goes until April 12. Don’t wait!
At the end of this post, I’m going to provide you with some additional links to get machine learning prerequisites (calculus, linear algebra, Python, etc…) for $10 too! If you don’t know what order to take the courses in, please check here: https://deeplearningcourses.com/course_order Here are the links for my courses: Deep Learning Prerequisites: Linear Regression in Python https://www.udemy.com/data-science-linear-regression-in-python/?couponCode=APR123 Deep Learning Prerequisites: Logistic Regression in Python https://www.udemy.com/data-science-logistic-regression-in-python/?couponCode=APR123 Deep Learning in Python https://www.udemy.com/data-science-deep-learning-in-python/?couponCode=APR123 Practical Deep Learning in Theano and TensorFlow https://www.udemy.com/data-science-deep-learning-in-theano-tensorflow/?couponCode=APR123 Deep Learning: Convolutional Neural Networks in Python https://www.udemy.com/deep-learning-convolutional-neural-networks-theano-tensorflow/?couponCode=APR123 Unsupervised Deep Learning in Python https://www.udemy.com/unsupervised-deep-learning-in-python/?couponCode=APR123 Deep Learning: Recurrent Neural Networks in Python https://www.udemy.com/deep-learning-recurrent-neural-networks-in-python/?couponCode=APR123 Advanced Natural Language Processing: Deep Learning in Python https://www.udemy.com/natural-language-processing-with-deep-learning-in-python/?couponCode=APR123 Advanced AI: Deep Reinforcement Learning in Python https://www.udemy.com/deep-reinforcement-learning-in-python/?couponCode=APR123 Easy Natural Language Processing in Python https://www.udemy.com/data-science-natural-language-processing-in-python/?couponCode=APR123 Cluster Analysis and Unsupervised Machine Learning in Python https://www.udemy.com/cluster-analysis-unsupervised-machine-learning-python/?couponCode=APR123 Unsupervised Machine Learning: Hidden Markov Models in Python https://www.udemy.com/unsupervised-machine-learning-hidden-markov-models-in-python/?couponCode=APR123 Data Science: Supervised Machine Learning in Python https://www.udemy.com/data-science-supervised-machine-learning-in-python/?couponCode=APR123 Bayesian Machine Learning in Python: A/B Testing https://www.udemy.com/bayesian-machine-learning-in-python-ab-testing/?couponCode=APR123 Ensemble Machine Learning in Python: Random Forest and AdaBoost https://www.udemy.com/machine-learning-in-python-random-forest-adaboost/?couponCode=APR123 Artificial Intelligence: Reinforcement Learning in Python https://www.udemy.com/artificial-intelligence-reinforcement-learning-in-python/?couponCode=APR123 SQL for Newbs and Marketers https://www.udemy.com/sql-for-marketers-data-analytics-data-science-big-data/?couponCode=APR123 And last but not least,$10 coupons for some helpful prerequisite courses. You NEED to know this stuff before you study machine learning:
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Python http://bit.ly/2nMqqGg
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Linalg 1 http://bit.ly/2ocf4hO
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# New course! Reinforcement Learning in Python
January 27, 2017
I would like to announce my latest course – Artificial Intelligence: Reinforcement Learning in Python.
This has been one of my most requested topics since I started covering deep learning. This course has been brewing in the background for months.
The result: This is my most MASSIVE course yet.
Usually, my courses will introduce you to a handful of new algorithms (which is a lot for people to handle already). This course covers SEVENTEEN (17!) new algorithms.
This will keep you busy for a LONG time.
If you’re used to supervised and unsupervised machine learning, realize this: Reinforcement Learning is a whole new ball game.
There are so many new concepts to learn, and so much depth. It’s COMPLETELY different from anything you’ve seen before.
That’s why we build everything slowly, from the ground up.
There’s tons of new theory, but as you’ve come to expect, anytime we introduce new theory it is accompanied by full code examples.
What is Reinforcement Learning? It’s the technology behind self-driving cars, AlphaGo, video game-playing programs, and more.
You’ll learn that while deep learning has been very useful for tasks like driving and playing Go, it’s in fact just a small part of the picture.
Reinforcement Learning provides the framework that allows deep learning to be useful.
Without reinforcement learning, all we have is a basic (albeit very accurate) labeling machine.
With Reinforcement Learning, you have intelligence.
Reinforcement Learning has even been used to model processes in psychology and neuroscience. It’s truly the closest thing we have to “machine intelligence” and “general AI”.
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#artificial intelligence #deep learning #reinforcement learning
# New course! Bayesian Machine Learning in Python: A/B Testing
November 17, 2016
[If you already know you want to sign up for my Bayesian machine learning course, just scroll to the bottom to get your $10 coupon!] Boy, do I have some exciting news today! You guys have already been keeping up with my deep learning series. Hopefully, you’ve noticed that I’ve been releasing non-deep learning machine learning courses as well, in parallel (and they often tie into the deep learning series quite nicely). Well today, I am announcing the start of a BRAND NEW series on Bayesian machine learning. Bayesian methods require an entirely new way of thinking – a paradigm shift. But don’t worry, it’s not just all theory. In fact, the first course I’m releasing in the series is VERY practical – it’s on A/B testing. Every online advertiser, e-commerce store, marketing team, etc etc etc. does A/B testing. But did you know that traditional A/B testing is both horribly confusing and inefficient? Did you know that there are cool, new adaptive methods inspired by reinforcement learning that improve on those old crusty tests? (Those old methods, and the way they are traditionally taught, are probably the reason you cringe when you hear the word “statistics”) Well, Bayesian methods not only represent a state-of-the-art solution to many A/B testing challenges, they are also surprisingly theoretically simpler! You’ll end the course by doing your own simulation – comparing and contrasting the various adaptive A/B testing algorithms (including the final Bayesian method). This is VERY practical stuff and any digital media, newsfeed, or advertising startup will be EXTREMELY IMPRESSED if you know this stuff. This WILL advance your career, and any company would be lucky to have someone that knows this stuff on their team. Awesome coincidence #1: As I mentioned above, a lot of these techniques cross-over with reinforcement learning, so if you are itching for a preview of my upcoming deep reinforcement learning course, this will be very interesting for you. Awesome coincidence #2: Bayesian learning also crosses over with deep learning, one example being the variational autoencoder, which I may incorporate into a more advanced deep learning course in the future. They heavily rely on concepts from both Bayesian learning AND deep learning, and are very powerful state-of-the-art algorithms. Due to all the black Friday madness going on, I am going to do a ONE-TIME ONLY$10 special for this course. With my coupons, the price will remain at $10, even if Udemy’s site-wide sale price goes up (which it will). See you in class! As promised, here is the coupon: https://www.udemy.com/bayesian-machine-learning-in-python-ab-testing/?couponCode=EARLYBIRDSITE2 UPDATE: The Black Friday sale is over, but the early bird coupon is still up for grabs: https://www.udemy.com/bayesian-machine-learning-in-python-ab-testing/?couponCode=EARLYBIRDSITE LAST THING: Udemy is currently having an awesome Black Friday sale.$10 for ANY course starting Nov 15, but the price goes up by $1 every 2 days, so you need to ACT FAST. I was going to tell you earlier but I was hard at work on my course. =) Just click this link to get ANY course on Udemy for$10 (+\$1 every 2 days): http://bit.ly/2fY3y5M
#bayesian #data science #machine learning #statistics
# Linear Regression
July 25, 2014
Code for this tutorial is here:
https://github.com/lazyprogrammer/machine_learning_examples/blob/master/linear_regression_class/lr_1d.py
Prerequisites for understanding this material:
• calculus (taking partial derivatives)
Linear regression is one of the simplest machine learning techniques you can use. It is often useful as a baseline relative to more powerful techniques.
To start, we will look at a simple 1-D case.
Like all regressions, we wish to map some input X to some input Y.
ie.
Y = f(X)
With linear regression:
Y = aX + b
Or we can say:
h(X) = aX + b
Where “h” is our “hypothesis”.
You may recall from your high school studies that this is just the equation for a straight line.
When X is 1-D, or when “Y has one explanatory variable”, we call this “simple linear regression”.
When we use linear regression, we are using it to model linear relationships, or what we think may be linear relationships.
As with all supervised machine learning problems, we are given labeled data points:
(X1, Y1), (X2, Y2), (X3, Y3), …, (Xn, Yn)
And we will try to fit the line (aX + b) as best we can to these data points.
This means we have to optimize the parameters “a” and “b”.
How do we do this?
We will define an error function and then find the “a” and “b” that will make the error as small as possible.
You will see that many regression problems work this way.
What is our error function?
We could use the difference between the predicted Y and the actual Y like so:
But if we had equal amounts of errors where Y was bigger than the prediction, and where Y was smaller than the prediction, then the errors would cancel out, even though the absolute difference in errors is large.
Typically in machine learning, the squared error is a good place to start.
Now, whether or not the difference in the actual and predicted output is positive or negative, its contribution to the total error is still positive.
We call this sum the “sum of squared errors”.
Recall that we want to minimize it.
Recall from calculus that to minimize something, you want to take its derivative.
Because there are two parameters, we have to take the derivatives both with respect to a and with respect to b, set them to 0, and solve for a and b.
Luckily, because the error function is a quadratic it increases as (a,b) get further and further away from the minimum.
As an exercise I will let you calculate the derivatives.
You will get 2 equations (the derivatives) and 2 unknowns (a, b). From high school math you should know how to solve this by rearranging the terms.
Note that these equations can be solved analytically. Meaning you can just plug and chug the values of your inputs and get the final value of a and b by blindly using a formula.
Note that this method is also called “ordinary least squares”.
Measuring the error (R-squared)
To determine how well our model fits the data, we need a measure called the “R-square”.
Note that in classification problems, we can simply use the “classification rate”, which is the number of correctly classified inputs divided by the total number of inputs. With the real-valued outputs we have in regression, this is not possible.
Here are the equations we use to predict the R-square.
SS(residual) is the sum of squared error between the actual and predicted output. This is the same as the error we were trying to minimize before!
SS(total) is the sum of squared error between each sample output and the mean of all the sample outputs, i.e. What the residual error would be if we just predicted the average output every time.
So the R-square then, is just how much better our model is compared to predicting the mean each time. If we just predicted the mean each time, the R-square would be 1-1=0. If our model is perfect, then the R-square would be 1-0=1.
Something to think about: If our model performs worse than predicting the mean each time, what would be the R-square value?
Limitations of Linear Regression
• It only models linear equations. You can model higher order polynomials (link to later post) but the model is still linear in its parameters.
• It is sensitive to outliers. Meaning if we have one data point very far away from all the others, it could “pull” the regression line in its direction, away from all the other data points, just to minimize the error.
#calculus #linear regression #machine learning #statistics
|
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https://web.ma.utexas.edu/users/m408s/m408d/CurrentWeb/LM15-3-3.php
|
Home
#### Integration by Parts
Integration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles
#### Integrals of Trig Functions
Antiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (only even powers)
Product of Secants and Tangents
Other Cases
#### Trig Substitutions
How Trig Substitution Works
Summary of trig substitution options
Examples
Completing the Square
#### Partial Fractions
Introduction to Partial Fractions
Linear Factors
Improper Rational Functions and Long Division
Summary
#### Strategies of Integration
Substitution
Integration by Parts
Trig Integrals
Trig Substitutions
Partial Fractions
#### Improper Integrals
Type 1 - Improper Integrals with Infinite Intervals of Integration
Type 2 - Improper Integrals with Discontinuous Integrands
Comparison Tests for Convergence
#### Modeling with Differential Equations
Introduction
Separable Equations
A Second Order Problem
#### Euler's Method and Direction Fields
Direction Fields
Euler's method revisited
#### Separable Equations
The Simplest Differential Equations
Separable differential equations
Mixing and Dilution
#### Models of Growth
Exponential Growth and Decay
The Zombie Apocalypse (Logistic Growth)
#### Linear Equations
Linear ODEs: Working an Example
The Solution in General
Saving for Retirement
#### Parametrized Curves
Three kinds of functions, three kinds of curves
The Cycloid
Visualizing Parametrized Curves
Tracing Circles and Ellipses
Lissajous Figures
#### Calculus with Parametrized Curves
Video: Slope and Area
Video: Arclength and Surface Area
Summary and Simplifications
Higher Derivatives
#### Polar Coordinates
Definitions of Polar Coordinates
Graphing polar functions
Video: Computing Slopes of Tangent Lines
#### Areas and Lengths of Polar Curves
Area Inside a Polar Curve
Area Between Polar Curves
Arc Length of Polar Curves
#### Conic sections
Slicing a Cone
Ellipses
Hyperbolas
Parabolas and Directrices
Shifting the Center by Completing the Square
#### Conic Sections in Polar Coordinates
Foci and Directrices
Visualizing Eccentricity
Astronomy and Equations in Polar Coordinates
#### Infinite Sequences
Examples of Infinite Sequences
Limit Laws for Sequences
Theorems for and Examples of Computing Limits of Sequences
Monotonic Covergence
#### Infinite Series
Introduction
Geometric Series
Limit Laws for Series
Test for Divergence and Other Theorems
Telescoping Sums
#### Integral Test
Preview of Coming Attractions
The Integral Test
Estimates for the Value of the Series
#### Comparison Tests
The Basic Comparison Test
The Limit Comparison Test
#### Convergence of Series with Negative Terms
Introduction, Alternating Series,and the AS Test
Absolute Convergence
Rearrangements
The Ratio Test
The Root Test
Examples
#### Strategies for testing Series
Strategy to Test Series and a Review of Tests
Examples, Part 1
Examples, Part 2
#### Power Series
Finding the Interval of Convergence
Power Series Centered at $x=a$
#### Representing Functions as Power Series
Functions as Power Series
Derivatives and Integrals of Power Series
Applications and Examples
#### Taylor and Maclaurin Series
The Formula for Taylor Series
Taylor Series for Common Functions
Adding, Multiplying, and Dividing Power Series
Miscellaneous Useful Facts
#### Applications of Taylor Polynomials
Taylor Polynomials
When Functions Are Equal to Their Taylor Series
When a Function Does Not Equal Its Taylor Series
Other Uses of Taylor Polynomials
#### Functions of 2 and 3 variables
Functions of several variables
Limits and continuity
#### Partial Derivatives
One variable at a time (yet again)
Definitions and Examples
An Example from DNA
Geometry of partial derivatives
Higher Derivatives
Differentials and Taylor Expansions
#### Differentiability and the Chain Rule
Differentiability
The First Case of the Chain Rule
Chain Rule, General Case
Video: Worked problems
#### Multiple Integrals
General Setup and Review of 1D Integrals
What is a Double Integral?
Volumes as Double Integrals
#### Iterated Integrals over Rectangles
How To Compute Iterated Integrals
Examples of Iterated Integrals
Fubini's Theorem
Summary and an Important Example
#### Double Integrals over General Regions
Type I and Type II regions
Examples 1-4
Examples 5-7
Swapping the Order of Integration
Area and Volume Revisited
#### Double integrals in polar coordinates
dA = r dr (d theta)
Examples
#### Multiple integrals in physics
Double integrals in physics
Triple integrals in physics
#### Integrals in Probability and Statistics
Single integrals in probability
Double integrals in probability
#### Change of Variables
Review: Change of variables in 1 dimension
Mappings in 2 dimensions
Jacobians
Examples
Bonus: Cylindrical and spherical coordinates
### Examples 1-4
In the following video, we will compute Example 1 and Example 2:
Example 1: Evaluate $$\iint_R f(x,y)\,dA,$$ where $f(x,y)= x^2y$ and $R$ is the upper half of the unit disk (shown here). Example 2: Evaluate $$\iint_R f(x,y)\,dA,$$ where $f(x,y) = 4xe^{2y}$ and the region $R$ is bounded by the $x$-axis, the $y$-axis, the line $y=2$ and the curve $y=\ln(x)$ (shown here).
Now, we look at some additional examples.
Example 3: Evaluate the integral $$I \iint _D\, (x+y)\, dA$$ where $D$ consists of all points $(x,\,y)$ such that $0 \ \le \ y \ \le \sqrt{9-x^2}\,, \quad 0\ \le \ x \ \le 3\,.$
DOGraph the region $D$ before reading further. Then try to set up a Type I iterated integral.
Solution 3: Since $y^2 \ = \ 9 - x^2$ is a circle of radius $3$ centered at the origin, $D$ consists of all points in the first quadrant inside this circle as shown here. This is described as a Type I region, so we fix $x$ in and integrate with respect to $y$ along the black vertical line as shown, and then integrate with respect to $x$ from $x=0$ to $x=3$ (all possible black vertical lines). So the double integral $I$ becomes the interated integral \begin{eqnarray} \int_0^3\left(\int_0^{\sqrt{9-x^2}}\, (x+y)\, dy\right)\,dx &=& \int_0^3\, \Bigl[\, xy +\frac{1}{2}y^2 \,\Bigl]_0^{\sqrt{9 - x^2}}\,dx\\ &=&\int_0^3\, \Bigl( x\sqrt{9 - x^2} +\frac{1}{2} (9 - x^2)\Bigr)\, dx\\ \end{eqnarray}
DO: Evaluate the above integral. The answer is 18.
----------------------------------------------------------------------------------
Example 4: Evaluate the integral $\displaystyle I=\iint_R\, (x+y)\, dA,$ where $R$ consists of all points $(x,y)$ with $0\le y\le 3$ and $0\le x\le\sqrt{9-y^2}$.
DO: Graph this region $R$. Is it the same as $D$ above? Set up and evaluate the integral above as a Type II integral over $R$, which will have black horizontal lines. You should get the same answer as in Example 3.
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|
https://www.futurelearn.com/info/courses/unlocking-design-potential/0/steps/266446
|
# SimScale: Importing geometry
In this video, Dr. Ico Broekhuizen explains how to import your model into SimScale and generate a virtual wind tunnel for simulation.
2.2
Hi, in this video, I will start to show you how to perform wind simulation of urban areas using the online SimScale platform. The first thing we need to do is import a model that we’ve created previously, for example, in Revit or SketchUp. So here on the left hand side, you can click the plus icon on the geometries and upload almost any file, any model file that you may have, and then SimScale imports this and shows you a quick representation of what the model looks like. And you have some control over this view and what it will look like using the buttons here at the top.
37.9
The first thing we then need to do is to translate this model of the buildings to a model of the wind tunnel that we will actually be simulating. So we will edit this model in the CAD mode. So once you go there, you see the same model as before. The first thing we will do is to define an external flow volume. And we can then specify the dimensions that this wind tunnel should have. So the bottom will usually be at zero meters, so it matches that, so it matches the bottom of the buildings that we have.
74.3
And for the height of the model, there is a rule of thumb that says that if the highest building is, say, 20 meters high, you use six times that height as the height of the wind tunnel. And in the same way, you can also specify the other directions so that the - If the wind will be coming from the right hand side of the view here, we want five times that height of the tallest building on the right hand side, on the bottom, and at the top. And we want around 15 times the height and the downwind side of the model.
116.1
So with those basic dimensions set up, we can then use this seed face option and we can simply select a roof of a building. This isn’t always necessary, but sometimes we need to do this so SimScale can figure out how to create this volume. And then we simply click apply and it will create this box representing the wind tunnel that we will be simulating.
138.5
So then we just need to get rid of all the buildings that we added because they won’t be part of the simulation, so you can either use this view on the right here to select all of the buildings, or you can also simply select the volume of the wind tunnel and then right click to invert that selection. So if you look underneath, you can see that all the buildings are selected. And with all the buildings selected, we can simply delete them from the model.
171.8
So as you’ll see the buildings have now disappeared, but the imprints of the buildings are still present in the wind volume that we will be simulating later on. And you can simply click Export to return to the CFD environment. And there you will once again see the wind tunnel volume that we have just created. In the next video, I’ll go over all the settings you need to put up before we can start the simulation.
SimScale allows you to import models that you have previously created in 3D modelling programs such as Revit or Sketchup. The CAD mode in SimScale then allows you to convert a model of buildings to a model of the wind volume around the buildings, which needs to be sufficiently large to get accurate simulation results.
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|
https://codereview.stackexchange.com/questions/78355/data-structure-to-count-occurrences-of-entries
|
# Data structure to count occurrences of entries
I would love to hear any thoughtful suggestions on how to improve my programming style in order to be more understandable.
Listed below is a sample of my code which I wrote in Eclipse:
//Implement using a linked list
public class FrequencyBag<T>
{
// TO DO: Instance Variables
private Node firstNode;
private int numOfItems;
private class Node{
//Node Instance Variables
private T data;
private int frequency;
private Node next;
private Node(T Data, Node nextNode){
data= Data;
next=nextNode;
frequency=1;
}
frequency++;
}
private int getF(){
return frequency;
}
}
/**
* Constructor
* Constructs an empty frequency bag.
*/
public FrequencyBag()
{
firstNode=null;
numOfItems =0;
}
/**
* Adds new entry into this frequency bag.
* @param aData the data to be added into this frequency bag.
*/
{
boolean found =false;
Node currNode=firstNode;
while(currNode !=null){
found=true;
break;
}
currNode= currNode.next;
}
if(!found){
Node tempNode=firstNode;
}
numOfItems++;
}
/**
* Gets the number of occurrences of aData in this frequency bag.
* @param aData the data to be checked for its number of occurrences.
* @return the number of occurrences of aData in this frequency bag.
*/
{
Node currNode= firstNode;
while(currNode!=null){
return currNode.getF();
}
currNode= currNode.next;
}
return 0;
}
/**
* Gets the maximum number of occurrences in this frequency bag.
* @return the maximum number of occurrences of an entry in this
* frequency bag.
*/
public int getMaxFrequency()
{
if(firstNode!=null){
Node currNode= firstNode;
Node maxNode= firstNode;
while(currNode!=null){
if(currNode.getF()>=maxNode.getF()){
maxNode=currNode;
}
currNode=currNode.next;
}
return maxNode.getF();
}
else{
return 0;
}
}
/**
* Gets the probability of aData
* @param aData the specific data to get its probability.
* @return the probability of aData
*/
{
if(firstNode!=null){
boolean flag=true;
double dataF=0;
double prob=0;
Node currNode= firstNode;
while(currNode!=null){
dataF=(double)currNode.getF();
flag=false;
break;
}
currNode= currNode.next;
}
if(!flag){
prob= dataF/(double)numOfItems;
}
return prob;
}
else{
return 0;
}
}
/**
* Empty this bag.
*/
public void clear()
{
firstNode=null;
numOfItems=0;
}
/**
* Gets the number of entries in this bag.
* @return the number of entries in this bag.
*/
public int size()
{
return numOfItems;
}
}
• Welcome to Code Review! To make life easier for reviewers, please add sufficient context to your question. The more you tell us about what your code does and what the purpose of doing that is, the easier it will be for reviewers to help you. See also this meta question – Vogel612 Jan 22 '15 at 20:32
### Make the inner Node class static
You can do this, because this class doesn't use anything in the enclosing class. A non-static class contains a private reference to the enclosing class, which is just a waste when you don't really need it.
When you make the class static you will also need to add a template parameter of its own, like this:
private static class Node<T> {
// ...
}
However, this will also mean that when you use variables of type Node, you will also need to specify the template parameter T, changing all occurrences to Node<T>.
### Naming
The getF and addF methods are poorly named. It would be easier to read if you spell them out as getFrequency, and incrementFrequency. On the other hand, in getFrequencyOf, I find the "Of" redundant, I think you can just drop that. Data is not a good variable name in Java, because the convention is to use camelCase, for example data instead.
### Unnecessary operations
In getMaxFrequency, this part pointlessly compares the first node against itself:
if (firstNode != null) {
Node currNode = firstNode;
Node maxNode = firstNode;
while (currNode != null) {
Since the first if already ensures that the first node is not null, this way would be more optimal:
if (firstNode != null) {
Node maxNode = firstNode;
Node currNode = firstNode.next;
while (currNode != null) {
### Simplify using early returns
It can be a good idea to return early when the first node is null, this way you could reduce one nesting level, which is slightly more readable, like this:
if (firstNode == null) {
return 0;
}
Node maxNode = firstNode;
Node currNode = firstNode.next;
while (currNode != null) {
if (currNode.getF() >= maxNode.getF()) {
maxNode = currNode;
}
currNode = currNode.next;
}
return maxNode.getF();
You can apply the same logic to the getProbabilityOf method (drop the "Of", return early, iterate from firstNode.next).
You should put some spacing in between your operators and other things.
boolean found =false;
Node currNode=firstNode;
while(currNode !=null){
found=true;
break;
}
currNode= currNode.next;
Should look like this
boolean found = false;
Node currNode = firstNode;
while (currNode != null) {
found = true;
break;
}
currNode = currNode.next;
Make sure that you do the following
• Indent consistently
• space out the operators and the opening braces
• Use Egyptian Style bracing (unless coding in C#
• Do away with unneeded comments
Then it looks something like this
public class FrequencyBag<T> {
private Node firstNode;
private int numOfItems;
private class Node {
private T data;
private int frequency;
private Node next;
private Node(T Data, Node nextNode) {
data = Data;
next = nextNode;
frequency = 1;
}
frequency++;
}
private int getF() {
return frequency;
}
}
public FrequencyBag() {
firstNode = null;
numOfItems = 0;
}
/**
* Adds new entry into this frequency bag.
* @param aData the data to be added into this frequency bag.
*/
boolean found = false;
Node currNode = firstNode;
while(currNode != null){
found = true;
break;
}
currNode = currNode.next;
}
if(!found) {
Node tempNode = firstNode;
}
numOfItems++;
}
/**
* Gets the number of occurrences of aData in this frequency bag.
* @param aData the data to be checked for its number of occurrences.
* @return the number of occurrences of aData in this frequency bag.
*/
Node currNode= firstNode;
while(currNode!=null){
return currNode.getF();
}
currNode= currNode.next;
}
return 0;
}
/**
* Gets the maximum number of occurrences in this frequency bag.
* @return the maximum number of occurrences of an entry in this
* frequency bag.
*/
public int getMaxFrequency() {
if(firstNode!=null){
Node currNode= firstNode;
Node maxNode= firstNode;
while(currNode!=null){
if(currNode.getF()>=maxNode.getF()){
maxNode=currNode;
}
currNode=currNode.next;
}
return maxNode.getF();
} else {
return 0;
}
}
/**
* Gets the probability of aData
* @param aData the specific data to get its probability.
* @return the probability of aData
*/
if(firstNode != null) {
boolean flag = true;
double dataF = 0;
double prob = 0;
Node currNode = firstNode;
while(currNode != null) {
dataF = (double)currNode.getF();
flag = false;
break;
}
currNode = currNode.next;
}
if (!flag) {
prob = dataF / (double)numOfItems;
}
return prob;
}
else {
return 0;
}
}
/**
* Empty this bag.
*/
public void clear() {
firstNode = null;
numOfItems = 0;
}
/**
* Gets the number of entries in this bag.
* @return the number of entries in this bag.
*/
public int size() {
return numOfItems;
}
}
And is much easier to read.
I left the block comments because they looked like they were there for intellisense.
Your Variable naming was pretty good, but I would reconsider these
• aData
• dataF
• prob
• flag
flag isn't so bad except I don't know what the flag means.
I assume prob is probability, but probability of what?
And that leads to this Method name getProbabilityOf()
Get probability of .... what?
Another one that isn't so bad getFrequencyOf() you could probably drop the Of off the end on this one, or elaborate what you are getting the frequency of, these last two items might just be really nit-picky, so take them with a grain of salt.
|
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|
http://www.emathhelp.net/notes/differential-equations/nth-order-linear-ode-with-constant-coefficients/variation-of-parameters/
|
# Variation of Parameters
Variation of parameters, like method of undetermined coefficients, is another method for finding a particular solution of the nth-order linear differential equation L(y)=phi(x) once the solution of the associated homogeneous equation L(y) = 0 is known.
Recall from linear independence note, that if y_1(x),\ y_2(x),\ ...,\ y_n(x) are n linearly independent solutions of L(y)=0, then the general solution of L(y)=0 is y_h=c_1 y_1(x)+c_2 y_2(x)+...+c_n y_n(x) .
A variation of parameter method assumes that particular solution has form of homogeneous solution except that constants c_i (i=1, 2, ..., n) are functions of x (that's why it is called variation of parameter): y_p=c_1(x) y_1(x)+c_2(x)y_2(x)+...+c_n(x)y_n(x) .
We know y_i(x) (i=1, 2, ..., n) but we need to determine c_i(x) (i=1, 2, ..., n).
For this set up following linear system of equations:
{(c_1'y_1+c_2'y_2+...+c_n'y_n=0),(c_1'y_1'+c_2'y_2'+...+c_n'y_n'=0),(...),(c_1'y_1^((n-1))+c_2'y_2^((n-1))+...+c_n'y_n^((n-1))=0),(c_1'y_1^((n))+c_2'y_2^((n))+...+c_n'y_n^((n))=0):}
Then integrate each c_i' to obtain c_i , disregarding all constants of integration. This is permissible because we are seeking only one particular solution.
Since y_1(x),\ y_2(x),\ ...,\ y_n(x) are n linearly independent solutions of the same equation L(y) = 0, their Wronskian is not zero. This means that the system has a nonzero determinant and can be solved uniquely for c_1'(x),\ c_2'(x),\ ...,\ c_n'(x) .
The method of variation of parameters can be applied to all linear differential equations. It is therefore more powerful than the method of undetermined coefficients, which is restricted to linear differential equations with constant coefficients and particular forms of phi(x) . Nonetheless, in those cases where both methods are applicable, the method of undetermined coefficients is usually the more efficient and, hence, preferable.
As a practical matter, the integration of v_i'(x) may be impossible to perform. In such an event, other methods (in particular, numerical techniques) must be employed.
Example 1. Solve y''-2y'+y=(e^x)/x .
Homogeneous solution is y_h=c_1e^(x)+c_2xe^x .
To find particular solution, set up system:
{(c_1'e^x+c_2'xe^x=0),(c_1'(e^x)'+c_2'(xe^x)'=(e^x)/x):}
or
{(c_1'e^x+c_2'xe^x=0),(c_1'e^x+c_2'(xe^x+e^x)=(e^x)/x):}
Subtract first equation from second: c_2'e^x=(e^x)/x or c_2'=1/x .
From first equation c_1'=-c_2'x=-1/x x=-1 .
So, c_2=int 1/x dx=ln(|x|) and c_1=int -1dx=-x .
So, y_p=c_1e^x+c^2xe^x=-xe^x+ln(|x|)xe^x .
Finally, general solution is y=y_h+y_p=c_1e^x+c_2xe^x-xe^x+ln(|x|)xe^x=c_1e^x+c_3xe^x+ln(|x|)xe^x where c_3=c_2-1 .
Example 2. Solve 2y''-3y'+y=e^x .
Corresponding homogeneous equation is 2y''-3y'+y=0 . Characteristic equation is 2r^2-3r+1=0 which has roots r_1=1, r_2=1/2 .
So, y_h=c_1e^x+c_2e^(1/2 x) .
Now, be careful with applying variation of parameters. To apply it correctly coefficient near the highest derivative must be 1, so first divide both sides of differential equation by 2: y''-1.5y'+0.5y=1/2 e^x .
Now, set up system:
{(c_1'e^x+c_2'e^(1/2 x)=0),(c_1'(e^x)'+c_2'(e^(1/2 x))'=1/2 e^x):}
Or
{(c_1'e^x+c_2'e^(1/2 x)=0),(c_1'e^x+1/2 c_2'e^(1/2 x)=1/2 e^x):}
Subtract first equation from second: -1/2c_2'e^(1/2 x)=1/2e^x or c_2=-e^(1/2 x) .
From first equation c_1'=-c_2'e^(-1/2x)=-(-e^(1/2 x))e^(-1/2 x)=1 .
So, c_1=int 1dx=x and c_2=int -e^(1/2 x)dx=-2e^(1/2 x) .
Therefore, y_p=c_1e^x+c_2e^(1/2 x)=xe^x-2e^x .
Finally, y=y_h+y_p=c_1e^x+c_2e^(1/2 x)+xe^x-2e^x=c_3e^x+c_2e^(1/2 x)+xe^x where c_3=c_1-2 .
Example 3. Find general solution of y'''+y'=1/(cos(x)) .
Solution of the corresponding homogeneous equation is y_h=c_1+c_2cos(x)+c_3sin(x) .
To find particular solution set up system:
{(c_1'*1+c_2'cos(x)+c_3'sin(x)=0),(c_1'*(1)'+c_2'(cos(x))'+c_3'(sin(x))'=0),(c_1'*(1)''+c_2'(cos(x))''+c_3'(sin(x))''=1/(cos(x))):}
Or
{(c_1'+c_2'cos(x)+c_3'sin(x)=0),(-c_2'sin(x)+c_3'cos(x)=0),(-c_2'cos(x)-c_3'sin(x)=1/(cos(x))):}
Solving this system gives c_1'=1/(cos(x)),\ c_2'=-1,\ c_3'=-tan(x) .
So,
c_1=int 1/(cos(x))dx=ln(|(1+sin(x))/(cos(x))|)
c_2=int -1dx=-x
c_3=int -tan(x)dx=ln(|cos(x)|) .
Thus, y_p=c_1+c_2cos(x)+c_3sin(x)=ln(|(1+sin(x))/(cos(x))|)-xcos(x)+ln(|cos(x)|)sin(x) .
Finally, general solution is
y=y_h+y_p=c_1+c_2cos(x)+c_3sin(x)+ln(|(1+sin(x))/(cos(x))|)-xcos(x)+ln(|cos(x)|)sin(x)
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http://mathhelpforum.com/algebra/156023-not-sure-if-algebra.html
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# Thread: not sure if it is algebra...
1. ## not sure if it is algebra...
but im not sure how i would solve this (question in attachment!)
could someone please point me in the right direction to solving this question!?!
Thanks!!
2. Originally Posted by andyboy179
but im not sure how i would solve this (question in attachment!)
could someone please point me in the right direction to solving this question!?!
Thanks!!
$\displaystyle \frac {2x+1} {3x-7}= 2$
multiply all with 3x-7
$2x+1= 2\cdot (3x-7)$
$2x+1 = 6x-14$
$4x = 15 \Rightarrow x= 15/4$
3. if i multiply all by 3x-7 it would be, 6x+7/3x-7=2? then what would i do?
4. Originally Posted by andyboy179
but im not sure how i would solve this (question in attachment!)
could someone please point me in the right direction to solving this question!?!
Thanks!!
Dear andyboy179,
First multiply both sides of the equation by 3x-7. Afterwards you can substract 2x from both sides. Hope you can continue.
5. so it would be, 6x+7/ 9x-49=2 then 4x+7/ 7x-49=2???
6. Originally Posted by andyboy179
if i multiply all by 3x-7 it would be, 6x+7/3x-7=2? then what would i do?
$\displaystyle \frac {2x+1} {3x-7}= 2 \Rightarrow
\frac {(2x+1)\cdot (3x-7)} {(3x-7) }= 2\cdot (3x-7 ) \Rightarrow 2x+1= 2\cdot (3x-7)$
so you will lose fraction after dividing $\displaystyle \frac {(2x+1)\cdot (3x-7)}{(3x-7)} = (2x+1)$
do you understand ?
P.S. when said multiply all .... means that you multiply and left and right side of equation !!!
7. i really don't understand this!! could i do box method with 2x+1 and 3x-7? to get 6x^2-x-6?
8. Originally Posted by andyboy179
i really don't understand this!! could i do box method with 2x+1 and 3x-7? to get 6x^2-x-6?
let's look at this this way ...
$2x = 2 \Rightarrow x = 2/2 = 1$
multiply both sides of equation with 2 and you will have
$4x= 4 \Rightarrow x = 4/4 = 1$
do you see that nothing is changed ?
now with fractions ....
$\frac {2x}{2} = 1$
because of that under fraction is 2 (can be anything) to lose that fraction you multiply both sides with that whatever is under fraction ....
in this case multiply with 2
$\frac {2x}{2}\cdot 2 = 1 \cdot 2 \Rightarrow \frac {2x \cdot 2 }{2} = 1\cdot 2 \Rightarrow 2x = 2 \Rightarrow x =2/2 = 1$
9. i kinda understand now. you say multiply both sides with 2 so how would i do 2x+1x2? and 3x-7x2?
10. Originally Posted by andyboy179
i kinda understand now. you say multiply both sides with 2 so how would i do 2x+1x2? and 3x-7x2?
you don't multiply by two in your problem there... i just do that with my example to show you that nothing changes if you multiply both sides (or add or divide or ... ) Whatever is "down" in fraction (can't figure out how to write it on English ) you multiply both sides with THAT in your case it's 3x-7
so you will be free of the fraction
P.S. when multiplying fraction with number you don't multiply down expression
$\displaystyle \frac {x+y}{a+b} \cdot 10 = \frac {10x +10y}{a+b}$
but only if you are multiplying fraction with fraction ...
$\displaystyle \frac {x+y}{a+b} \cdot \frac {10}{3} = \frac {10x+10y}{3a+3b}$
11. OHHH so would it be 6x^2 - 10x -6?
12. Originally Posted by andyboy179
OHHH so would it be 6x^2 - 10x -6?
what would that be ... ????
lol... don't know what to do now .... probably someone who write better in English can help you maybe that's the problem
sorry...
13. would the answer be 2.3?? don't worry i can understand the english but im just finding it hard to pick up how to do these sort of questions!
14. Originally Posted by andyboy179
would the answer be 2.3?? don't worry i can understand the english but im just finding it hard to pick up how to do these sort of questions!
you have solution in my first post (#2)
it's not problem for you with English ... it's mine
P.S. you need to get familiar with basic operations with fractions, and on fractions (as multiplying , divide, add , subtract .... ) so you will not have problem piking up stuff like this
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http://energyresources.asmedigitalcollection.asme.org/article.aspx?articleid=1414985
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0
Research Papers
# Hydraulics of Drilling With Aerated Muds Under Simulated Borehole Conditions
[+] Author and Article Information
L. Zhou, R. M. Ahmed, S. Z. Miska, N. E. Takach, M. Yu
University of Tulsa, North Campus, Tulsa, OK 74110
A. Saasen1
StatoilHydro ASA, Stavanger, N-4035 Norway
1
Present address: University of Stavanger, Norway.
J. Energy Resour. Technol 132(1), 011002 (Mar 26, 2010) (8 pages) doi:10.1115/1.4001133 History: Received March 19, 2008; Revised April 14, 2009; Published March 26, 2010; Online March 26, 2010
## Abstract
Maintaining optimum circulation rates is important in aerated mud drilling operations. However, reliable predictions of the optimum rates require accurate modeling of the frictional pressure loss at bottom-hole conditions. This paper presents a mechanistic model for underbalanced drilling with aerated muds. Extensive experiments in a unique field-scale high pressure and high temperature flow loop were performed to verify the predictions of the model. This flow loop has a $150×89 mm2$$(6″×3.5″)$ horizontal annular geometry and is 22 m long. In the experiments, cuttings were introduced at a rate of 7.5 kg/min, representing a penetration rate of 15 m/h in the annular test section. The liquid phase flow rates were in the range of $0.30–0.57 m3/min$, representing superficial liquid velocities in the range of 0.47–0.90 m/s. The gas liquid ratio (gas volume fraction under in situ condition) was varied from 0.0 to 0.38. Test pressures and temperatures ranged from 1.28 to 3.45 MPa, and $27°C$ to $80°C$, respectively. Gas liquid ratios were chosen to simulate practical gas liquid ratios under downhole conditions. For all the test runs, pressure drop and cuttings bed height over the entire annular section were measured. Flow patterns were identified by visual observations through a view port. The hydraulic model determines the flow pattern and predicts frictional pressure losses in a horizontal concentric annulus. The influences of the gas liquid ratio and other flow parameters on the frictional pressure loss are analyzed using this model. Comparisons between the model predictions and experimental measurements show a satisfactory agreement. The present model is useful for the design of underbalanced drilling applications in a horizontal wellbore.
<>
## Figures
Figure 6
Simplified slug flow configurations
Figure 7
Measured pressure drop versus elapsed time
Figure 1
A simplified schematic drawing of the flow loop
Figure 2
Test facility showing separation tower (right) and injection tower (left)
Figure 3
Test section of the flow loop showing the experimental setup
Figure 4
Schematic of flow of aerated muds with cuttings
Figure 5
Stratified aerated mud flow configurations with stationary cuttings bed
Figure 10
Measured and predicted differential pressure versus GLR for test group No. 2 (QL=0.38 m3/min, T=27°C, P=1.28 MPa)
Figure 11
Measured and predicted differential pressure versus GLR for test group No. 2 (QL=0.45 m3/min, T=27°C, P=1.28 MPa)
Figure 12
Measured and predicted differential pressure versus GLR for test group No. 3 (QL=0.38 m3/min, T=77°C, P=1.52 MPa)
Figure 13
Measured and predicted differential pressure versus GLR for test group No. 3 (QL=0.45 m3/min, T=77°C, P=1.52 MPa)
Figure 14
Measured and predicted differential pressure versus GLR for test group No. 4 (QL=0.38 m3/min, T=80°C, P=3.45 MPa)
Figure 15
Measured and predicted differential pressure versus GLR for test group No. 4 (QL=0.45 m3/min, T=80°C, P=3.45 MPa)
Figure 8
Measured differential pressure versus GLR for test group No. 1 (T=49°C, P=1.38 MPa)
Figure 9
Measured differential pressure versus liquid flow rate for test group No. 1 (T=49°C, P=1.38 MPa)
## Errata
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https://www.mersenneforum.org/showthread.php?s=c5cd80d0ad41115032e9c498f0c34939&p=549072
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mersenneforum.org IBM June 2020
Register FAQ Search Today's Posts Mark Forums Read
2020-06-25, 17:40 #12
EdH
"Ed Hall"
Dec 2009
52×131 Posts
Quote:
Originally Posted by bsquared Code: >> x=2^7* 5 * 23 * 127 * 659 * 53323 * 1876187 * 97544836889 * 665320793909 7998766649128898059663516612687535453720960 >> totient(x) 3031634148236289733373855928919180891127808 >> sigma(x,1)-x 12142697391577851168337274092012830083559040 >>
What program gave you totient() and sigma() functions? I expected YAFU from the ">>" prompts, but my YAFU doesn't like them.
2020-06-25, 19:21 #13 bsquared "Ben" Feb 2007 22·32·7·13 Posts It is yafu starting from a r381 (wip-branch).
2020-06-25, 19:31 #14
EdH
"Ed Hall"
Dec 2009
1100110010112 Posts
Quote:
Originally Posted by bsquared It is yafu starting from a r381 (wip-branch).
Of course! The two machines I checked were only at 380!
Thanks!
2020-06-25, 19:38 #15 yae9911 "Hugo" Jul 2019 Germany 31 Posts PARI/GP confirms Code: x=2^7* 5 * 23 * 127 * 659 * 53323 * 1876187 * 97544836889 * 665320793909 %111 = 7998766649128898059663516612687535453720960 (21:22) gp > eulerphi(x) %112 = 3031634148236289733373855928919180891127808 (21:22) gp > sigma(x)-x %113 = 12142697391577851168337274092012830083559040 @Dieter: The solution doesn't have prime factors > 2^64.
2020-06-26, 12:28 #16 Dieter Oct 2017 5016 Posts Thank you for the confirmations! @yae9911: Thank you. Otherwise I would have given up. It is a critical point, if a number fits into one register or not.
2020-07-05, 22:21 #17 uau Jan 2017 73 Posts Here's the program I used: Code: #!/usr/bin/python3 from gmpy2 import is_prime def rec(n, target, used=set(), res=1, divsum=1, last1=None, last2=None): if n == 1: if divsum - res == target: print(res) if 2 not in used and divsum * 3 - 2*res == target: print(2*res) return p, i = divs[n] e = p-1 if n % e == 0: used.add(p) rec(n//e//p**i, target, used, res*p**(i+1), divsum*((p**(i+2)-1)//(p-1))) used.remove(p) r = n // p for k in divisors(r): if p == last1 and k >= last2: continue t = k*p + 1 if t in primes and t not in used: rec(r//k, target, used, res*t, divsum*(t+1), p, k) factors = [(2, 18), (3, 3), (7, 2), (11, 1), (13, 1), (47, 1), (3169, 1), (8887, 1), (66643, 1), (72161, 1), (2495839, 1), (3847619, 1)] target = 12142680281284711468101282998309016699980172 divs = {1:None} for p, i in factors: prev = list(divs.keys()) for j in range(1, i+1): pp = p ** j for d in prev: divs[d * pp] = (p, j) def divisors(n, divs=divs): if n == 1: yield 1 return p, i = divs[n] pows = [1] for j in range(i): pows.append(pows[-1]*p) for d in divisors(n // pows[-1]): for m in pows: yield d * m primes = set(d+1 for d in divs if is_prime(d+1)) rec(max(divs), target) Given the number of smaller relative primes, RP=3031634148236289733373855928919180891127808, the program finds all possible numbers for which euler_phi(n) equals this given value, and checks whether the divisor sum has the desired property. Since each prime power factor p^i in n produces a factor of (p-1)p^(i-1) in RP, it follows that (p-1) divides RP, and p is of the form d+1 for some divisor d or RP. This limits the set of primes possibly appearing in n to that set. Thus the problem essentially becomes a packing problem - find a subset of powers of those primes such that the factors of (p-1)p^(i-1) add up to match exactly those in RP. The program iterates through possible solutions by trying different ways to select a prime power for n that reduces or eliminates the largest remaining prime factor in RP, then recursively solving the remaining values. There are two separate cases - eliminating a factor p with p^i with i > 1 (under "if n% e == 0:") and eliminating it a single larger prime of the form k*p+1. The "used" set is needed to avoid a case like 3^2 being used to eliminate a factor of 3 from RP, then trying to use 3 again to eliminate a factor of 2. The program is careful to avoid repeating work by trying the same solution again. It won't try both selecting 2 and then 3, and later 3 then then 2. Eliminating a factor p with a power p^i with i > 1 always eliminates all the remaining powers of p, so it'll always be the last operation for that prime. The "last1" and "last2" arguments are used to ensure that factors removing same prime are in decreasing order - to eliminate powers of 2, adding 5 then 3 is allowed, but not vice versa. The divisor sum is also calculated recursively, as it can also be expressed as a product of independent terms from each p^i factor in n.
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http://superuser.com/questions/120660/where-does-the-get-command-in-psftp-putty-save-the-file?answertab=active
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# where does the “get” command in PSFTP (PuTTY) save the file?
I'm used to running ssh on a Unix command-line and am working for the first time with PuTTY on Windows. When I type
get file.txt
on the PSFTP command line, where does file.txt go? PSFTP returned:
remote:/somedirectories/file.txt => local:file.txt
but I can't find the file locally.
Thanks!
-
lpwd
lcd \path\to\new\dir
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http://canadam.math.ca/2011/program/abs/cmg.html
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CanaDAM 2011 University of Victoria, May 31 - June 3, 2011 www.cms.math.ca//2011
Bioinformatics
Org: Miklos Csuros (University of Montreal)
[PDF]
CEDRIC CHAUVE, Simon Fraser University
Mapping ancestral genomes with massive gene loss: a matrix sandwich problem [PDF]
Reconstructing ancestral genomes generally requires markers that are present in all extant descendants. Motivated by the reconstruction of plant and vertebrate genomes, we introduce a new method that handles non-universal markers, by combining the consecutive-ones property with the classical notion of sandwich graph. This leads to a notion of sandwich consecutive-ones matrix. We initiate a study of this problem and apply our results on real datasets. Collaboration with Eric Tannier, Jerome Salse and Haris Gavranovic.
LUCIAN ILIE, University of Western Ontario
Fast combinatorial computation of good seeds for genome alignment [PDF]
Aligning entire genomes requires high sensitivity and speed. Whereas other methods trade one for the other, multiple spaced seeds increase both. They have many applications to homology search, alignment of next generation sequencing reads, oligonucleotide design, etc. Finding optimal seeds is a hard problem and even heuristic algorithms are exponential. We present the only polynomial-time algorithm, whose ideas stemmed from stringology. It is much faster and computes betters seeds than all the other programs.
BIN MA, University of Waterloo
Algorithms for Protein/Peptide Sequencing with Mass Spectrometry [PDF]
The talk reviews some computational problems arising in mass spectrometry data analysis for protein identification and sequencing. In particular, the peptide de novo sequencing problem and its algorithm will be introduced. The possible sequencing errors also affect the traditional sequence homology search model (the Smith-Waterman algorithm). In the talk we will also examine such effect and introduce a new homology search model that tolerates both the de novo sequencing errors and the evolutionary mutations.
PAUL MEDVEDEV, University of California, San Diego
Paired de Bruijn Graphs: a Novel Approach for Incorporating Mate Pair Information into Genome Assemblers [PDF]
Genome assembly can be viewed as a problem of reconstructing contiguous portions of a string (contigs) given a random sampling of its substrings. Algorithms based on deBruijn graphs are some of the most powerful and practical methods for assembly. Mate pairs, which are pairs of reads between which the distances are approximately known, have been algorithmically incorporated into most assemblers as various heuristic post-processing steps to correct the deBruijn graph or to link contigs into scaffolds. Such methods have allowed the identification of longer contigs in the presence of long repeating regions; however, they can still fail to resolve complex repeats.
Here, we introduce the paired de Bruijn graph, a generalization of the deBruijn graph that incorporates mate pair information into the graph structure itself instead of analyzing mate pairs at a post-processing step. This graph has the potential to be used in place of the deBruijn graph in any deBruijn graph based assembler, maintaining all other assembly steps such as error-correction and repeat resolution.
This is joint work with SonPham, MarkChaisson, GlennTesler, and PavelPevzner.
JURAJ STACHO, Caesarea Rothschild Institute, University of Haifa
Unique perfect phylogeny is NP-hard [PDF]
We answer, in the affirmative, the following question proposed in 1992 by Mike Steel as a \$100 challenge: {\em Is the following problem NP-hard? Given a ternary phylogenetic$X$-tree$\cal T$and a collection$\cal Q$of quartet subtrees on$X$, is$\cal T$the only tree that displays$\cal Q\$?''} As a particular consequence of this, we show that the unique chordal sandwich problem is also NP-hard.
Joint work with Michel Habib.
Handling of online submissions has been provided by the CMS.
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http://kncourseworkyibe.hyve.me/fermilab-thesis-2008-15.html
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# Fermilab thesis 2008 15
The fermilab tevatron is currently the world's highest energy colliding beam facility 15 pm , thesis or dissertation, august 1, 2008. S mixing at the d-zero detector at fermilab using the s mixing at the d-zero detector at fermilab using the semi-leptonic decay b0 s d this thesis describes. Good research paper ideas fermilab thesis 2008 15 why does medicine cost so much why does our govt good research paper ideas computer operating systems essay. Design, simulation, commissioning and test of the of an intense group work during my internship at fermilab on 2008 3 conceptual design of the tertiary beam 15. Expository essay on music heathcliff anti hero essay fermilab thesis 2008 15 so the companies may have complied the lowered the nicotine level and added more garbage. Fermilab annual users meeting, june 4-5, 2008 2 outline a little about the lhc what is the cms detector who is us cms is the cms detector ready15 april 2008.
Users’ executive committee introduction 14:00 ura thesis prize winners fred bernthal major uec projects 2007-2008. Università degli studi di trieste 2008 fermilab-thesis-2008-111 devoted to trieste 24 the mixing effect in the neutral mesons 15. The genie neutrino monte carlo generator - andreopoulos, c et al nuclinstrummeth a614 (2010) 87-104 arxiv:09052517 [hep-ph] fermilab-pub-09-418-cd : measurement. The cdf experiment, which uses p{bar p} collisions at {radical}s = 19 tev produced at the fermilab tevatron, is unique in its ability to observe all flavors of b.
Fermilab-thesis-2008-65 research paper reference page mla group organic sales, which exclude healthcare and personal care, were down 1 as the volume growth was. Batavia wants federal funding restored for fermilab daily herald jan 8, 2008 by about 15 percent and stop thesis related to work conducted at fermilab or in. Fermilab cdf collaboration publishes representing 63 institutions in 15 countries was no longer collecting new data fourth phd thesis.
Fermilab today is online at: wwwfnal elected in 2008 conducted at fermilab or in collaboration with fermilab scientists the thesis must be completed. 2017-11-15: measurement of the fermilab-thesis-2008-108 added: 2016-10-13: measurements of the top-quark decay width and mass at cdf using the template method. Ospanov r 2008 (university of texas at austin) fermilab-thesis-2008-04 phd thesis marshall j s 2008 (university of cambridge) fermilab-thesis-2008-20 phd thesis. Fermilab thesis 2008 63 anyhow, if you have any ideas or techniques for new blog owners please share marriage rate essay une grande partie de l'rgie se par le soleil.
Fermilab thesis 2008 15 dov gordon phd thesis seems to me, that they really don39t alot of the time globalization colonialism essay and technology are plotting a. Fermilab-thesis-2008-15: han, bo-young: fnal-e-0830 (cdf) rochester u measurement of the $w$ boson production charge asymmetry in $p\bar{p}$ collisions.
Fermilab thesis 2008 15
Rated 4/5 based on 30 review
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https://nofima.no/publikasjon/1137235/
|
Publisert 2007
## Publikasjonsdetaljer
Tidsskrift : Aquaculture , vol. 262 , p. 78–85 , 2007
Utgiver : Elsevier
Internasjonale standardnummer :
Trykt : 0044-8486
Elektronisk : 1873-5622
Publikasjonstype : Vitenskapelig artikkel
Bidragsytere : Siikavuopio, Sten Ivar; Dale, Trine; Mortensen, Atle
Har du spørsmål om noe vedrørende publikasjonen, kan du kontakte Nofimas bibliotekleder.
Kjetil Aune
Bibliotekleder
[email protected]
## Sammendrag
In this study the effects of different stocking densities on survival, gonad growth and feed intake in adult green sea urchin
(Strongylocentrotus droebachiensis) were examined. Two size groups of sea urchins with respective initial mean weight of 45 g (S)
and 70 g (L) were used. The experiments were carried out in 755 l plastic tanks divided into chambers by vertical fibreglass
lamellae. In the two experiments stocking densities of 6, 12, 14 and 16 kg m−2 (Exp I) and 3, 6 and 8 kg m−2 (Exp II) were used.
Sea urchins reared individually in compartmentalised raceways were used as controls in both experiments. All groups were fed a
formulated moist feed ad libitum for 60 days at 8 °C (±0.5). Mortality was observed in all groups, except for the control group and
the lowest density group of large sea urchins (3 kg m−2, L). Both mortality and occurrence of injuries increased significantly with
increasing stocking density in both experiments and for both size groups. In the highest density groups mortality was 60% (L) and
80% (S). There was a significant increase in gonad index during the experimental period in both experiments. Increased stocking
density had a significantly negative effect on gonad growth in both size groups while feed intake was unaffected. The results show
that adult S. droebachiensis can maintain high survival rate and high gonad growth at stocking densities up 6 kg m−2 in holding
facilities of the design used in the present study.
(Strongylocentrotus droebachiensis) were examined. Two size groups of sea urchins with respective initial mean weight of 45 g (S)
and 70 g (L) were used. The experiments were carried out in 755 l plastic tanks divided into chambers by vertical fibreglass
lamellae. In the two experiments stocking densities of 6, 12, 14 and 16 kg m−2 (Exp I) and 3, 6 and 8 kg m−2 (Exp II) were used.
Sea urchins reared individually in compartmentalised raceways were used as controls in both experiments. All groups were fed a
formulated moist feed ad libitum for 60 days at 8 °C (±0.5). Mortality was observed in all groups, except for the control group and
the lowest density group of large sea urchins (3 kg m−2, L). Both mortality and occurrence of injuries increased significantly with
increasing stocking density in both experiments and for both size groups. In the highest density groups mortality was 60% (L) and
80% (S). There was a significant increase in gonad index during the experimental period in both experiments. Increased stocking
density had a significantly negative effect on gonad growth in both size groups while feed intake was unaffected. The results show
that adult S. droebachiensis can maintain high survival rate and high gonad growth at stocking densities up 6 kg m−2 in holding
facilities of the design used in the present study.
|
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|
https://python.quantecon.org/eig_circulant.html
|
# 6. Circulant Matrices¶
## 6.1. Overview¶
This lecture describes circulant matrices and some of their properties.
Circulant matrices have a special structure that connects them to useful concepts including
• convolution
• Fourier transforms
• permutation matrices
Because of these connections, circulant matrices are widely used in machine learning, for example, in image processing.
We begin by importing some Python packages
import numpy as np
from numba import njit
import matplotlib.pyplot as plt
%matplotlib inline
np.set_printoptions(precision=3, suppress=True)
## 6.2. Constructing a Circulant Matrix¶
To construct an $$N \times N$$ circulant matrix, we need only the first row, say,
$\begin{bmatrix} c_{0} & c_{1} & c_{2} & c_{3} & c_{4} & \cdots & c_{N-1} \end{bmatrix} .$
After setting entries in the first row, the remaining rows of a circulant matrix are determined as follows:
(6.1)$\begin{split} C=\left[\begin{array}{ccccccc} c_{0} & c_{1} & c_{2} & c_{3} & c_{4} & \cdots & c_{N-1}\\ c_{N-1} & c_{0} & c_{1} & c_{2} & c_{3} & \cdots & c_{N-2}\\ c_{N-2} & c_{N-1} & c_{0} & c_{1} & c_{2} & \cdots & c_{N-3}\\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ c_{3} & c_{4} & c_{5} & c_{6} & c_{7} & \cdots & c_{2}\\ c_{2} & c_{3} & c_{4} & c_{5} & c_{6} & \cdots & c_{1}\\ c_{1} & c_{2} & c_{3} & c_{4} & c_{5} & \cdots & c_{0} \end{array}\right] \end{split}$
It is also possible to construct a circulant matrix by creating the transpose of the above matrix, in which case only the first column needs to be specified.
Let’s write some Python code to generate a circulant matrix.
@njit
def construct_cirlulant(row):
N = row.size
C = np.empty((N, N))
for i in range(N):
C[i, i:] = row[:N-i]
C[i, :i] = row[N-i:]
return C
# a simple case when N = 3
construct_cirlulant(np.array([1., 2., 3.]))
array([[1., 2., 3.],
[3., 1., 2.],
[2., 3., 1.]])
### 6.2.1. Some Properties of Circulant Matrices¶
Here are some useful properties:
Suppose that $$A$$ and $$B$$ are both circulant matrices. Then it can be verified that
• The transpose of a circulant matrix is a circulant matrix.
• $$A + B$$ is a circulant matrix
• $$A B$$ is a circulant matrix
• $$A B = B A$$
Now consider a circulant matrix with first row
$c = \begin{bmatrix} c_0 & c_1 & \cdots & c_{N-1} \end{bmatrix}$
and consider a vector
$a = \begin{bmatrix} a_0 & a_1 & \cdots & a_{N-1} \end{bmatrix}$
The convolution of vectors $$c$$ and $$a$$ is defined as the vector $$b = c * a$$ with components
(6.2)$b_k = \sum_{i=0}^{n-1} c_{k-i} a_i$
We use $$*$$ to denote convolution via the calculation described in equation (6.2).
It can be verified that the vector $$b$$ satisfies
$b = C^T a$
where $$C^T$$ is the transpose of the circulant matrix defined in equation (6.1).
## 6.3. Connection to Permutation Matrix¶
A good way to construct a circulant matrix is to use a permutation matrix.
Before defining a permutation matrix, we’ll define a permutation.
A permutation of a set of the set of non-negative integers $$\{0, 1, 2, \ldots \}$$ is a one-to-one mapping of the set into itself.
A permutation of a set $$\{1, 2, \ldots, n\}$$ rearranges the $$n$$ integers in the set.
A permutation matrix is obtained by permuting the rows of an $$n \times n$$ identity matrix according to a permutation of the numbers $$1$$ to $$n$$.
Thus, every row and every column contain precisely a single $$1$$ with $$0$$ everywhere else.
Every permutation corresponds to a unique permutation matrix.
For example, the $$N \times N$$ matrix
(6.3)$\begin{split} P=\left[\begin{array}{cccccc} 0 & 1 & 0 & 0 & \cdots & 0\\ 0 & 0 & 1 & 0 & \cdots & 0\\ 0 & 0 & 0 & 1 & \cdots & 0\\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ 0 & 0 & 0 & 0 & \cdots & 1\\ 1 & 0 & 0 & 0 & \cdots & 0 \end{array}\right] \end{split}$
serves as a cyclic shift operator that, when applied to an $$N \times 1$$ vector $$h$$, shifts entries in rows $$2$$ through $$N$$ up one row and shifts the entry in row $$1$$ to row $$N$$.
Eigenvalues of the cyclic shift permutation matrix $$P$$ defined in equation (6.3) can be computed by constructing
$\begin{split} P-\lambda I=\left[\begin{array}{cccccc} -\lambda & 1 & 0 & 0 & \cdots & 0\\ 0 & -\lambda & 1 & 0 & \cdots & 0\\ 0 & 0 & -\lambda & 1 & \cdots & 0\\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ 0 & 0 & 0 & 0 & \cdots & 1\\ 1 & 0 & 0 & 0 & \cdots & -\lambda \end{array}\right] \end{split}$
and solving
$\textrm{det}(P - \lambda I) = (-1)^N \lambda^{N}-1=0$
Eigenvalues $$\lambda_i$$ can be complex.
Magnitudes $$\mid \lambda_i \mid$$ of these eigenvalues $$\lambda_i$$ all equal $$1$$.
Thus, singular values of the permutation matrix $$P$$ defined in equation (6.3) all equal $$1$$.
It can be verified that permutation matrices are orthogonal matrices:
$P P' = I$
## 6.4. Examples with Python¶
Let’s write some Python code to illustrate these ideas.
@njit
def construct_P(N):
P = np.zeros((N, N))
for i in range(N-1):
P[i, i+1] = 1
P[-1, 0] = 1
return P
P4 = construct_P(4)
P4
array([[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.],
[1., 0., 0., 0.]])
# compute the eigenvalues and eigenvectors
𝜆, Q = np.linalg.eig(P4)
for i in range(4):
print(f'𝜆{i} = {𝜆[i]:.1f} \nvec{i} = {Q[i, :]}\n')
𝜆0 = -1.0+0.0j
vec0 = [-0.5+0.j 0. -0.5j 0. +0.5j -0.5+0.j ]
𝜆1 = 0.0+1.0j
vec1 = [ 0.5+0.j 0.5+0.j 0.5-0.j -0.5+0.j]
𝜆2 = 0.0-1.0j
vec2 = [-0.5+0.j -0. +0.5j -0. -0.5j -0.5+0.j ]
𝜆3 = 1.0+0.0j
vec3 = [ 0.5+0.j -0.5+0.j -0.5-0.j -0.5+0.j]
In graphs below, we shall portray eigenvalues of a shift permutation matrix in the complex plane.
These eigenvalues are uniformly distributed along the unit circle.
They are the $$n$$ roots of unity, meaning they are the $$n$$ numbers $$z$$ that solve $$z^n =1$$, where $$z$$ is a complex number.
In particular, the $$n$$ roots of unity are
$z = \exp\left(\frac{2 \pi j k }{N} \right) , \quad k = 0, \ldots, N-1$
where $$j$$ denotes the purely imaginary unit number.
fig, ax = plt.subplots(2, 2, figsize=(10, 10))
for i, N in enumerate([3, 4, 6, 8]):
row_i = i // 2
col_i = i % 2
P = construct_P(N)
𝜆, Q = np.linalg.eig(P)
circ = plt.Circle((0, 0), radius=1, edgecolor='b', facecolor='None')
for j in range(N):
ax[row_i, col_i].scatter(𝜆[j].real, 𝜆[j].imag, c='b')
ax[row_i, col_i].set_title(f'N = {N}')
ax[row_i, col_i].set_xlabel('real')
ax[row_i, col_i].set_ylabel('imaginary')
plt.show()
For a vector of coefficients $$\{c_i\}_{i=0}^{n-1}$$, eigenvectors of $$P$$ are also eigenvectors of
$C = c_{0} I + c_{1} P + c_{2} P^{2} +\cdots + c_{N-1} P^{N-1}.$
Consider an example in which $$N=8$$ and let $$w = e^{-2 \pi j / N}$$.
It can be verified that the matrix $$F_8$$ of eigenvectors of $$P_{8}$$ is
$\begin{split} F_{8}=\left[\begin{array}{ccccc} 1 & 1 & 1 & \cdots & 1\\ 1 & w & w^{2} & \cdots & w^{7}\\ 1 & w^{2} & w^{4} & \cdots & w^{14}\\ 1 & w^{3} & w^{6} & \cdots & w^{21}\\ 1 & w^{4} & w^{8} & \cdots & w^{28}\\ 1 & w^{5} & w^{10} & \cdots & w^{35}\\ 1 & w^{6} & w^{12} & \cdots & w^{42}\\ 1 & w^{7} & w^{14} & \cdots & w^{49} \end{array}\right] \end{split}$
The matrix $$F_8$$ defines a Discete Fourier Transform.
To convert it into an orthogonal eigenvector matrix, we can simply normalize it by dividing every entry by $$\sqrt{8}$$.
• stare at the first column of $$F_8$$ above to convince yourself of this fact
The eigenvalues corresponding to each eigenvector are $$\{w^{j}\}_{j=0}^{7}$$ in order.
def construct_F(N):
w = np.e ** (-complex(0, 2*np.pi/N))
F = np.ones((N, N), dtype=complex)
for i in range(1, N):
F[i, 1:] = w ** (i * np.arange(1, N))
return F, w
F8, w = construct_F(8)
w
(0.7071067811865476-0.7071067811865475j)
F8
array([[ 1. +0.j , 1. +0.j , 1. +0.j , 1. +0.j ,
1. +0.j , 1. +0.j , 1. +0.j , 1. +0.j ],
[ 1. +0.j , 0.707-0.707j, 0. -1.j , -0.707-0.707j,
-1. -0.j , -0.707+0.707j, -0. +1.j , 0.707+0.707j],
[ 1. +0.j , 0. -1.j , -1. -0.j , -0. +1.j ,
1. +0.j , 0. -1.j , -1. -0.j , -0. +1.j ],
[ 1. +0.j , -0.707-0.707j, -0. +1.j , 0.707-0.707j,
-1. -0.j , 0.707+0.707j, 0. -1.j , -0.707+0.707j],
[ 1. +0.j , -1. -0.j , 1. +0.j , -1. -0.j ,
1. +0.j , -1. -0.j , 1. +0.j , -1. -0.j ],
[ 1. +0.j , -0.707+0.707j, 0. -1.j , 0.707+0.707j,
-1. -0.j , 0.707-0.707j, -0. +1.j , -0.707-0.707j],
[ 1. +0.j , -0. +1.j , -1. -0.j , 0. -1.j ,
1. +0.j , -0. +1.j , -1. -0.j , 0. -1.j ],
[ 1. +0.j , 0.707+0.707j, -0. +1.j , -0.707+0.707j,
-1. -0.j , -0.707-0.707j, 0. -1.j , 0.707-0.707j]])
# normalize
Q8 = F8 / np.sqrt(8)
# verify the orthogonality (unitarity)
Q8 @ np.conjugate(Q8)
array([[ 1.+0.j, -0.+0.j, -0.+0.j, -0.+0.j, -0.+0.j, 0.+0.j, 0.+0.j,
0.+0.j],
[-0.-0.j, 1.+0.j, -0.+0.j, -0.+0.j, -0.+0.j, -0.+0.j, 0.+0.j,
0.+0.j],
[-0.-0.j, -0.-0.j, 1.+0.j, -0.+0.j, -0.+0.j, -0.+0.j, 0.+0.j,
0.+0.j],
[-0.-0.j, -0.-0.j, -0.-0.j, 1.+0.j, -0.+0.j, -0.+0.j, -0.+0.j,
-0.+0.j],
[-0.-0.j, -0.-0.j, -0.-0.j, -0.-0.j, 1.+0.j, -0.+0.j, -0.+0.j,
-0.+0.j],
[ 0.-0.j, -0.-0.j, -0.-0.j, -0.-0.j, -0.-0.j, 1.+0.j, -0.+0.j,
-0.+0.j],
[ 0.-0.j, 0.-0.j, 0.-0.j, -0.-0.j, -0.-0.j, -0.-0.j, 1.+0.j,
-0.+0.j],
[ 0.-0.j, 0.-0.j, 0.-0.j, -0.-0.j, -0.-0.j, -0.-0.j, -0.-0.j,
1.+0.j]])
Let’s verify that $$k$$th column of $$Q_{8}$$ is an eigenvector of $$P_{8}$$ with an eigenvalue $$w^{k}$$.
P8 = construct_P(8)
diff_arr = np.empty(8, dtype=complex)
for j in range(8):
diff = P8 @ Q8[:, j] - w ** j * Q8[:, j]
diff_arr[j] = diff @ diff.T
diff_arr
array([ 0.+0.j, -0.+0.j, -0.+0.j, -0.+0.j, -0.+0.j, -0.+0.j, -0.+0.j,
-0.+0.j])
## 6.5. Associated Permutation Matrix¶
Next, we execute calculations to verify that the circulant matrix $$C$$ defined in equation (6.1) can be written as
$C = c_{0} I + c_{1} P + \cdots + c_{n-1} P^{n-1}$
and that every eigenvector of $$P$$ is also an eigenvector of $$C$$.
We illustrate this for $$N=8$$ case.
c = np.random.random(8)
c
array([0.288, 0.499, 0.78 , 0.585, 0.872, 0.081, 0.766, 0.271])
C8 = construct_cirlulant(c)
Compute $$c_{0} I + c_{1} P + \cdots + c_{n-1} P^{n-1}$$.
N = 8
C = np.zeros((N, N))
P = np.eye(N)
for i in range(N):
C += c[i] * P
P = P8 @ P
C
array([[0.288, 0.499, 0.78 , 0.585, 0.872, 0.081, 0.766, 0.271],
[0.271, 0.288, 0.499, 0.78 , 0.585, 0.872, 0.081, 0.766],
[0.766, 0.271, 0.288, 0.499, 0.78 , 0.585, 0.872, 0.081],
[0.081, 0.766, 0.271, 0.288, 0.499, 0.78 , 0.585, 0.872],
[0.872, 0.081, 0.766, 0.271, 0.288, 0.499, 0.78 , 0.585],
[0.585, 0.872, 0.081, 0.766, 0.271, 0.288, 0.499, 0.78 ],
[0.78 , 0.585, 0.872, 0.081, 0.766, 0.271, 0.288, 0.499],
[0.499, 0.78 , 0.585, 0.872, 0.081, 0.766, 0.271, 0.288]])
C8
array([[0.288, 0.499, 0.78 , 0.585, 0.872, 0.081, 0.766, 0.271],
[0.271, 0.288, 0.499, 0.78 , 0.585, 0.872, 0.081, 0.766],
[0.766, 0.271, 0.288, 0.499, 0.78 , 0.585, 0.872, 0.081],
[0.081, 0.766, 0.271, 0.288, 0.499, 0.78 , 0.585, 0.872],
[0.872, 0.081, 0.766, 0.271, 0.288, 0.499, 0.78 , 0.585],
[0.585, 0.872, 0.081, 0.766, 0.271, 0.288, 0.499, 0.78 ],
[0.78 , 0.585, 0.872, 0.081, 0.766, 0.271, 0.288, 0.499],
[0.499, 0.78 , 0.585, 0.872, 0.081, 0.766, 0.271, 0.288]])
Now let’s compute the difference between two circulant matrices that we have constructed in two different ways.
np.abs(C - C8).max()
0.0
The $$k$$th column of $$P_{8}$$ associated with eigenvalue $$w^{k-1}$$ is an eigenvector of $$C_{8}$$ associated with an eigenvalue $$\sum_{h=0}^{7} c_{j} w^{h k}$$.
𝜆_C8 = np.zeros(8, dtype=complex)
for j in range(8):
for k in range(8):
𝜆_C8[j] += c[k] * w ** (j * k)
𝜆_C8
array([ 4.143+0.j , -0.51 -0.532j, -0.385+0.276j, -0.658-0.503j,
1.27 +0.j , -0.658+0.503j, -0.385-0.276j, -0.51 +0.532j])
We can verify this by comparing C8 @ Q8[:, j] with 𝜆_C8[j] * Q8[:, j].
# verify
for j in range(8):
diff = C8 @ Q8[:, j] - 𝜆_C8[j] * Q8[:, j]
print(diff)
[0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.-0.j -0.-0.j -0.-0.j -0.-0.j -0.-0.j -0.-0.j -0.+0.j]
[-0.+0.j -0.-0.j -0.-0.j -0.+0.j 0.-0.j -0.-0.j -0.-0.j -0.+0.j]
[-0.+0.j 0.-0.j -0.-0.j -0.+0.j 0.-0.j -0.-0.j 0.+0.j -0.-0.j]
[-0.-0.j -0.-0.j 0.-0.j 0.+0.j -0.-0.j -0.+0.j 0.-0.j 0.+0.j]
[ 0.+0.j -0.-0.j 0.-0.j 0.+0.j -0.-0.j 0.-0.j -0.+0.j 0.-0.j]
[-0.+0.j -0.-0.j 0.-0.j 0.+0.j -0.-0.j 0.-0.j 0.-0.j 0.+0.j]
[0.-0.j 0.-0.j 0.-0.j 0.-0.j 0.-0.j 0.-0.j 0.-0.j 0.+0.j]
## 6.6. Discrete Fourier Transform¶
The Discrete Fourier Transform (DFT) allows us to represent a discrete time sequence as a weighted sum of complex sinusoids.
Consider a sequence of $$N$$ real number $$\{x_j\}_{j=0}^{N-1}$$.
The Discrete Fourier Transform maps $$\{x_j\}_{j=0}^{N-1}$$ into a sequence of complex numbers $$\{X_k\}_{k=0}^{N-1}$$
where
$X_{k}=\sum_{n=0}^{N-1}x_{n}e^{-2\pi\frac{kn}{N}i}$
def DFT(x):
"The discrete Fourier transform."
N = len(x)
w = np.e ** (-complex(0, 2*np.pi/N))
X = np.zeros(N, dtype=complex)
for k in range(N):
for n in range(N):
X[k] += x[n] * w ** (k * n)
return X
Consider the following example.
$\begin{split} x_{n}=\begin{cases} 1/2 & n=0,1\\ 0 & \text{otherwise} \end{cases} \end{split}$
x = np.zeros(10)
x[0:2] = 1/2
x
array([0.5, 0.5, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ])
Apply a discrete Fourier transform.
X = DFT(x)
X
array([ 1. +0.j , 0.905-0.294j, 0.655-0.476j, 0.345-0.476j,
0.095-0.294j, -0. +0.j , 0.095+0.294j, 0.345+0.476j,
0.655+0.476j, 0.905+0.294j])
We can plot magnitudes of a sequence of numbers and the associated discrete Fourier transform.
def plot_magnitude(x=None, X=None):
data = []
names = []
xs = []
if (x is not None):
data.append(x)
names.append('x')
xs.append('n')
if (X is not None):
data.append(X)
names.append('X')
xs.append('j')
num = len(data)
for i in range(num):
n = data[i].size
plt.figure(figsize=(8, 3))
plt.scatter(range(n), np.abs(data[i]))
plt.vlines(range(n), 0, np.abs(data[i]), color='b')
plt.xlabel(xs[i])
plt.ylabel('magnitude')
plt.title(names[i])
plt.show()
plot_magnitude(x=x, X=X)
The inverse Fourier transform transforms a Fourier transform $$X$$ of $$x$$ back to $$x$$.
The inverse Fourier transform is defined as
$x_{n} = \sum_{k=0}^{N-1} \frac{1}{N} X_{k} e^{2\pi\left(\frac{kn}{N}\right)i}, \quad n=0, 1, \ldots, N-1$
def inverse_transform(X):
N = len(X)
w = np.e ** (complex(0, 2*np.pi/N))
x = np.zeros(N, dtype=complex)
for n in range(N):
for k in range(N):
x[n] += X[k] * w ** (k * n) / N
return x
inverse_transform(X)
array([ 0.5+0.j, 0.5-0.j, -0. -0.j, -0. -0.j, -0. -0.j, -0. -0.j,
-0. +0.j, -0. +0.j, -0. +0.j, -0. +0.j])
Another example is
$x_{n}=2\cos\left(2\pi\frac{11}{40}n\right),\ n=0,1,2,\cdots19$
Since $$N=20$$, we cannot use an integer multiple of $$\frac{1}{20}$$ to represent a frequency $$\frac{11}{40}$$.
To handle this, we shall end up using all $$N$$ of the availble frequencies in the DFT.
Since $$\frac{11}{40}$$ is in between $$\frac{10}{40}$$ and $$\frac{12}{40}$$ (each of which is an integer multiple of $$\frac{1}{20}$$), the complex coefficients in the DFT have their largest magnitudes at $$k=5,6,15,16$$, not just at a single frequency.
N = 20
x = np.empty(N)
for j in range(N):
x[j] = 2 * np.cos(2 * np.pi * 11 * j / 40)
X = DFT(x)
plot_magnitude(x=x, X=X)
What happens if we change the last example to $$x_{n}=2\cos\left(2\pi\frac{10}{40}n\right)$$?
Note that $$\frac{10}{40}$$ is an integer multiple of $$\frac{1}{20}$$.
N = 20
x = np.empty(N)
for j in range(N):
x[j] = 2 * np.cos(2 * np.pi * 10 * j / 40)
X = DFT(x)
plot_magnitude(x=x, X=X)
If we represent the discrete Fourier transform as a matrix, we discover that it equals the matrix $$F_{N}$$ of eigenvectors of the permutation matrix $$P_{N}$$.
We can use the example where $$x_{n}=2\cos\left(2\pi\frac{11}{40}n\right),\ n=0,1,2,\cdots19$$ to illustrate this.
N = 20
x = np.empty(N)
for j in range(N):
x[j] = 2 * np.cos(2 * np.pi * 11 * j / 40)
x
array([ 2. , -0.313, -1.902, 0.908, 1.618, -1.414, -1.176, 1.782,
0.618, -1.975, -0. , 1.975, -0.618, -1.782, 1.176, 1.414,
-1.618, -0.908, 1.902, 0.313])
First use the summation formula to transform $$x$$ to $$X$$.
X = DFT(x)
X
array([2. +0.j , 2. +0.558j, 2. +1.218j, 2. +2.174j, 2. +4.087j,
2.+12.785j, 2.-12.466j, 2. -3.751j, 2. -1.801j, 2. -0.778j,
2. -0.j , 2. +0.778j, 2. +1.801j, 2. +3.751j, 2.+12.466j,
2.-12.785j, 2. -4.087j, 2. -2.174j, 2. -1.218j, 2. -0.558j])
Now let’s evaluate the outcome of postmultiplying the eigenvector matrix $$F_{20}$$ by the vector $$x$$, a product that we claim should equal the Fourier tranform of the sequence $$\{x_n\}_{n=0}^{N-1}$$.
F20, _ = construct_F(20)
F20 @ x
array([2. +0.j , 2. +0.558j, 2. +1.218j, 2. +2.174j, 2. +4.087j,
2.+12.785j, 2.-12.466j, 2. -3.751j, 2. -1.801j, 2. -0.778j,
2. -0.j , 2. +0.778j, 2. +1.801j, 2. +3.751j, 2.+12.466j,
2.-12.785j, 2. -4.087j, 2. -2.174j, 2. -1.218j, 2. -0.558j])
Similarly, the inverse DFT can be expressed as a inverse DFT matrix $$F^{-1}_{20}$$.
F20_inv = np.linalg.inv(F20)
F20_inv @ X
array([ 2. +0.j, -0.313+0.j, -1.902+0.j, 0.908+0.j, 1.618-0.j,
-1.414-0.j, -1.176-0.j, 1.782-0.j, 0.618+0.j, -1.975+0.j,
-0. -0.j, 1.975+0.j, -0.618+0.j, -1.782-0.j, 1.176-0.j,
1.414+0.j, -1.618+0.j, -0.908-0.j, 1.902-0.j, 0.313+0.j])
|
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http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0001244
|
Research Article
# Admixture Mapping Provides Evidence of Association of the VNN1 Gene with Hypertension
• To whom correspondence should be addressed. E-mail: [email protected]
Affiliation: Department of Epidemiology and Biostatistics, School of Medicine, Case Western Reserve University, Cleveland, Ohio, United States of America
X
• Affiliation: Department of Preventive Medicine and Epidemiology, Stritch School of Medicine, Loyola University, Maywood, Illinois, United States of America
X
• Published: November 28, 2007
• DOI: 10.1371/journal.pone.0001244
## Abstract
Migration patterns in modern societies have created the opportunity to use population admixture as a strategy to identify susceptibility genes. To implement this strategy, we genotyped a highly informative ancestry marker panel of 2270 single nucleotide polymorphisms in a random population sample of African Americans (N = 1743), European Americans (N = 1000) and Mexican Americans (N = 581). We then examined the evidence for over-transmission of specific loci to cases from one of the two ancestral populations. Hypertension cases and controls were defined based on standard clinical criteria. Both case-only and case-control analyses were performed among African Americans. With the genome-wide markers we replicated the findings identified in our previous admixture mapping study on chromosomes 6 and 21 [1]. For case-control analysis we then genotyped 51 missense SNPs in 36 genes spaced across an 18.3 Mb region. Further analyses demonstrated that the missense SNP rs2272996 (or N131S) in the VNN1 gene was significantly associated with hypertension in African Americans and the association was replicated in Mexican Americans; a non-significant opposite association was observed in European Americans. This SNP also accounted for most of the evidence observed in the admixture analysis on chromosome 6. Despite these encouraging results, susceptibility loci for hypertension have been exceptionally difficult to localize and confirmation by independent studies will be necessary to establish these findings.
### Introduction
Hypertension is a consequence of common lifestyle patterns in modern society and makes an important contribution to risk of cardiovascular disease. The prevalence of hypertension varies among ethnic populations in the US from 25 to 40% and is an attributable cause for approximately 13% of deaths in whites and 24% in blacks [2]. Blood pressure is a moderately heritable trait and results from the combined effect of a complex set of genetic and environmental influences, with genes cumulatively accounting for 30% of the population variance [3]. Genome-wide linkage analysis has been widely applied in efforts to identify genomic regions harboring genes affecting the risk of hypertension. A recent review of 20 genome scans suggested that a large number genes, each exerting a small effect, is the most likely molecular architecture underlying hypertension [4]. The observed effects are highly inconsistent, however, and it is well recognized that linkage analysis has limited power when applied to complex traits [5]; locus heterogeneity may further contribute to this observed inconsistency.
As an alternative to linkage methods, numerous candidate genes selected on physiological and/or metabolic criteria have been examined using single nucleotide polymorphisms (SNPs) or associated haplotypes. Despite the myriad of reports, meta-analyses have identified few candidate loci with consistent effects across population samples [6]. For example, the genes underlying physiologic systems that control BP, like the renin-angiotensin axis, have been extensively studied, and yielding inconsistent results [7], [8]. Genome-wide association studies based on 100,000 or more SNPs are now technically feasible [9], [10] and initial results with macular degeneration, obesity, type 1 and type 2 diabetes, prostate cancer and multiple sclerosis, among others, suggest promise for this method [11][19]. These studies are still quite expensive, however, and can only be conducted by a limited number of laboratories.
On the basis of recent theoretical work it has been suggested that the information generated by recent admixture of historically separated populations can help to map disease-associated genes [20][29]. Admixture mapping can be more powerful than traditional linkage analysis when the relative risk in the parental populations is substantially different and much less genotyping is required in comparison to association analysis based on linkage disequilibrium. Admixture mapping may also be less sensitive to genetic heterogeneity [30]. Based on these theoretical propositions, Zhu et al. performed the first large-scale genome wide admixture mapping study in African Americans using the markers designed for a family-based linkage study [1]. In these analyses the distribution of marker location-specific ancestry was shifted upward in hypertensive cases versus normotensives and this shift was largely due to the loci on 6q24 and 21q21, indicating that genetic variants in these two regions may influence the risk of hypertension. Since the marker information content for inferring ancestry was relatively low in this initial study, the findings require further confirmation. Consequently using a large, multi-ethnic population sample, we conducted an admixture mapping study by genotyping a marker panel that is highly informative for ancestry for the African-American population [31]. In this paper we describe the admixture linkage results for hypertension in the Dallas Heart Study, followed by an association study of all missense SNPs in the region identified by the admixture mapping.
### Results
The demographic and descriptive characteristics of the hypertensive cases and controls are presented in Table 1 for the European-American, African-American and Mexican-American population samples. Cases were on average older than controls in all three groups, as anticipated; the percentage of treated cases was similar.
2,270 ancestry informative SNPs located on 22 autosomes selected from the SNP panel of Smith et al.[31] were successfully genotyped. After examination of Hardy-Weinberg equilibrium (HWE) for possible genotyping errors and background linkage disequilibrium which may violate the assumption of the method [25], only 1,890 SNPs were used in further analyses. Our analysis used the software ADMIXPROGRAM, which is based on the hidden Markov model using the continuous gene flow model [25]. The estimated number of generations since the occurrence of population admixture was 12 in this African-American sample. We estimated each individual's average African and European ancestries (Table S1)(European ancestry = 15.8±7.6% in cases, and 16.9±8.3% in controls) as well as ancestry at each marker locus in cases and controls separately (Table S2). We then calculated the genome-wide case-only and case-control Z scores, as presented in figure 1. The Z score can be used to evaluate evidence for a disease variant at each location and it asymptotically follows the standard normal distribution [21], [25]. We observed 6 markers with both |Zcase| and |Zcase-control|>2.0 distributed on 6 chromosomes (Table 2). Among them, the signal identified by SNP rs703193 (137cM) on chromosome 6 falls within the region identified in our previous study [1]. To further rule out that the possibility that the evidence observed on chromosome 6 results from the bias resulting either from mis-estimation of a specific marker allele's frequency in ancestral populations or background linkage disequilibrium, we calculated both the case-only and case-control Z scores using different sets of SNPs as suggested by Reich et al. [32] (Table 3). Similar evidence was observed at rs703193 when we used the SNPs with an adjacent distance greater than 1 cM. The evidence remains when either odd SNPs or even SNPs were used. Gender-specific analysis suggested that women contribute more evidence, which may in part reflect the inclusion of more hypertensive women in the study (Table 1). The relative risk of hypertension due to two copies of African ancestry allele in the region around SNP rs703193 was 1.32 (95% CI: (1.04, 1.67), p = 0.023). We also examined the region on chromosome 21 identified in our previous study [1]. Interestingly, the admixture mapping evidence in the region around rs380417 on chromosome 21 was weaker than on chromosome 6q, but with a stronger relative risk of African ancestry at rs380417 = 1.48 (viz, 95%CI: (1.15, 1.89), p = 0.0021).
We next empirically explored the probability of Zcase and Zcase-control scores greater than we observed on chromosome 6 and 21 in the African-American sample when no genetic variants contributed to a trait. We applied a one-sided test for the African-American sample because of previous evidence in this region. We then simulated 1,000 data sets for both samples with the estimated parental allele frequencies and 12 generations based on a continuous gene flow model [21]. The numbers of analyses with Zcase>2.1, Zcase-control>2.8 for chromosome 6, and Zcase>2.1, Zcase-control>1.4 for chromosome 21, were summarized. Among 1,000 simulations, we observed 184 instances where both Zcase>2.1, Zcase-control>2.8 and 688 instances where both Zcase>2.1 and Zcase-control>1.4 respectively, indicating that our observations on both 6q and 21q do not reach genome-wide significance. However, when we restricted the analysis to the regions between 129–166 cM on chromosome 6 and between 0–30 cM on chromosome 21 identified in our previous study [1], we only observed 4 and 11 instances respectively (p = 0.004 and 0.011), suggesting that our results do in fact replicate the previous findings. We performed similar analyses with the other 5 regions, using a two-side test since no prior evidence was observed in these regions, and none reached genome-wide significance (Table 2).
We performed similar analysis using the software STRUCTURE. Among the African Americans, European ancestry was estimated as 15.8%±8.3% in cases, and 17.0±9.1% in controls, which are the same as we obtained with ADMIXPROGRAM. The detailed European ancestry for each individual estimated by both methods is presented in Supplement Table S1. The correlation between the two methods is 99.96%. We also calculated the case-only and case-control Z scores by excluding the estimates of an individual's marker-location specific ancestry if the difference of the estimates between the two methods is greater than 0.1. No substantial changes in the Z scores were observed (Table S2).
#### Association analysis on chromosome 6
We next focused on the region around rs703193 defined by Zcase>1.0 on chromosome 6 which encompassed 18.3 Mb and 36 genes. We hypothesized that missense SNPs are more likely responsible for the evidence identified by admixture mapping [5], [33]. We identified 51 missense SNPs in the 36 genes from public databases and typed them in the African-American sample (Figure 2). Eight of these SNPs were found to have a MAF<5% and an additional 4 were in strong HWD (p<0.01). Admixture mapping has extremely limited power to identify rare variants so these 12 SNPs were excluded from further analyses. We performed logistic regression on each of the remaining 39 SNPs assuming an additive model with adjustment for gender, age, BMI and estimated individual ancestry (IA) based on the original 1890 marker panel. We chose to focus only on the additive model in this step because the reduction of multiple comparisons more than compensates for the small sacrifice in power associated with this strategy.
We also adjusted for IA to reduce the likelihood of false association that results from population stratification. Association with hypertension was identified at α = 0.05 significance level at rs2244008 (A/G) and rs2272996(C/T) in the LAMA2 and VNN1 genes, respectively (Table 4). We then examined whether these two SNPs captured the evidence from admixture mapping. First, we attempted to isolate the ancestry effect. After inferring each individual's ancestry at the admixture peak (137cM) we repeated the logistic regression analysis in the subgroup whose African ancestry was >80% at this locus, assuming that this reduced any potential effects of population stratification. While the result for rs2244008 was unchanged, the association of rs2272996 with hypertension was strengthened (p = 0.00248) despite the reduction in sample size. Based on a permutation test this SNP remained significant (p = 0.045) after adjustment for multiple comparisons (See Methods). SNP rs2272996 is located 3.6 Mb from rs703193, with virtually no linkage disequilibrium between these two SNPs (D' = 0.008, 95% CI (−0.01–0.12)). To determine if two SNPs with this relationship can potentially be in LD in an admixed population similar to African-Americans, we calculated the LD between these two SNPs in a synthetic admixed population using HapMap YRI and CEU date. We assumed that the admixture proportions were 84% African and 16% European. Under these conditions D' was estimated as 0.095, which is within the 95% CI of the finding in our data, suggesting that an AIM used for admixture mapping is not necessarily in strong LD with a SNP associated with the phenotype. We also performed logistic regression for SNP rs703193 adjusting for gender, age, BMI and IA and no evidence of association was found. To further evaluate the plausibility of the evidence for rs2244008 we compared the allele frequency between YRI and CEU samples from HapMap data [10], as well as in our own European-American sample. The frequencies were almost the same, confirming that this SNP is unlikely to account for the evidence observed by the admixture mapping. In contrast, for rs2272996 the allele frequencies were substantially different between YRI and CEU and between YRI and our own European-American sample (Table 4). Further analysis suggested that applying a recessive model rs2272996 (TT vs TC and CC) yielded the most significant association, with hypertension risk increased in the presence of the TT genotype (p = 0.0021, Table 5). Further correction for multiple comparisons of 39 SNPs and additive and recessive modes of inheritance yielded a p-value of 0.06 for rs2272996. We therefore hypothesized that the excess of African ancestry at the peak location (137cM) in cases was accounted for by those who carried the TT genotype. Figure 3 presents African ancestry at the peak location for people who carry TT compared to the remaining genotypes between cases and controls. As expected, we observed a significant excess of African ancestry between cases and controls who were TT (p = 0.00045) but not those that were TC and CC (p = 0.34). These results suggest that rs2272996 is a potential candidate to explain the admixture mapping evidence. When we added rs2272996 in an admixture mapping analysis and the Z score at rs227299 did not improve. This result is reasonable because the information content after adding rs2272996 does not increase, given the AIMs used in this region.
We then analyzed rs2272996 by assuming a recessive model in both European Americans and Mexican Americans using logistic regression with adjustment for gender, age, age2, and BMI. We observed significant evidence of association between rs2272996 and hypertension in Mexican Americans (p = 0.021), where the TT genotype increased the risk of hypertension (Table 5). Among European Americans, on the other hand, a similar analysis demonstrated the opposite–albeit non-significant–association (TT genotype protective, odds ratio = 0.79 (p = 0.089). This result is consistent with the findings in African Americans, where the association increased when analysis was limited to individuals with >80% African ancestry at the peak by admixture mapping. We then estimated the population attributable risk of rs2272996 in the African-American and Mexican populations. Under the recessive model we obtained a population attributable risk of 16% in African-Americans, and 35% in Mexican-Americans; this result occurs because T-the risk allele–is relatively common in both populations.
### Discussion
Admixture mapping has been proposed as an alternative to traditional linkage and association studies and in theory holds great promise for selected traits [20][29]. In the first application of this strategy to mapping complex traits, Zhu et al. performed a genome-wide admixture mapping of hypertension in an African-American sample based on a set of microsatellite markers designed for traditional linkage analysis and identified two regions on chromosome 6 and 21 that potentially harbored hypertension susceptibility genes [1]. Reich et al. [32] also reported a locus on chromosome 1 associated with multiple sclerosis by admixture mapping. More recently, linkage analysis followed by fine mapping identified a chromosome region harboring genes for susceptibility to prostate cancer [34] and this locus was subsequently replicated with admixture mapping [35]. In this report we present additional evidence from genome-wide admixture mapping for hypertension in 1743 unrelated African Americans using a highly informative SNP panel [31]. This panel extracted on average 89% of the information of ancestry (measured by SIC) [25] for the African-American sample and as a consequence the results from both case-only and case-control tests were reasonably robust. Our estimate of the average information for ancestry is higher than was found in the original report for this SNP panel [31]. This may be explained by the fact that we assumed a 50%–50% mixture when no SNPs are genotyped while Smith et al. assumed a 79%–21% mixture. Under the latter assumption the estimated average information was 65%, slightly less than the 71% suggested by Smith et al. [31]. The estimated ancestral allele frequencies in the parental populations are close to the corresponding observed frequencies in contemporary African and European populations, suggesting that our model fits the data well. We observed 6 regions with consistent excess of African or European ancestry in both case-only and case-control analyses, including the region on chromosome 6 identified in our previous study [1]. However, simulation studies indicate that we did not find any region that reaches genome-wide significance in this study. Although the regions on chromosome 6 and 21 identified in our previous study are large (37cM and 30 cM, respectively), our simulations indeed suggest that the present result is unlikely to be due to chance. It is interesting that we observed stronger evidence but less significant association with the African-derived allele on chromosome 6 than on chromosome 21. Several reasons may explain this outcome. 1) The power of admixture mapping is dependent on the underlying genetic model, with the recessive mode of inheritance being more powerful than additive or dominant modes [21]. A recessive effect for the T allele of missense SNP rs2272996 in VNN1 gene best explains the evidence, suggesting it is reasonable to observe better admixture mapping evidence on chromosome 6 than 21. 2) The power of admixture mapping is dependent on the disease allele frequency difference between two ancestral populations, while the power of association is dependent on the linkage disequilibrium between the underlying disease variant and the test marker, which is the ancestry in this case, and the disease allele frequency in the admixed population. We performed a power analysis by assuming that the missense SNP rs2272996 is the true causative variant. We further assumed that the odds ratio of the TT genotype vs others in African ancestry population is 1.57, as estimated in Table 5. Since we failed to observe evidence of association in the European American population, the odds ratio was simply placed at 1.0, which leads to the estimate of the relative population risk ratio of 1.38. Under these assumptions, our power analysis suggests that, post hoc, we had 38% power to detect a region reaching the genome wide significance with the sample size in the current study. Thus, our study clearly has relatively low power to find similar locus. 3) A spurious finding is still possible because of the statistical fluctuation despite our previous report. Further association analysis is necessary to rule out the possibility that this is a false positive finding.
We performed our analysis based on a method which directly maximizes the likelihood function from the hidden Markov Model using the EM algorithm, allowing for uncertainty in model parameters, such as the allele frequencies in the parental populations [25]. Simulations suggested that this method can perform as well as the widely used Bayesian MCMC method STRUCTURE for the data generated from various population admixture models.[25] However, we believe the results can be regarded with greater confidence if different approaches lead to similar results, as suggested by others [36]. We thus performed similar analysis using STRUCTURE, although we are also aware that other similar MCMC based software has become available [22][24]. The difference between ADMIXPROGRAM and STRUCTURE includes the approach to estimation of a large number of parameters, eg, ADMIXPROGRAM directly maximizing the likelihood function based on EM algorithm while STRUCTURE uses a Gibbs sampling scheme. The other difference involves the transition probability in the Hidden Markov model. ADMIXPROGRAM uses the transition probability derived from a continuous-gene-flow model and STRUCTURE uses linkage model by assuming that chunks of chromosomes are derived from ancestral populations and the breakpoints between successive chunks occur randomly [25], [37]. Despite the substantial difference of the two approaches, the results are almost identical, providing further confidence that our results are not biased of the selection of the statistical method.
Several publications [22], [23], [25], [26], [38] have demonstrated that admixture mapping can be seriously biased by background LD between adjacent SNPs when this phenomenon is not properly considered. We thus examined the background LD in European Americans and dropped the SNPs that are in strong LD. Since the maker panel was initially selected to minimize background LD, eliminating additional selected markers based on this characteristic had a very limited effect. We further repeated the analyses using different sets of SNPs: (eg, odd or even SNPs , those with adjacent distance>1 cM) and the results on chromosome 6 were essentially the same. We note, however, that more information might have been obtained by keeping those SNPs that were in LD when using the Markov Hidden Markov Model method recently proposed by Tang et al.[26].
We next followed up the region on chromosome 6 by genotyping 51 missense SNPs in 36 genes spaced across the 18.3 Mb region. Searching for disease variants by testing all functional SNPs has been advocated by Risch [5] and Risch and Botstein [33] and this strategy successfully identified the sixth type 1 diabetes locus by examining all functional SNPs across the genome [13]. We adapted this strategy in the chromosome 6 region and identified a missense SNP rs2272996 (or N131S) in the VNN1 gene significantly associated with hypertension in African Americans after adjusting for multiple comparisons; this association was replicated in Mexican Americans. A non-significant association in the opposite direction was observed in European Americans. (No correction was made for multiple comparisons in Mexican Americans and European Americans since we tested only rs2272996 in these two populations.) Further analysis also indicates that this SNP accounts for most of the evidence of excess of African ancestry observed in this region for African Americans. Thus, the association of SNP rs2272996 to hypertension is unlikely to be due to chance alone, although additional replication studies in independent studies are necessary. It should also be noted that our search of causative variants was not comprehensive and other susceptibility variants may well exist in this region.
We were also puzzled by the direction of the risk estimate associated with allele T in different populations. Theory suggests that the divergent risk relationship at this locus in ancestral populations will increase the power of admixture mapping method. However, the different patterns of risk in these populations cannot be explained with the data currently available, but could reflect gene-gene or gene-environmental interactions [39]. It is possible that this locus was under different selective pressure in different populations, however, the evolutionary processes that have molded susceptibility to chronic cardiovascular disease have not been defined. Whether the at-risk alleles arose under positive selection or a neutral-equilibrium model therefore cannot be determined. The suggestion has been made that susceptibility variants for hypertension may have been under selection pressure due to the climate adaptation, however most of the loci identified under this assumption have not been replicated in association analyses [40][42]. Under this model, the variants are unlikely to be deleterious and could be common. Voight et al.[43] proposed a method to detect signals of very recent positive selection in the human genome using HapMap data and the VNN1 gene is located in one of the regions with strong positive selection pressure in YRI sample. VNN1 belongs to the vanin family of proteins, including secreted and membrane-associated proteins which have been reported to participate in hematopoietic cell trafficking and to possess pantetheinase activity which may play a role in oxidative-stress response [44]. It has been recently suggested that increased oxidative stress may antedate hypertension and contribute to its pathogenesis [45]. More recently, VNN1 has been suggested as a novel gene for cardiovascular disease risk, strongly associated with expression levels of several lipid metabolism/CVD-risk genes, [46], [47] although the underlying pathway of VNN1 and other CVD-risk genes remains unknown.
In summary, we conducted a genome-wide search for susceptibility loci for hypertension using admixture mapping in African Americans. Further association studies identified a missense SNP rs2272996 in the VNN1 gene that may explain the evidence identified through admixture analysis. While requiring further confirmation, this finding demonstrates the potential for the admixture approach and suggests it could be a tool for use in studies to define genes affecting selected complex traits. In addition, our study only surveyed the non-coding SNPs on the region on chromosome 6. A more comprehensive assessment of variants in this region will be required to provide assurance that the causative variants associated with hypertension have been identified.
### Materials and Methods
#### Samples
The design and methodology of the Dallas Heart Study have been reported elsewhere [48]. In brief, a multistep probability sample of civilian, non-institutionalized English- or Spanish-speaking Dallas County residents were recruited from households. African Americans were oversampled to ensure that they represented 50% of the final cohort. Eligible subjects were invited to participate in three stages of the project including two home visits during which a survey was administered and blood and urine specimens were obtained and a third visit at the University of Texas at Southwestern Medical Center during which imaging studies were accomplished. Three thousand three hundred and ninety eight individuals (52% black) participated in the blood drawing that led to DNA isolation. Informed consent was obtained from all participants and the Institutional Review Board of the University of Texas Southwestern Medical Center approved the study protocol.
Race-ethnicity was based on self-identification. Subjects were asked in separate questions “Are you of Mexican American origin” and “What is your primary racial or ethnic identity.” The following options were provided for the latter question: Black/African American; White/Caucasian; American Indian, Alaska Native; Asian, Pacific Islander, East Indian; Other (Specify). Self-identified whites were used as a proxy for the European founding populations in the genetic analyses.
#### Phenotype
##### Blood pressure/hypertension.
At each of the three visits (home visits 1 and 2 and visit 3), 5 sets of blood pressure measurements were obtained using an automatic oscillometric device (Welch Allyn, Series #52,000, Arden, NC) with an appropriately sized blood pressure cuff. This device has been validated against catheter measurement of arterial pressure [48]. The BP for analysis was considered the average of measurements 3 through 5 at each visit (total 9 readings). Hypertensive cases were defined as persons with either a systolic BP> = 140 or diastolic BP> = 90, or current treatment with an antihypertensive medication.
#### Genotyping
For each subject, DNA sample was individually genotyped by Perlegen Sciences for the complete marker set defined by Smith et al [31]. Among them, 2,270 SNPs were successfully genotyped. Fifty one additional missense SNPs in 36 genes on chromosome 6 were identified from National Center for Biotechnology Information (NCBI) build 34, and then genotyped by Perlegen Sciences.
#### Selection of admixture marker set
Hardy-Weinberg equilibrium (HWE) was first examined for all the 2,270 successfully genotyped SNPs on 22 autosomes in the three populations separately using the software Haploview [49]. Thirty two SNPs were identified with significant departure from HWE at significance level α<0.001 and were excluded in future analyses. To study the LD in the ancestral populations, pairwise linkage disequilibrium defined by D' values between SNPs on the same chromosome was calculated using the software Haploview in Whites. We identified 251 sets of adjacent SNPs in strong LD (95% lower bound D'>0.5). Since strong LD between adjacent markers can seriously bias the estimation of marker location-specific ancestry [26], we retained only one SNP from each of these sets in the subsequent analyses. After these data verification procedures, we defined an analytic set of 1,890 from the original 2,270 SNPs. These SNPs were entered in the hidden Markov model (HMM) to estimate the marker locus specific ancestry in African-Americans based on EM algorithm using software ADMIXPROGRAM [25].
#### Estimation of marker location-specific ancestry
The genome-wide admixture mapping analysis was only performed in African-Americans since the SNP set of Smith et al. was specifically selected for the African-American population. We estimated marker location-specific ancestry using the HMM, in which the transmission probability was calculated based on the continuous gene flow (CGF) model [21], [25]. This method directly maximizes the likelihood function through an EM iterative algorithm and allows consideration of uncertainty of marker allele frequencies in the parental populations [25]. The number of generations since population admixture was estimated by maximizing the likelihood function for the number of generations. To estimate the marker location-specific ancestry, we assumed there were two parental populations for the African-American population. If our model fit the data well, we would expect the estimated allele frequencies in ancestral African and European populations to be close to what is observed in contemporary populations, although not the same. To allow for the uncertainty of ancestral marker allele frequencies, we compared the estimated ancestral allele frequencies and marker location-specific ancestries when no ancestral population information was used to a situation where only observed European allele frequencies were used as the initial European ancestral allele frequencies in the model. The results were essentially the same and we then reported the results using the European allele frequencies. The correlation between the observed and estimated allele frequencies in the European sample was 97.1% and the correlation between estimated African ancestral allele frequencies with that in panel described by Smith et al [31] (calculated from the weighted average allele frequencies of Ghana and Cameroon) was 84.5% (figure 4 A and B). The lower correlation for African allele frequencies is apparently due to inconsistent designation of the minor allele. However, this inconsistency has no effect to the results because no African ancestral information was used in our analysis.
To test for linkage we calculated two test statistics: the Z score of the case-only test and the Z score of the case-control test [21], [25]. We also estimated the marker location-specific ancestry using the software STRUCTURE [31], [50]. STRUCTURE was run under the linkage model without haplotype phase information, with 50,000 burn-in iterations followed by an additional 50,000 iterations. We specified SITEBYSITE = 1 and STRUCTURE provided output for the joint posterior assignment probabilities of population origin for the two alleles at each marker location. We next compared the marker-specific ancestry obtained with the software STRUCTURE to the results obtained from the EM method.
We directly simulated admixed populations according to the continuous gene flow model [21], [25]. The ancestral allele frequencies, the number of generations since the occurrence, and average ancestry were based on the estimates in the African American samples. To simulate African-American samples, at the first generation the marker genotypes of 10,000 unrelated people were simulated according to the African allele frequencies assuming HWE and independence of the markers. An admixed population was then formed by taking a proportion of 3.3% randomly selected from the simulated population to mate with people generated according to the marker allele frequencies in the European population, with the remaining individuals randomly mating among themselves. The number of children produced by each marriage was assumed to follow a Poisson distribution with mean size 2. The number of crossovers between two marker loci at a distance d cM was assumed to follow a Poisson distribution with mean d/100. This process was repeated in the following generations to form the current African American populations.
#### Testing association between and marker and hypertension
We applied a logistic model regressing hypertension status on gender, age, age2 and the genotype effect assuming additive model. For African Americans, individual ancestry estimated by HMM was included in the model. For Mexican Americans, we applied the genome-control method [51] to control for population stratification by randomly selecting 100 unlinked SNPs. SNPs with significant association were further analyzed using different models of inheritance.
#### Permutation test
To obtain the significance level of SNP rs2272996 in VNN1 accounting for multiple tests, we performed permutation tests for those SNPs with allele frequency difference between African Americans and Europeans greater than that of SNP rs2272996. We permutated the hypertension status together with gender, age, BMI and African ancestry 10,000 time and analyzed the individuals whose African ancestral>80% at each permutation. Logistic regression was then performed for each SNP and the minimum P-value was recorded at each permutation. These minimum P-values were tallied to obtain the null distribution of the test adjusting for multiple tests.
### Supporting Information
Table S1.
Individual European Ancestral estimated by ADMIXPROGRAM and STRUCTURE
doi:10.1371/journal.pone.0001244.s001
(0.14 MB XLS)
Table S2.
Case-only and case-control Z-scores across the genome
doi:10.1371/journal.pone.0001244.s002
(0.46 MB XLS)
### Acknowledgments
We would like to thank Helen Hobbs and Jonathan Cohen for their generous support with access to the clinical samples and in providing the genotype data. We also thank Dr. Hua Tang for helpful discussion and D. Kan for his assistance in programming.
### Author Contributions
Conceived and designed the experiments: RC XZ. Analyzed the data: XZ. Wrote the paper: RC XZ.
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https://pos.sissa.it/340/405/
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Volume 340 - The 39th International Conference on High Energy Physics (ICHEP2018) - Parallel: Neutrino Physics
Three Neutrino Oscillations in Uniform Matter
A. Ioannisyan,* S. Pokorski
*corresponding author
Full text: pdf
Published on: August 02, 2019
Abstract
Following similar approaches in the past, the Schrodinger equation for three neutrino propagation in
matter of constant density is solved analytically by two successive diagonalizations of 2x2 matrices.
The final result for the oscillation probabilities is obtained directly in the conventional parametric
form as in the vacuum but with explicit simple modification of two mixing angles ($\theta_{12}$ and $\theta_{13}$) and
mass eigenvalues.
DOI: https://doi.org/10.22323/1.340.0405
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https://wiki.inspircd.org/Windows_Installation
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# Windows Installation
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## Installing InspIRCd on Windows via the installer
InspIRCd will install natively on Windows. This guide assumes you are using the install package, and not building from source.
To install InspIRCd, first double click the InspIRCd installer icon:
Step One: Welcome screen Just click next here.
Step Two: License agreement The license is GPL version 2, just click next again, you aren't signing away your first-born or eternal soul.
Step Three: Choose install location The default path should do, change it if you want.
Step Four: Choose install components Leaving this as default is recommended. You can cut down the install size by not installing modules.
## Locations of files in the Windows installation
In the windows installation of InspIRCd, the locations of files are as follows:
• Core system: C:\Program Files\InspIRCd
• Core shared objects (DLL files): C:\Program Files\InspIRCd\bin.
• Modules: C:\Program Files\InspIRCd\modules.
• Conf Files: C:\Program Files\InspIRCd\conf.
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http://sciencehq.com/chemistry/applications-of-bond-energies.html
|
# Applications of Bond Energies
Applications of Bond Energies are listed below:-
1. Determination of enthalpy of reaction
The bond energies can be used for determining enthalpies of reactions $Delta H_{Reaction} = E(B.E)_R- E(B.E.)_P$ for example, we want to determine the enthalpy of the following reaction:
$HC \equiv CH(g) +2H_2(g) \to H_3C- CH_3(g) \hspace{5mm}\Delta H = ?$
In this reaction a triple bond $(C \equiv C)$ breaks in acetylene and two H — H bonds break in 4H. In turn, one C C- bond and four C — H bonds are formed in$C_2H_6$. Therefore
$\Delta H = [\Delta H_{C- C} +4 \Delta H_{C-H}] + [\Delta H_{C \equiv C} + 2\Delta H_{H- H}]$
$= -[3.47.3 + 4 \times 416.2] + [811.7 + 2 \times 435.1] \\[3mm] =-2.12.1 + 1681.9 \\[3mm] = -330.2 kJ mol^{-1}$
2. Determination of enthalpies of formation of compounds
The bond energies can be used for determining enthalpies of formation of compounds. For example, we want to determine the enthalpy of formation of ethyl alcohol:
Determination of enthalpies of formation of compounds
The formation of ethyl alcohol involves:
(i) Breaking of 3H-H bonds to give 6H, breaking bf 1/2O-O bond to give O and sublimation of 2 atoms of C(s) to give 2C(g).
(ii) Formation of one C-C bond, five bonds, one C-0 bond and one bond.
Therefore,
$\Delta H_f = [3 \Delta H_{H- H} + \dfrac{1}{2} \Delta H_{O- O} + 2 \Delta H_{C(s) \to C(g)}]- [\Delta H_{C- C} + 5\Delta H_{C- H} + \Delta H_{C-O} + \Delta H_{O- H}]$
$= 3 \times 435.1 + \dfrac{1}{2} \times 489.5 + 2 \times 719.6]- [347.3 + 5 \times 416.2 + 351.4 + 464.4]$
$2989.2- 3244.1 = -254.9 k J mol^{-1}$
3. Determination of resonance energy
Resonance energy is taken to be equal to the difference between the actual bond energy of the molecule and that of the most stable of the resonating structures. Let us determine the resonance energy of benzene.
The dissociation of benzene may be given as:
$C_6H_6(g) \to 6C(g) + 6H(g)$
According to Kekule's structure there are three C-C bonds, three C = C bonds and six C-H bonds in benzene. Therefore dissociation energy of benzene may be given as:
$\Delta H_d = 3 \Delta H_{C-C} + 3 \Delta H_{C = C} + 6\Delta H_{C-H}$
$= 3 \times 347.3 + 3 \times 615.0 + 6 \times 416.2 \\[3mm] = 5384.1 k J mol^{-1}$
Thus, dissociation energy of benzene is $5384.1 kJ mol^{-1}$. But experimental value is known to be $5535.1 kJ mol^{-1}$. Evidently, the resonance energy of benzene is $5384.1 = 151 kJ \hspace{2mm} mol^{-1}$.
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|
http://mathhelpforum.com/geometry/78932-sphere-cone-geometry.html
|
# Math Help - Sphere in Cone Geometry
1. ## Sphere in Cone Geometry
That's a question on my textbook.... i can't solve it and my teacher is away. Anyone help?
Thanks.
2. Originally Posted by anonymous_maths
...
That's a question on my textbook.... i can't solve it and my teacher is away. Anyone help?
Thanks.
1. The cross-section of the cone is an equilateral triangle with AM = R.
In the top right triangle you get:
$R \cdot \tan(30^\circ) = r~\implies~R=\dfrac r{\tan(30^\circ)} = \dfrac r{\frac13 \sqrt{3}}~\implies~\boxed{R=r \cdot \sqrt{3}}$
2. Let denote x the distance in question. Use Pythagorean theorem:
$R^2+r^2=(r+x)^2~\implies~3r^2+r^2 = (r+x)^2~\implies~2r=r+x~\implies~x=r$
Unfortunately I have to leave now ...
Attached Thumbnails
3. Originally Posted by anonymous_maths
...
That's a question on my textbook.... i can't solve it and my teacher is away. Anyone help?
Thanks.
Let h denote the height of the cone. Then:
$h^2+R^2=(2R^2)~\implies~h=R\cdot \sqrt{3}$
The volume of a cone is calculated by:
$V=\dfrac13 \cdot \pi \cdot R^2 \cdot h$
That means:
$V=\dfrac13 \cdot \pi \cdot R^2 \cdot R \cdot \sqrt{3} = \dfrac{\pi \sqrt{3}}3 R^3$
------------------------------------------------------------------------------------
From a) you know that
$R=r \cdot \sqrt{3}~\implies~r=\dfrac{\sqrt{3}}3 R$
The volume of the sphere is calculated by:
$V=\dfrac43 \pi r^3$
That means:
$V=\dfrac43 \pi \left(\dfrac{\sqrt{3}}3 R\right)^3 = \dfrac{4 \pi \sqrt{3}}{27} R^3$
------------------------------------------------------------------------------------
The percentage is calculated by $percentage = \dfrac{partial\ amount}{total\ amount} \cdot 100$
$p=\dfrac{\dfrac{4\pi \sqrt{3}}{27} R^3}{\dfrac{\pi \sqrt{3}}3 R^3}\cdot 100 = \dfrac49 \cdot 100 \approx 44.4\%$
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https://socratic.org/questions/what-are-the-major-and-minor-products-obtained-in-the-reaction-of-e-3-methyl-2-p
|
Organic Chemistry
Topics
# What are the major and minor products obtained in the reaction of (E)-3-methyl-2-pentene and HBr?
Jun 28, 2015
The major product by far is 3-bromo-3-methylpentane; there may be a small amount of 2-methyl-3-bromopentane.
#### Explanation:
The structure of ($E$)-3-methylpent-2-ene is
According to Markovnikov's rule, the ${\text{H}}^{+}$ from $\text{HBr}$ will add to $\text{C-2}$ of the alkene and form a 3° carbocation at $\text{C-3}$.
The ${\text{Br}}^{-}$ will add to $\text{C-3}$ and form 3-bromo-3-methylpentane
There may be a small amount of product formed when the ${\text{H}}^{+}$ adds to $\text{C-3}$ of the alkene to form the less stable 2° carbocation at $\text{C-2}$.
The ${\text{Br}}^{-}$ will then add to $\text{C-2}$ and form 2-bromo-3-methylpentane.
##### Impact of this question
5618 views around the world
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http://mathhelpforum.com/algebra/4348-need-help-variation.html
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# Math Help - Need HELP: Variation
1. ## Need HELP: Variation
The Problem
(1)
The time T needed to mill a channel varies directly as the length, width, and depth of the channel, assuming the cutting tool and material being machined stay constant.
a) Write this as an equation using a constant of proportionality;
b) A channel 30 cm long, 5.0cm wide and 4.5 cm deep took 36 minutes to mill. Use this information to determine the constant proportionality, with units.
c) How long will it take to mill a channel in the same material, 45 cm long, 6.4 cm wide, and 3.75 cm deep?
d) How long would the machining job of b) above take, if the length, width, and depth were all doubled
(2) It takes three men three hours to assemble three shelving units. How long will it take nine men to assemble twelve shelving units? Prove your answer
(3) The time taken to machine out the interior of a hollow cylinder in a shaft on a lathe varies directly as the length of the cylinder and directly as the square of the internal diameter.
a) Write this as an equation using a constant of proportionality;
b) It took 22 minutes to machine out a cylinder 14.5 cm long and 3.45 cm in diameter. Use this information to determine the constant of proportionality, with units.
c) How long would it take to machine out a cylinder 9.6 cm long, and 5.90 cm in diameter?
(4) The cutting speed of a milling cutter varies directly as the diameter of the cutter and directly as the RPM of the cutter.
a) Write this as an equation using a constant of proportionality;
b) Turing a milling cutter 8.5 cm in diamter at 6250 RPM results in a cutting speed of 2.78 m/s. Use this information to determine the constant of proportionality, with units.
c) Calculate the needed RPM to produce a recommended cutting speed of 4.25 m/s (in another material), using a 12.5 diameter cutter.
2. Originally Posted by bigstarz
The Problem
(1)
The time T needed to mill a channel varies directly as the length, width, and depth of the channel, assuming the cutting tool and material being machined stay constant.
a) Write this as an equation using a constant of proportionality;
$T=\kappa \times l \times w \times d$
b) A channel 30 cm long, 5.0cm wide and 4.5 cm deep took 36 minutes to mill. Use this information to determine the constant proportionality, with units.
Given the above data we have:
$36= \kappa \times 30 \times 5 \times 4.5$
so:
$\kappa=\frac{36}{30 \times 5 \times 4.5}\approx 0.0533 \mbox{ min/cm^3}$
c) How long will it take to mill a channel in the same material, 45 cm long, 6.4 cm wide, and 3.75 cm deep?
d) How long would the machining job of b) above take, if the length, width, and depth were all doubled
I'm sure you can now do these two parts yourself.
RonL
3. Originally Posted by bigstarz[B
(2) [/B] It takes three men three hours to assemble three shelving units. How long will it take nine men to assemble twelve shelving units? Prove your answer
If it takes three men three hours to assemble three shelving units, it will
take one man three hours to assemble one shelving unit. therefore each
man can assemble 1/3 of a shelving unit per hour.
Twelve shelving units is 36 thirds of a shelving unit, so 36 man hours of
work is required to assemble them, which is 4 hours of work by nine men.
RonL
4. Originally Posted by bigstarz
(4) The cutting speed of a milling cutter varies directly as the diameter of the cutter and directly as the RPM of the cutter.
a) Write this as an equation using a constant of proportionality;
b) Turing a milling cutter 8.5 cm in diamter at 6250 RPM results in a cutting speed of 2.78 m/s. Use this information to determine the constant of proportionality, with units.
$\kappa=\frac{\mbox{speed}}{\mbox{diameter}}$
Thus,
$\kappa=\frac{\frac{2\pi r}{t}}{2\pi r}=\frac{1}{t}$
Notes:
Where "t" is time for revolution.
To find the speed you divide distance by time.
Distance in this case the circumfurence of circle.
5. Originally Posted by ThePerfectHacker
[QUOTE=bigstarz
(4) The cutting speed of a milling cutter varies directly as the diameter of the cutter and directly as the RPM of the cutter.
a) Write this as an equation using a constant of proportionality;
b) Turing a milling cutter 8.5 cm in diamter at 6250 RPM results in a cutting speed of 2.78 m/s. Use this information to determine the constant of proportionality, with units.
$\kappa=\frac{\mbox{speed}}{\mbox{diameter}}$[/QUOTE]
The cutting speed of a milling cutter varies directly as the diameter of the cutter and directly as the RPM of the cutter.
So you should have:
$a)\ speed=\kappa \times diameter \times RPM$,
then:
$
\kappa=\frac{speed}{diameter \times RPM}
$
,
and so:
$
b)\ \kappa=\frac{2.78}{8.5 \times 6250}=0.0000523\ \mbox{(m/s)/(cm/s)}
$
RonL
|
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https://codegolf.stackexchange.com/questions/112935/sort-useless-characters
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# Sort useless characters
This challenge is inspired by this very nice answer by TidB.
In TidB's answer, every eight character is in the correct order: gnilwoB edoC (Code Bowling backwards). The other strings however are were in a strange, random order.
Your challenge is to fix this.
Take a (non-empty) string and a positive integer n as input. The string will contain ASCII characters in the range: 32-126 (space to tilde).
You must sort the string in ascending order (seen from the left, based on the ASCII-code value), but skip every nth character, starting from the end of the string. As an example, let's take the string abcdABC123 as input, and n=4, then we'll get:
abcdABC123 <- Input string. (n=4)
_b___B___3 <- These will not be sorted (every 4th starting from the end)
1_2AC_acd_ <- The remaining characters, sorted
1b2ACBacd3 <- The final string (the output)
Another example:
9876543210 <- Input string (n=2)
_8_6_4_2_0 <- These will not be sorted
1_3_5_7_9_ <- The remaining characters, sorted
1836547290 <- The final string (the output)
The input string can be taken on an optional format (string, list of characters, list of single character strings ...). The input integer can also be taken on an optional format.
Test cases:
The format will be n=__, followed by the input string on the next line. The output is on the line below.
n=1 (All elements will stay in place)
nafgaksa1252#"%#
nafgaksa1252#"%#
n=214 (The last character will stay in place. All other are sorted.
&/lpfAVD
&/AVflpD
n=8
g7L9T E^n I{><#ki XSj!uhl y= N+|wA}Y~Gm&o?'cZPD2Ba,RFJs% V5U.W;1e 0_zM/d$bH@vKoQ 43Oq*C g n !#$%&'i*+,./01l234579;w<=>?@ADoEFGHIJKBLMNOPQR STUVWXYeZ^_abcdhjkmqsuovyz{|}~C
# MATL, 15 14 bytes
ttfiX\qgP)S5M(
Inputs are a string enclosed in single quotes and a number. Single-quote symbols in the string should be escaped by duplicating (as in MATLAB and Octave).
### Explanation
Consider inputs 'abcdABC123' and 4.
tt % Implicitly input string. Duplicate twice
% STACK: 'abcdABC123', 'abcdABC123', 'abcdABC123'
f % Find: indices of nonzero elements: gives [1 2 ... n] where n is input length
% STACK: 'abcdABC123', 'abcdABC123', [1 2 3 4 5 6 7 8 9 10]
i % Input n
% STACK: 'abcdABC123', 'abcdABC123', [1 2 3 4 5 6 7 8 9 10], 4
X\ % 1-based modulo
% STACK: 'abcdABC123', 'abcdABC123', [1 2 3 4 1 2 3 4 1 2 3 4]
qg % Subtract 1, convert to logical: gives true (1) for 1, false (0) otherwise
% STACK: 'abcdABC123', 'abcdABC123', [0 1 1 1 0 1 1 1 0 1]
P % Flip
% STACK: 'abcdABC123', 'abcdABC123', [1 0 1 1 1 0 1 1 1 0]
) % Use as logical index into the string
% STACK: 'abcdABC123', 'acdAC12'
S % Sort
% STACK: 'abcdABC123', '12ACacd'
5M % Push logical index again
% STACK: 'abcdABC123', '12ACacd', [1 0 1 1 1 0 1 1 1 0]
( % Write into original string as specified by the index. Implicitly display
% STACK: 1b2ACBacd3
1-based modulo means that mod([1 2 3 4 5], 3) gives [1 2 3 1 2] instead of the usual (0-based) [1 2 0 1 2]. This is needed here to handle the case n=1 adequately.
• I wish 05AB1E had that last command... – mbomb007 Mar 15 '17 at 20:55
# PHP, 101 bytes
negative string indexes (PHP 7.1) save 21 bytes - and possibly the day:
for([,$s,$n]=$argv;a&$c=$s[$i-=1];)$i%$n+1?$a[]=$c:0;for(sort($a);++$i;)echo$i%$n+1?$a[+$k++]:$s[$i];
Run with php -nr '<code>' '<string>' <N>.
breakdown
for([,$s,$n]=$argv; # import command line arguments to$s and $n a&$c=$s[$i-=1];) # loop backward through string
$i%$n+1?$a[]=$c:0; # if index is not n-th, copy character to array
for(sort($a); # sort array ++$i;) # loop forward through string:
echo$i%$n+1 # if index is not n-th
?$a[+$k++] # print character from array
:$s[$i] # else print character from string
;
• why $i-=1 and not$i-- ? – Jörg Hülsermann Mar 15 '17 at 16:26
• @JörgHülsermann Because $i-- doesn´t work if$i is NULL. – Titus Mar 15 '17 at 18:18
# Perl 5, 94 bytes
88 bytes of code + -F -pl flags.
$_=join"",(map{(--$i%$n?"":$F[$#F-$i--]),$_}sort grep$i++%$n,reverse@F),chop if($n=<>)>1
Try it online!
It's quite too long in my opinion, but already not that ugly... I'm still trying to golf it further anyway.
# Jelly, 14 13 bytes
FṢṁ
ṚsṚµḢ€ż@Ç
Full program that prints the string to STD out*.
Try it online!
### How?
ṚsṚµḢ€ż@Ç - Main link: string s, non-negative number n
Ṛ - reverse s
s - split into chunks of size n
Ṛ - reverse the resulting list
µ - monadic chain separation (call that list x)
Ḣ€ - head €ach - yield a list of the first entries of each of x and modify x
Ç - call the last link (1) as a monad - get the sorted and re-split list
ż@ - zip together (with reversed @rguments)
FṢṁ - link 1, sort and reshape like self: list of lists
F - flatten into a single list
Ṣ - sort
ṁ - mould the result like the input
I can't help but think there is a way to use the fact that modifies its input
* for a function one would want to flatten the output into a single list with F.
For example an input of "abcdABC123", 4 yields:
[[['1'],['b']],[['2','A','C'],['B']],[['a','c',',d'],['3']]]
rather than:
['1','b','2','A','C','B','a','c',',d','3']
# Python + NumPy, 115 114 bytes
from numpy import *
def f(x,n):l=len(x);x=array(x);m=[1<2]*l;m[-1::-n]=[1>2]*len(m[0::n]);x[m]=sort(x[m]);return x
Takes a regular Python list as input (wasn't sure whether taking an array would be considered kosher); returns a NumPy array containing the result.
Works by masking out the relevant indices and sorting the rest.
## Python 2, 119 113 bytes
n,l=input()
i=range(len(l))
print"".join(sorted(l[~a]for a in i if a%n)[-a+a/n]if a%n else l[~a]for a in i)[::-1]
Builds a list of all characters to be sorted, sorts them and merges them for printing, while avoiding some of the reversing via negative indexing.
• print"".join(sorted(l[~a]for a in i if a%n)[-a+a/n]if a%n else l[~a]for a in i)[::-1] saves 5 bytes – TidB Mar 16 '17 at 9:26
• @TidB Thanks, almost eliminated the scrollbar! (Apparantly there was a trailing newline involved in my previous count, therefore it seems to be 113 now instead of 114.) – moooeeeep Mar 16 '17 at 10:25
# Burlesque, 36 bytes
pe<-jJ-.hdcoJ)-]j)[-++<>#acoz[\[\[<-
Try it online!
Takes input as N "String"
pe # Parse and push
<- # Reverse the string
j # Put N at the top of the stack
J-.hd # Store N-1 for later
co # Split string into chunks of N
J)-] # Duplicate and take the heads
j)[- # Take the tails of the other duplicate
++ # Reduce all the "useless" chars to string
<> # Reverse sort
#aco # Split into chunks of N-1
z[ # Zip the two lists
\[\[ # Flatten to string
<- # Reverse the string
# Perl 6, 53 bytes
{(my@a=$^a.comb)[grep (@a-*-1)%$^n,^@a].=sort;[~] @a}
Try it online!
It feels like there should be a shorter way of doing this
# Ruby, 64 bytes
Uses regex to grab all irrelevant characters, both for replacement and for sorting.
->i,s,j=-1{s.gsub(r=/.(?!(?=.{#{i}})*\$)/){s.scan(r).sort[j+=1]}}
Try it online
# Python 3.8 (pre-release), 111 109 bytes
lambda n,s:(l:=len(s),r:=sorted(s[~i]for i in range(l)if i%n),[r.insert(i,s[i])for i in range(~-l%n,l,n)])[1]
Try it online!
# 05AB1E, 14 bytes
I/O of the string as a list of characters.
Try it online or verify all test cases (feel free to remove the S and J in the test suite to see the actual I/O with character lists).
And I agree with @mbomb007's comment, although it's still pretty short this way. :)
Explanation:
# Example inputs: s=["a","b","c","d","A","B","C","1","2","3"] and n=4
D # Duplicate the (implicit) character-list input
# STACK: [["a","b","c","d","A","B","C","1","2","3"],
# ["a","b","c","d","A","B","C","1","2","3"]]
ā # Push a list in the range [1,list-length] (without popping the list)
# STACK: [s, s, [1,2,3,4,5,6,7,8,9,10]]
R # Reverse it to range [length,1]
# STACK: [s, s, [10,9,8,7,6,5,4,3,2,1]]
< # Decrease each by 1 to range (length,0]
# STACK: [s, s, [9,8,7,6,5,4,3,2,1,0]]
IÖ # Check for each if it's divisible by the integer-input
# STACK: [s, s, [0,1,0,0,0,1,0,0,0,1]]
≠ # And invert those truthy/falsey values
# STACK: [s, s, [1,0,1,1,1,0,1,1,1,0]]
© # Store this list of truthy/falsey values in variable ®
Ï # Only keep the characters in the list at the truthy indices
# STACK: [s, ["a","c","d","A","C","1","2"]]
{ # Sort those
# STACK: [s, ["1","2","A","C","a","c","d"]]
® # Push the truthy/falsey list again from variable ®`
# STACK: [s, ["1","2","A","C","a","c","d"], [1,0,1,1,1,0,1,1,1,0]]
ƶ # Multiply each by their 1-based index
# STACK: [s, ["1","2","A","C","a","c","d"], [1,0,3,4,5,0,7,8,9,0]]
< # Decrease everything by 1 to make it 0-based indexing
# STACK: [s, ["1","2","A","C","a","c","d"], [0,-1,2,3,4,-1,6,7,8,-1]]
ǝ # Insert the sorted characters at those indices in the list
# (NOTE: Unlike almost all other 05AB1E builtins that use indices, this
# insert builtin ignores negative and too large indices instead of using
# modular indexing, so the -1 are conveniently ignored here.)
# STACK: [["1","b","A","C","a","B","d","1","2","3"]]
# (after which this list is output implicitly as result)
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https://mca2017.org/fr/prog/session/fid
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# Systèmes hamiltoniens en dimension finie et infinie
Tous les résumés
Taille : 94 kb
Organisateurs :
• Carlos García Azpeitia (Universidad Nacional Autónoma de México)
• Renato Calleja (Universidad Nacional Autónoma de México)
• Andrés Contreras Marcillo (New Mexico State University)
• Walter Craig (McMaster University)
• Geordie Richards
University of Rochester
On invariant Gibbs measures for generalized KdV
Résumé en PDF
Taille : 39 kb
We will discuss some recent results on invariant Gibbs measures for the periodic generalized KdV equations (gKdV). Proving invariance of the Gibbs measure for gKdV is nontrivial due to the low regularity of functions in the support of this measure. Bourgain proved this invariance for KdV and mKdV, which have quadratic and cubic nonlinearities, respectively. Previously, we proved invariance of the Gibbs measure for the quartic gKdV by exploiting a nonlinear smoothing induced by initial data randomization. More recently, in joint work with Tadahiro Oh (Edinburgh) and Laurent Thomann (Lorraine), we have established this invariance for gKdV with any odd power (defocusing) nonlinearity. The proof relies on a probabilistic construction of solutions using the Skorokhod representation theorem.
• Robert L. Jerrard
University of Toronto
dynamics of nearly-parallel vortex filaments in the Gross-Pitaevskii equations
Résumé en PDF
Taille : 39 kb
We study the motion of thin, nearly parallel vortex filaments in 3d solutions of the Gross-Pitaevskii equations. In particular, we show that in a certain scaling limit, these filaments are governed by a system of nonlinear Schrödinger equations formally derived by Klein, Majda, and Damodaran in the mid '90s in the context of the Euler equations. This is the first rigorous justification of the Klein-Majda-Damodaran model in any setting. This is joint work with Didier Smets.
• Luis Vega
Sans titre
Résumé en PDF
Taille : 25 kb
• Andres Contreras
New Mexico State University
Eigenvalue preservation for the Beris-Edwards system
Résumé en PDF
Taille : 38 kb
Eigenvalue preservation in the Beris-Edwards system is the property that ensures that Q-tensors remain physical along the flow. The Beris-Edwards system is a simplified model for the evolution of nematic liquid crystals. The preservation of eigenvalues property is known to hold for the evolution in the whole space thanks to the work of Xiang-Zarnescu. In this talk I present a simpler and shorter proof that also applies to the bounded domain case. This is joint work with Xiang Xu and Wujun Zhang.
• Cheng Yu
University of Texas at Austin
Sans titre
Résumé en PDF
Taille : 25 kb
• Stefan Le Coz
Institut de Mathématiques de Toulouse
Stability of multi-solitons for the derivative nonlinear Schrödinger equation
Résumé en PDF
Taille : 38 kb
The nonlinear Schrödinger equation with derivative cubic nonlinearity (dNLS) is a model quasilinear dispersive equation. It admits a family of solitons, which are orbitally stable in the energy space. After a review of the many interesting properties of dNLS, we will present a result of orbital stability of multi-solitons configurations in the energy space, and some ingredients of the proof.
• Walter Craig
McMaster University
A Hamiltonian and its Birkhoff normal form for water waves
Résumé en PDF
Taille : 39 kb
A 1968 paper by VE Zakharov gives a formulation of the equations for water waves as a Hamiltonian dynamical system, and shows that the equilibrium solution is an elliptic stationary point. This talk will discuss two aspects of the water wave equations in this context. Firstly, we generalize the formulation of Zakharov to include overturning wave profiles, answering a question posed to the speaker by T. Nishida. Secondly, we will discuss the question of Birkhoff normal forms for the water waves equations in the setting of spatially periodic solutions. We transform the water wave problem with nonzero surface tension to third order Birkhoff normal form, and in the case of zero surface tension in deep water, to fourth order Birkhoff normal form. The result includes a discussion of the dynamics of the normal form, and a quantification of the function space mapping properties of these transformations.
• Renato Calleja
Symmetries and choreographies in families that bifurcate from the polygonal relative equilibrium of the n-body problem
Résumé en PDF
Taille : 40 kb
In my talk I will describe numerical continuation and bifurcation techniques in a boundary value setting used to follow Lyapunov families of periodic orbits. These arise from the polygonal system of n bodies in a rotating frame of reference. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship, the orbit is also periodic in the inertial frame. We prove that a dense set of Lyapunov orbits, with frequencies satisfying a Diophantine equation, correspond to choreographies. We present a sample of the many choreographies that we have determined numerically along the Lyapunov families and bifurcating families, namely for the cases n=4,6,7,8 and, 9. We also present numerical results for the case where there is a central body that affects the choreography, but that does not participate in it. This is joint work with Eusebius Doedel and Carlos García Azpeitia.
• Michela Procesi
Universitá di Roma Tre
Finite dimensional invariant tori in PDEs
Résumé en PDF
Taille : 37 kb
I shall discuss the existence and stability of quasi-periodic invariant tori for classes of evolution PDEs, both in Hamiltonian and reversible setting,trying to give an idea of the general strategy and the main difficulties in problems of this kind. I will also discuss the related problem of unstable solutions.
• Yannick Sire
John Hopkins University
A posteriori KAM for PDEs
Résumé en PDF
Taille : 37 kb
I will describe recent results in collaboration with R. de la Llave on an a posteriori KAM method for PDEs. In particular, our methods uses very little of symplectic geometry and does not use transformation theory. It applies to ill-posed equations in the Hadamard sense and we will give applications to the so-called Boussinesq equation by constructing periodic solutions for it.
• Slim Ibrahim
University of Victoria
Ground State Solutions of the Gross Pitaevskii Equation Associated to Exciton-Polariton Bose-Einstein Condensates
Résumé en PDF
Taille : 39 kb
We investigate the existence of ground state solutions of a Gross-Pitaevskii equation modeling the dynamics of pumped Bose Einstein condensates (BEC). The main interest in such BEC comes from its important nature as macroscopic quantum system, constituting an excellent alternative to the classical condensates which are hard to realize because of the very low temperature required. Nevertheless, the Gross Pitaevskii equation governing the new condensates presents some mathematical challenges due to the presence of the pumping and damping terms. Following a self-contained approach, we prove the existence of ground state solutions of this equation under suitable assumptions: This is equivalent to say that condensation occurs in these situations. We also solve the Cauchy problem of the Nonlinear Schr\"{o}dinger equation and prove some corresponding laws
• Rosa María Vargas Magaña
Whitham-Boussinesq model for variable depth topography. Results on normal and trapped modes for non trivial geometries.
Résumé en PDF
Taille : 42 kb
The water-wave problem describes the evolution of an incompressible ideal, irrotational fluid with a free surface under the influence of gravity. A significant development in water-wave theory was the discovery by Zakharov in 1968 that the problem has a Hamiltonian structure and later W. Craig and C. Sulem introduced the Dirichlet-Neumann operator explicitly on the Hamiltonian. In this talk I will present a joint work with Prof. Panayotis Panayotaros and Prof. Antonmaria Minzoni from Universidad Nacional Autónoma de México, we propose a simplified long wave model combining a variable depth generalization of the exact nonlocal dispersion with the standard Boussinesq nonlinearity. The model relies on an approximate Dirichlet-Neumann operator that preserves some key structural properties of the exact operator and is simpler than alternative perturbative or implicit expressions. We examine the accuracy of this approximation by studying linear (2-D) normal modes and (3-D) longitudinal and Ursell modes for some geometries for which there are exact results.
• Livia Corsi
Georgia Institute of Technology
A non-separable locally integrable Hamiltonian system
Résumé en PDF
Taille : 72 kb
A mechanical Hamiltonian on ${\mathbf{T}}^2\times{\mathbf{R}}^2$ is said to be "separable" if in some coordinate system $(q,p)$ it has the form $$H(q,p) =\frac{1}{2} |p|^2+V_1(q_1)+V_2(q_2).$$ Clearly such an Hamiltonian is globally Liouville-integrable. I will show that there exists an analytic, non-separable, mechanical Hamiltonian which is only locally integrable. Precisely I will show that $H$ is integrable on an open subset $\mathcal U$ of the energy surface ${\mathcal S}:=\{H = 1/2\}$, whereas on $\mathcal S \setminus \mathcal U$ it exhibits cahotic behavior. This is a joint work with V. Kaloshin
• Nicholas Faulkner
University of Ontario Institute of Technology
Equivariant KAM
Résumé en PDF
Taille : 47 kb
Kolmogorov-Arnold-Moser (KAM) theory has a rich and well developed history. In this talk we present a KAM theory for $\Gamma$-equivariant Hamiltonian systems. Hamiltonian systems with discrete symmetry groups $\Gamma$ arise naturally in many settings including for instances the $N$-body problem. If $\Gamma$ is Abelian, then KAM theorem applies, but for $\Gamma$ non-Abelian, $1\colon1$ resonance effects lead to small divisor problems. These problems can be overcome by combining the isotypic decomposition of phase space with a detailed study of $\Gamma$ and Torus invariants, all within the classical iterative proof structure. This is joint work with Dr. Luciano Buono.
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https://astronomy.stackexchange.com/questions/13544/does-every-object-in-the-universe-have-gravity-space-has-no-gravity-why
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# Does every object in the Universe have gravity? Space has no gravity, why?
My science teacher told me that every object in Universe has gravity but space is a part of Universe too, so, why does the space have no gravity?
• Are you saying that "space" is an "object"? I don't think that's what your teacher meant. Mar 10, 2018 at 19:28
• When you say "space has no gravity" do you mean that empty space doesn't pull things towards it (which is more or less true) or are you referring to the way astronauts (and other things) float around in space and are not pulled towards the floor of the ISS or whatever. That's because the floor and the astronaut are being pulled equally be Earth's gravity and constantly falling around the Earth. There is a gravitational force between the astronaut and the ISS (or anything else in it) but it is too weak to notice without sensitive instruments. Can you clarify? Mar 10, 2018 at 19:32
A quick search up on google you would find this:
Gravity causes every object to pull every other object toward it. Some people think that there is no gravity in space. In fact, a small amount of gravity can be found everywhere in space. Gravity is what holds the moon in orbit around Earth.
Why is this? That's because:
Outer space is the closest known approximation to a perfect vacuum. It has effectively no friction, allowing stars, planets and moons to move freely along their ideal orbits. However, even the deep vacuum of intergalactic space is not devoid of matter, as it contains a few hydrogen atoms per cubic meter.
If there's matter in space, thus this makes this statement valid.
Yes, everything that has mass will cause a gravitational pull on other objects.
• This isn't really an answer. The OP states that the universe has "objects" and "space" and wants to know if the "space" has gravity. Your answer boils down to "there are objects throughout space, and objects have gravity". Feb 5, 2016 at 15:59
In the intergalactic medium — the most dilute regions of the Universe between the galaxies — as CipherBot writes you'll find roughly one hydrogen per cubic meter, i.e. the density is $\sim10^{-6}\,\mathrm{atoms}\,\mathrm{cm}^{-3}$, or $\sim10^{-30}\,\mathrm{g}\,\mathrm{cm}^{-3}$, or, in terms of energy (since mass and energy are equivalent through $E=mc^2$), $\sim10^{-9}\,\mathrm{erg}^\dagger$. In addition to this, you'll find 5–6 times as much dark matter.
Space itself can't really be considered "an object". Nevertheless, even ignoring the normal and dark matter, space does have energy: the so-called dark energy. We don't really know much about it, but we can measure its presence through its effect on the expansion of the Universe. But whereas normal and dark matter decelerates this expansion, dark energy has the opposite effect of accelerating the expansion. And since the energy density of dark energy is more than twice that of the other two components together, it actually dominates the dynamics of the Universe.
So, in this regard you can say that space does have gravity, although it's a "negative gravity". This phrasing is a bit misinterpreted, though. The dark energy is thought to be a negative pressure. Pressure has a energy density associated with is, so negative pressure has a negative energy density.
$^\dagger$$1\,\mathrm{erg}\equiv10^{-7}\,\mathrm{Joule}$.
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https://www.physicsforums.com/threads/another-indefinite-integral-question.208613/
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# Another indefinite integral question?
1. Jan 13, 2008
### uman
How to evaluate $$\int{\frac{\arccos{x}}{x^2}\,dx}$$?
2. Jan 13, 2008
### Rainbow Child
Try the substition
$$x=\cos u,\,d\,x=-\sin u\,d\,u$$
and then integrate by parts.
3. Jan 15, 2008
### rohanprabhu
Perfect..
$$x = cos(u)~;~du = -sin(u)$$
also,
$$x^2 = cos^2(u)$$
Therefore we have,
$$\int\frac{cos^{-1}(x)}{x^2}dx = I = \int\frac{u sin(u)}{cos^{2}(u)}du$$
$$I = -\int u tan(u)sec(u)du$$
$$I = -\left[u sec(u) - \int \frac{du}{du} \int sec(u)tan(u)du du\right]$$
$$I = -\left[u sec(u) - \int sec(u)du\right]$$
$$I = log_e|sec(u) + tan(u)| - u sec(u) + C$$
Then, you can replace the value of u with $cos(x)$ to get the required integral.
4. Jan 15, 2008
### arildno
Blunder there, you are to substitute $u=\cos^{-1}(x)$
Last edited: Jan 15, 2008
5. Jan 15, 2008
### rohanprabhu
$u = \cos^{-1}(x)~;~x = \cos(u)$.. it's the same thing within a restricted domain.
6. Jan 15, 2008
### arildno
You wrote substitute u with cos(x), which is wrong.
7. Jan 15, 2008
### rohanprabhu
ohh.. u mean in the last part.. yeah.. i get it now... ur right :D
Similar Discussions: Another indefinite integral question?
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https://www.physicsforums.com/threads/efficiency-of-an-infinite-series-of-carnot-cycles.76225/
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# Efficiency of an infinite series of Carnot cycles
1. May 19, 2005
### Iraides Belandria
Dear people of Physics Forums, I would like to have your opinion about the following problem: Suppose we are interested to evaluate the average efficiency ( e ) of an infinite series of carnot cycles. The temperature of the hot reservoir of each carnot Cycle of the series, Ta, is at 990K, but the cold reservoir of each cycle is at different temperatures ( Tb ) ranging from 295 K to 752K , in such a way that, the cold reservoir of the first carnot cycle is at 295 K and the cold reservoir of the last is at 752 K. ¿ What is the average efficiency of these series of Carnot cycles?. Now, we know that the efficiency of each Carnot cycle can be determined with the equation e= 1-Tb/Ta. Since we know the temperatures we can calculate the efficiency of each Carnot cycle of the series ranging from 295 to 752 K(e1, e2, e3, e4, e5, e6,e7............. ). ?How can we get the average efficiency from these set of individual values?. I notice that if I plot the efficiency of each Carnot Cycle versus Tb ( the cold resrvoir temperature of each cycle) I get an straight line. Then I applied the mean value theorem to get the average efficiency. I found that the average efficiency is 0.47. ? Is this procedure correct?.
2. May 20, 2005
### Andrew Mason
The average efficiency would be the total work (output) divided by the total heat input:
Qh is the same for each cycle. Qc is proportional to Tc (Qc/Tc = Qh/Th). Since, W = Qh - Qc,
$$\eta = \frac{W}{Q_h} = \frac{\sum_{i=1}^n Q_h - Q_c(i)}{nQ_h}$$
$$\eta = \frac{\sum_{i=1}^n 1 - Q_c(i)/Q_h}{n}$$
$$\eta = \frac{\sum_{i=1}^n 1 - T_c(i)/T_h}{n}$$
$$\eta = \frac{1}{n}\sum_{i=1}^n 1 - T_c(i)/T_h$$
$$\eta = \frac{1}{n}\sum_{i=1}^n \eta(i)$$
So the total efficiency over n cycles is 1/n times the sum of the efficiencies of each cycle.
AM
3. May 20, 2005
### Iraides Belandria
Thanks Andrew for your help, but I still have a question because I have to sum infinite cycles and divide by n. ¿How can I get a numerical answer?. Because of this I use the mean value theorem of calculus. ¿Is that correct?
4. May 20, 2005
### Iraides Belandria
Again, Andrew, ¿Why do you assume that each cycle receive the same amount of heat Qa? ¿ Will the average efficiency change if each cycle receive a different amount of heat, Qa1, Qa2, Qa3,......?. Thanks
5. May 20, 2005
### Andrew Mason
You would have to work out the series and determine the limit as $n \rightarrow \infty$
$$\eta = \frac{1}{n}\sum_{i=1}^n 1 - T_c(i)/T_h = \frac{1}{n}(n - \frac{1}{T_h}\sum_{i=1}^n T_c(i))$$
Now if Tc is linear and the increments of Tc are 1 degree at a time then n = $T_{cend} - T_{cbeg} + 1$ so
$$\sum_{i=1}^n T_c(i) = \frac{(T_{cend} + T_{cbeg})(T_{cend} - T_{cbeg} + 1)}{2}$$
So:
$$\eta = \frac{1}{n}(n - \frac{1}{T_h}\frac{(T_{cend} + T_{cbeg})(T_{cend} - T_{cbeg} + 1)}{2}) = (1 - \frac{(T_{cend} + T_{cbeg})(T_{cend} - T_{cbeg} + 1)}{2nT_h})$$
Substitute for $n = T_{cend} - T_{cbeg} + 1$:
$$\eta = (1 - \frac{(T_{cend} + T_{cbeg})(T_{cend} - T_{cbeg} + 1)}{2T_h(T_{cend} - T_{cbeg} + 1)}) = (1 - \frac{(T_{cend} + T_{cbeg})}{2T_h})$$
As you increase n and decrease the increments, the series should converge to something very very close to this (if it is linear).
AM
Last edited: May 20, 2005
6. May 20, 2005
### Andrew Mason
Why would Qh depend upon Qc?
AM
7. May 20, 2005
### Iraides Belandria
Excuse me, I don understand your answer to the second question.¿Would the average efficiency depends upon the heat received by each carnot cycle of the series or it is independen of it?
8. May 21, 2005
### Andrew Mason
The average efficiency would depend on the total heat received, which is the sum of the heats received in each carnot cycle. I am assuming they are the same but they may not be. I was asking you why they would depend on Qc.
AM
9. May 21, 2005
### Iraides Belandria
I appreciate very much your interest in trying to solve my doubts about this problem. Indeed I am not sure if Qh depend upon Qc. My principal doubt at this moment is if the average efficiency of the series is independent of the amount of heat received by each Carnot Cycle. In your solution you assume that each cycle receives the same amount of heat. But what happen, if the case is more general, and we assume different values for each carnot Cycle?. Would we obtain the same value?. Thanks
10. May 23, 2005
### Iraides Belandria
Other mathematical question is related to find an average for a set of infinite values of efficiencies. As I have stated at the beginning of the thread, we can estimate the numerical eficciency of each Carnot cycle of the series without problem, because I know the temperatures of each Cycle. ?How can we evaluate the average of these values of efficiencies of the infinite carnot cycles?.We also can see that these set of values of efficiency varies linearly with Tc. ¿If this is the case, would be correct to say that the average coincides with the value giving by the limit of above series?.
11. May 23, 2005
### Andrew Mason
As I said before, the average efficiency is the total Work done divided by the total heat input. You can't assume that the average efficiency is the average of all the individual efficiencies just as you cannot determine average speed by averaging speeds (ie. average speed it is total distance divided by total time not an average of speeds over the journey).
AM
12. May 25, 2005
### Iraides Belandria
Dear Mason, If we assume that each carnot cycle receive differents amounts of heat from the hot reservoir, Qh1, Qh2, Qh3,....Qhi, we get the following expression for the average efficiency (Using above procedure)
n = (Qh1/Qh) n1+ (Qh2/Qh) n2 + (Qh3/Qh) n3 + .....(Qhi/Qh) ni
Where Qh is the total heat received fom the hot reservoir equal to Qh=Qh1+Qh2+ Qh3+ ......+Qhi+.... , and ni are efficiencies of each cycle
This equation shows that the average eficciency, n , depends on the amount of heat received by the cycles. In a certain way each Qhi/Qh is a weigth to average the efficiency of the series of cycles. In your deduction you use a uniform weigth to get the average efficiency , Qhi /Qh = N , Where N is the number of carnot cycles. ¿Is this the weigth that we must use in order to compare the performance of any cycle against a series of carnot cycles?. ¿Statiscally , what will be the best weigth to compare an specific Cycle? ? What weight is fair, just ?
13. Jun 2, 2005
### Iraides Belandria
Dear Andrew Mason, I have tried to understand how you obtain the following expresions in the limit of the serie proposed by you
n= Tcend -Tcbeg + 1
and
summatory Tc(i)= [(Tcend + Tc beg) ( Tcend - Tc beg + 1)] / 2
Could you explain these equations with more details?
Thanks
14. Jun 2, 2005
### Andrew Mason
It is just the sum of an arithmetic series with increment of 1.
$$S = (n / 2) * [2i + (n-1)]$$ where n = Tcend - Tcbeg + 1 and i = Tcbeg
eg:
$$5 + 6 + 7 + 8 + 9 + 10$$
n = 6 (10-5+1); i = 5; S = (6/2) * (10 + 5) = 3 * 15 = 45
AM
15. Jun 3, 2005
### Iraides Belandria
Andrew, Thank you, very much. I appreciate your cooperation, and I would like to say that my empirical results coincide with your proposition, as you may verify in the begining of this thread. In any case, the most important consequence of this discussion is that I have found a thermodynamic cycle, operating between the temperatures levels proposed in this post, more efficient than an infinite series of carnot cycles. Because of this reason, I have insisted so much in the solution of this problem, from differents points of view. All of the alternatives, I have explored coincide with your results. thanks to god. Now, I think I am confident on my results. I am going to try to publish an article related to this cycle, and I am going to use this thread as a bibliographycal reference. ¿ Can I do this? . In the future, I will inform you about it.
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https://learnenglishnative.com/category/uncategorized/
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## 10 Ways to Say Thank you in English – Part III
Final Tips
Write these words in your notebook to be able to review them every day
Listen to the pronunciation many times then repeat it
This is an easy lesson, right?
Test yourself NOW to make sure that you understand this lesson.
👇👇
Correct! Wrong!
Correct! Wrong!
Correct! Wrong!
Correct! Wrong!
Correct! Wrong!
#### one of the ways to say thank you is ...........
Correct! Wrong!
10 Ways to Say Thank you in English Quiz
Try one more time
Excellent
Read More: Free online English course in AUC
## 10 Ways to Say Thank you in English – Part II
Now, Let’s Learn more about “10 Ways to Say Thank you in English + Their English Pronunciation” 💪
I really appreciate it
That’s very kind
Thanks a bunch
I can’t thank you enough
You’re the best
I owe you one
Thanks so much
I’m so grateful
How kind of you
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http://philpapers.org/s/Ji%C5%99%C3%AD%20Rosick%C3%BD
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## Works by Jiří Rosický
1. Tibor Beke & Jirí Rosický (2012). Abstract Elementary Classes and Accessible Categories. Annals of Pure and Applied Logic 163 (12):2008-2017.
My bibliography
Export citation
2. S. Awodey & Jiri Rosicky (2007). REVIEWS-Category Theory. Bulletin of Symbolic Logic 13 (3).
My bibliography
Export citation
3. Jiří Rosický (1997). Accessible Categories, Saturation and Categoricity. Journal of Symbolic Logic 62 (3):891-901.
Model-theoretic concepts of saturation and categoricity are studied in the context of accessible categories. Accessible categories which are categorical in a strong sense are related to categories of $M$-sets ($M$ is a monoid). Typical examples of such categories are categories of $\lambda$-saturated objects.
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https://kb.osu.edu/dspace/handle/1811/17649
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A FORBIDDEN BAND IN THE FAR INFRARED SPECTRUM OF $H^{1 3}CNO$
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/17649
Files Size Format View
1988-TB-11.jpg 112.1Kb JPEG image
Title: A FORBIDDEN BAND IN THE FAR INFRARED SPECTRUM OF $H^{1 3}CNO$ Creators: Winnewisser, M.; Wagner, G.; Winnewisser, B. P. Issue Date: 1988 Publisher: Ohio State University Abstract: The far infrared spectrum of HCNO exhibits a widely spread set of perpendicular transitions in the manifold of the quasilinear bending mode, $\nu_{o}$. and the corbiration manifold $\nu_{4} - n\nu$ where $\nu_{4}$ is the skeletal bending mode. We have analyzed the spectrum of the $^{13}C$ substituted species, and found a Q branch without any P or R branches and a P. R. subband without any Q branch. Neither of these features are observed in the spectrum of the parent species. They have been assigned to the vibrational transitions $(v_{i}v_{a})^{\ell} = (02)^{\prime\prime} (11)^{0*}$ and $(02)^{0*}= (11)^{0*}$ respectively. These transitions are only allowed due to a Conclis interaction between the levels $(02)^{0e}$ and $(10)^{1e}$ which was observed as a relatively weak interaction in the parent species. Description: Author Institution: Physikalich-Chemisches Institut, Justut Liebig Universitat URI: http://hdl.handle.net/1811/17649 Other Identifiers: 1988-TB-11
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https://www.ourxanadu.net/info/1115/18725.htm
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Exact overlaps on the projections of four corner Cantor set
The four corner Cantor set C is a planar self-similar set generated by the IFS {(x/4, y/4), ((x+3)/4,y/4), (x/4,(y+3)/4), ((x+3)/4,(y+3)/4)}. In this talk I will give a complete characterization on the set of ts in which the projection C_t:={x+ty: (x,y)\in C} is a self-similar set having an exact overlap; the distribution of these ts in the real line is also considered. This is joint work with Beibei Sun.
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http://papers.neurips.cc/paper/5226-near-optimal-density-estimation-in-near-linear-time-using-variable-width-histograms
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# NIPS Proceedingsβ
## Near-Optimal Density Estimation in Near-Linear Time Using Variable-Width Histograms
[PDF] [BibTeX] [Supplemental] [Reviews]
### Abstract
Let $p$ be an unknown and arbitrary probability distribution over $[0 ,1)$. We consider the problem of \emph{density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a hypothesis distribution that is close to $p$. The main contribution of this paper is a highly efficient density estimation algorithm for learning using a variable-width histogram, i.e., a hypothesis distribution with a piecewise constant probability density function. In more detail, for any $k$ and $\eps$, we give an algorithm that makes $\tilde{O}(k/\eps^2)$ draws from $p$, runs in $\tilde{O}(k/\eps^2)$ time, and outputs a hypothesis distribution $h$ that is piecewise constant with $O(k \log^2(1/\eps))$ pieces. With high probability the hypothesis $h$ satisfies $\dtv(p,h) \leq C \cdot \opt_k(p) + \eps$, where $\dtv$ denotes the total variation distance (statistical distance), $C$ is a universal constant, and $\opt_k(p)$ is the smallest total variation distance between $p$ and any $k$-piecewise constant distribution. The sample size and running time of our algorithm are both optimal up to logarithmic factors. The approximation factor'' $C$ that is present in our result is inherent in the problem, as we prove that no algorithm with sample size bounded in terms of $k$ and $\eps$ can achieve $C < 2$ regardless of what kind of hypothesis distribution it uses.
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https://www.physicsforums.com/threads/period-of-oscillation-of-a-rocking-semi-cylinder.289850/
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# Period of oscillation of a rocking semi cylinder?
1. Feb 4, 2009
### jaron_denson
1. The problem statement, all variables and given/known data
a thin rectangular plate is bent into a semicircular cylinder, dertermine the period of oscillation if it is allowed to rock on a horizantal surface.
3. The attempt at a solution
So I can figure out the rest of the problem if I know what the moment of inertia of a half cylinder is. My side note is a guess, but not sure if it is correct. I checked around online couldn't find anything that helpful
Can you offer guidance or do you also need help?
Draft saved Draft deleted
Similar Discussions: Period of oscillation of a rocking semi cylinder?
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https://arxiv.org/abs/hep-ph/0408191
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hep-ph
(what is this?)
# Title: Seesaw induced electroweak scale, the hierarchy problem and sub-eV neutrino masses
Abstract: We describe a model for the scalar sector where all interactions occur either at an ultra-high scale L_U ~ 10^{16}-10^{19} GeV or at an intermediate scale L_I ~ 10^{9}-10^{11} GeV. The interaction of physics on these two scales results in an SU(2) Higgs condensate at the electroweak (EW) scale, L_{EW}, through a seesaw-like Higgs mechanism, L_{EW} ~ L_I^2/L_U, while the breaking of the SM SU(2)XU(1) gauge symmetry occurs at the intermediate scale L_I. The EW scale is, therefore, not fundamental but is naturally generated in terms of ultra-high energy phenomena and so the hierarchy problem is alleviated. We show that the class of such seesaw Higgs'' models predict the existence of sub-eV neutrino masses which are generated through a two-step'' seesaw mechanism in terms of the same two ultra-high scales: m_nu ~ L_I^4/L_U^3 ~ L_{EW}^2/L_U. The neutrinos can be either Dirac or Majorana, depending on the structure of the scalar potential. We also show that our seesaw Higgs model can be naturally embedded in theories with tiny extra dimensions of size R ~ 1/L_U ~ 10^{-16} fm, where the seesaw induced EW scale arises from a violation of a symmetry at a distant brane; in particular, in the scenario presented there are 7 tiny extra dimensions.
Comments: latex, 25 pages, no figures. Version 2 is a shorter version (as accepted in EPJC), not including the discussion on the heavy seesaw Higgs model Subjects: High Energy Physics - Phenomenology (hep-ph) Journal reference: Eur.Phys.J.C45:219-225,2006 DOI: 10.1140/epjc/s2005-02403-x Report number: BNL-HET-04/10 Cite as: arXiv:hep-ph/0408191 (or arXiv:hep-ph/0408191v2 for this version)
## Submission history
From: Shaouly Bar-Shalom [view email]
[v1] Tue, 17 Aug 2004 18:56:24 GMT (25kb)
[v2] Mon, 19 Sep 2005 19:26:06 GMT (15kb)
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http://export.arxiv.org/list/cond-mat.dis-nn/1904?show=97
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# Disordered Systems and Neural Networks
## Authors and titles for cond-mat.dis-nn in Apr 2019
[ total of 97 entries: 1-97 ]
[ showing 97 entries per page: fewer | more ]
[1]
Title: The phase diagram of a two-dimensional dirty tilted Dirac semimetal
Authors: Yu-Li Lee, Yu-Wen Lee
Comments: 17 pages, 11 figures
Journal-ref: Phys. Rev. B 100, 075156 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el)
[2]
Title: Benchmarking the nonperturbative functional renormalization group approach on the random elastic manifold model in and out of equilibrium
Comments: 38 pages, 6 figures
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[3]
Title: Monte Carlo algorithms are very effective in finding the largest independent set in sparse random graphs
Comments: 14 pages, 12 figures
Journal-ref: Phys. Rev. E 100, 013302 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS)
[4]
Title: From ergodic to non-ergodic chaos in Rosenzweig-Porter model
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[5]
Title: Mean field theory of jamming of nonspherical particles
Comments: 30 pages, 5 figures
Journal-ref: J. Phys. A: Math. Theor 52, 344001 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Soft Condensed Matter (cond-mat.soft); Statistical Mechanics (cond-mat.stat-mech)
[6]
Title: The system of correlation kinetic equations and the generalized equivalent circuit for hopping transport
Journal-ref: Phys. Rev. B 100, 014202 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[7]
Title: Quantum quenches in isolated quantum glasses out of equilibrium
Comments: 5 pages, 3 figures + Supplementary Material
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[8]
Title: Locally self-consistent embedding approach for disordered electronic systems
Comments: 7 pages, 5 figures
Journal-ref: Phys. Rev. B 100, 054205 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[9]
Title: Entanglement in non-equilibrium steady states and many-body localization breakdown in a current driven system
Comments: 11 pages, 10 figures
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[10]
Title: Effective resistance of random percolating networks of stick nanowires : functional dependence on elementary physical parameters
Comments: 16 pages, 4 figures, regular article
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[11]
Title: Energy level dynamics across the many-body localization transition
Comments: version close to that accepted in PRB
Journal-ref: Phys. Rev. B 99, 224202 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
[12]
Title: Phonon localization in binary alloys with diagonal and off-diagonal disorder: A cluster Green's function approach
Journal-ref: Phys. Rev. B 99, 134203, 2019
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[13]
Title: Conductance distribution in 1D systems: dependence on the Fermi level and the ideal leads
Authors: I. M. Suslov (P.L.Kapitza Institute for Physical Problems, Moscow, Russia)
Comments: Latex, 22 pages, 11 included
Journal-ref: J.Exp.Theor.Phys. v.129, p.877 (2019) [Zh.Eksp.Teor.Fiz. v.156, p.950 (2019)]
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[14]
Title: Transport of light through a dense ensemble of cold atoms in a static electric field
Comments: Revised text. 9 pages, 3 figures
Journal-ref: Phys. Rev. A 100, 013821 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Atomic Physics (physics.atom-ph); Optics (physics.optics)
[15]
Title: On non-negative solutions to large systems of random linear equations
Comments: 10 pages, 5 figures
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Populations and Evolution (q-bio.PE)
[16]
Title: Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
Comments: 12 pages, 5 figures, Comments welcome
Journal-ref: Phys. Rev. B 100, 094201 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Chaotic Dynamics (nlin.CD); Quantum Physics (quant-ph)
[17]
Title: How collective asperity detachments nucleate slip at frictional interfaces
Journal-ref: Proc. Natl. Acad. Sci. U.S.A., 2019, 116(48):23977-23983
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[18]
Title: Learning a Local Symmetry with Neural-Networks
Comments: 4 pages, 4 figures + appendices
Journal-ref: Phys. Rev. E 100, 050102 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG)
[19]
Title: Dipolar Bose gas with three-body interactions in weak disorder
Comments: 6 pages, 3 figures
Journal-ref: Eur. Phys. J. D 73,115 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas)
[20]
Title: Maximum-energy records in glassy energy landscapes
Comments: 22 pages, 5 figures; revised presentation
Journal-ref: J. Stat. Mech. (2019) 093302
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[21]
Title: Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification
Comments: 5 pages, 5 figures
Journal-ref: EPL 127 (2019) 46001
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[22]
Title: Two critical localization lengths in the Anderson transition on random graphs
Comments: 6 pages, 3 figures; Corresponds to the published version
Journal-ref: Phys. Rev. Research 2, 012020 (2020)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
[23]
Title: High Entropy Alloys Mined From Phase Diagrams
Comments: 20 pages, 6 figures
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Materials Science (cond-mat.mtrl-sci)
[24]
Title: Condensation of degrees emerging through a first-order phase transition in classical random graphs
Comments: 8 pages, 6 figures
Journal-ref: Phys. Rev. E 100, 012305 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Physics and Society (physics.soc-ph)
[25]
Title: Many-Body Dynamical Localization in a Kicked Lieb-Liniger Gas
Comments: 5 pages, 2 figures
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[26]
Title: Resilience for stochastic systems interacting via a quasi-degenerate network
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Pattern Formation and Solitons (nlin.PS); Biological Physics (physics.bio-ph); Populations and Evolution (q-bio.PE)
[27]
Title: Analytical study of quasi-one dimensional flat band networks and slow light analogue
Authors: Atanu Nandy
Comments: 11 pages, 11 eps figures (Accepted in Acta Physica Polonica A). arXiv admin note: text overlap with arXiv:1901.09242
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
[28]
Title: Relaxation dynamics of the Ising $p$-spin disordered model with finite number of variables
Comments: 7 pages, 6 figures, final version
Journal-ref: EPL, 127 (2019) 16002
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[29]
Title: The Dyck bound in the concave 1-dimensional random assignment model
Comments: 31 pages, 5 figures
Journal-ref: Journal of Physics A: Mathematical and Theoretical, 2020, 53.6: 064001
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[30]
Title: Variational approach to unsupervised learning
Comments: 5 pages, 2 figures
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG)
[31]
Title: The interpretation of broad diffuse maxima using superspace crystallography
Journal-ref: Phys. Rev. B 100, 054201 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Materials Science (cond-mat.mtrl-sci)
[32]
Title: Robustness of delocalization to the inclusion of soft constraints in long-range random models
Comments: 10 pages, 5 figures, 94 references + 5 pages of Appendices
Journal-ref: Phys. Rev. B 99, 224208 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[33]
Title: Statistics of domain wall roughness: A survey of different scaling analyses
Comments: 11 pages, 10 figures
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[34]
Title: Can Local Stress Enhancement Induce Stability in Fracture Processes? Part II: The Shielding Effect
Comments: 8 pages, 11 figures
Journal-ref: Front. Phys. (2019) 7:156
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[35]
Title: Level Repulsion and Dynamics in the Finite One-Dimensional Anderson Model
Comments: 11 pages, 5 figures, version as published
Journal-ref: Phys. Rev. E 100, 022142 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[36]
Title: Correlations between avalanches in the depinning dynamics of elastic interfaces
Comments: 31 pages, 6 figures
Journal-ref: Phys. Rev. E 101, 032108 (2020)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Chaotic Dynamics (nlin.CD)
[37]
Title: Irreversible Eshelby description of aging in glasses
Authors: U. Buchenau
Comments: 3 pages, 3 figures
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Soft Condensed Matter (cond-mat.soft)
[38]
Title: On the Structure of Liquids: More order than expected
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Soft Condensed Matter (cond-mat.soft); Statistical Mechanics (cond-mat.stat-mech)
[39]
Title: Disordered Ising model with correlated frustration
Journal-ref: 2019 J. Phys. A: Math. Theor. 52 174002
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[40]
Title: Supplemental Material: Eshelby ensemble of highly viscous flow out of equilibrium
Authors: U. Buchenau
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
[41]
Title: Minimal model of permutation symmetry in unsupervised learning
Comments: 36 pages, 110 equations, 5 figures; a complete picture about physical laws of unsupervised learning in neural networks presented
Journal-ref: 2019 J. Phys. A: Math. Theor. 52 414001
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); Neurons and Cognition (q-bio.NC); Machine Learning (stat.ML)
[42]
Title: Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
Comments: v2: published version
Journal-ref: Phys. Rev. B 100, 224202 (2019)
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el)
[43] arXiv:1904.01593 (cross-list from cond-mat.str-el) [pdf, other]
Title: Fractal x-ray edge problem at the critical point of the Aubry-André model
Comments: 12 pages, 10 figures
Journal-ref: Phys. Rev. B 100, 165116 (2019)
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas)
[44] arXiv:1904.01813 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Intermediate deviation regime for the full eigenvalue statistics in the complex Ginibre ensemble
Comments: 10 pages, 3 Figures
Journal-ref: Phys. Rev. E 100, 012137 (2019)
Subjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mathematical Physics (math-ph)
[45] arXiv:1904.02174 (cross-list from cond-mat.str-el) [pdf, other]
Title: Transport and chaos in lattice Sachdev-Ye-Kitaev models
Comments: 25 pages, 26 figures; v2: Added a new Sec.II and a new figure; Added clarifications; Corrected Typos
Journal-ref: Phys. Rev. B 100, 045140 (2019)
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th)
[46] arXiv:1904.03047 (cross-list from cond-mat.mtrl-sci) [pdf, other]
Title: Common universal behaviors of magnetic domain walls driven by spin-polarized electrical current and magnetic field
Journal-ref: Phys. Rev. B 100, 184420 (2019)
Subjects: Materials Science (cond-mat.mtrl-sci); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
[47] arXiv:1904.03312 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: The matrix product approximation for the dynamic cavity method
Authors: Thomas Barthel
Comments: 23 pages, 14 figures; added data showing a linear temporal increase of computation costs for Glauber-Ising dynamics; codes provided at this http URL; published version
Journal-ref: J. Stat. Mech. (2020) 013217
Subjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[48] arXiv:1904.03463 (cross-list from cond-mat.stat-mech) [pdf, ps, other]
Title: Flat-band many-body localization and ergodicity breaking in the Creutz ladder
Comments: 24 pages, 14 figures, accepted version, to appear in New Journal of Physics
Journal-ref: New J. Phys. 22 013032 (2020)
Subjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas)
[49] arXiv:1904.04275 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Real-Space Visualization of Quantum Phase Transition by Network Topology
Comments: 7 pages, 6 figures
Journal-ref: Phys. Rev. E 100, 012304 (2019)
Subjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)
[50] arXiv:1904.04773 (cross-list from cond-mat.supr-con) [pdf, other]
Title: Defect-engineered, universal kinematic correlations among superconductivity and Fermi liquid transport
Comments: main text - pages 1 to 27, 7 figures; supplementary material - pages 28 to 42
Subjects: Superconductivity (cond-mat.supr-con); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[51] arXiv:1904.05079 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Eigenvalue and Eigenvector Statistics in Time Series Analysis
Comments: 8 pages, 3 figures
Subjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[52] arXiv:1904.05252 (cross-list from cond-mat.str-el) [pdf, other]
Title: Dynamics of Phase Separated States in the Double Exchange Model
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[53] arXiv:1904.05407 (cross-list from cond-mat.mtrl-sci) [pdf, other]
Title: Tuning the glass-forming ability of metallic glasses through energetic frustration
Journal-ref: Phys. Rev. Materials 3, 085602 (2019)
Subjects: Materials Science (cond-mat.mtrl-sci); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[54] arXiv:1904.05749 (cross-list from cond-mat.mtrl-sci) [pdf, other]
Title: Room temperature spin-ice physics in cadmium cyanide
Comments: 25 pages, 4 figures
Subjects: Materials Science (cond-mat.mtrl-sci); Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el)
[55] arXiv:1904.05872 (cross-list from cond-mat.str-el) [pdf, other]
Title: Tunable Giant Exchange Bias in an Intercalated Transition Metal Dichalcogenide
Comments: 18 pages, 4 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn); Materials Science (cond-mat.mtrl-sci)
[56] arXiv:1904.06928 (cross-list from cond-mat.str-el) [pdf, other]
Title: Slow dynamics and strong finite-size effects in many-body localization with random and quasi-periodic potential
Comments: 11 Figs, 11 pages
Journal-ref: Phys. Rev. B 100, 104204 (2019)
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[57] arXiv:1904.07251 (cross-list from cond-mat.str-el) [pdf, other]
Title: Electric Field Response In Breathing Pyrochlores
Authors: Ipsita Mandal
Journal-ref: Eur. Phys. J. B (2019) 92: 187
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn); Materials Science (cond-mat.mtrl-sci); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th)
[58] arXiv:1904.07359 (cross-list from cond-mat.soft) [pdf, other]
Title: Universal relaxation dynamics of sphere packings below jamming
Comments: 6 pages, 5 figures
Journal-ref: Phys. Rev. Lett. 124, 058001 (2020)
Subjects: Soft Condensed Matter (cond-mat.soft); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[59] arXiv:1904.09166 (cross-list from cond-mat.str-el) [pdf, other]
Title: Emergence of magnetism in bulk amorphous palladium
Comments: 6 Pages, 4 Figures, 1 Table
Journal-ref: Phys. Rev. B 100, 024422 (2019)
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Disordered Systems and Neural Networks (cond-mat.dis-nn); Materials Science (cond-mat.mtrl-sci)
[60] arXiv:1904.09932 (cross-list from cond-mat.mes-hall) [pdf, other]
Title: Higher-Order Topological Insulators in Quasicrystals
Comments: 5 pages, 4 figures, 8 pages of supplementary materials, accepted by Physical Review Letters
Journal-ref: Phys. Rev. Lett. 124, 036803 (2020)
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[61] arXiv:1904.10838 (cross-list from cond-mat.soft) [pdf, ps, other]
Title: Universal size and shape ratios for arms in star-branched polymers: theory and mesoscopic simulations
Journal-ref: Macromol. Theory Simul. 2019, 1900012(1-9)
Subjects: Soft Condensed Matter (cond-mat.soft); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[62] arXiv:1904.10966 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Integrable and chaotic dynamics of spins coupled to an optical cavity
Comments: v3: Published version. Included more data and updated the figures accordingly
Journal-ref: Phys. Rev. X 9, 041011 (2019)
Subjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)
[63] arXiv:1904.11522 (cross-list from cond-mat.mes-hall) [pdf, ps, other]
Title: Quasiperiodic magnetic chain as a spin filter for arbitrary spin states
Authors: Biplab Pal
Comments: 8 pages, 5 figures, published version
Journal-ref: Phys. Rev. B 99, 134431 (2019)
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[64] arXiv:1904.12944 (cross-list from cond-mat.soft) [pdf, other]
Title: Long-wavelength fluctuations and static correlations in quasi-2D colloidal suspensions
Authors: Bo Zhang, Xiang Cheng
Comments: 11 pages, 12 figures, Soft Matter (accepted)
Subjects: Soft Condensed Matter (cond-mat.soft); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[65] arXiv:1904.13181 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Dynamics of strongly coupled disordered dissipative spin-boson systems
Journal-ref: Phys. Rev. Research 2, 013198 (2020)
Subjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)
[66] arXiv:1904.00031 (cross-list from quant-ph) [pdf, other]
Title: NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
Journal-ref: SoftwareX 10, 100311 (2019)
Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el); Computational Physics (physics.comp-ph); Data Analysis, Statistics and Probability (physics.data-an)
[67] arXiv:1904.00057 (cross-list from nucl-th) [pdf, other]
Title: Statistical learnability of nuclear masses
Authors: Andrea Idini
Subjects: Nuclear Theory (nucl-th); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG)
[68] arXiv:1904.00493 (cross-list from physics.optics) [pdf, other]
Title: Self-starting nonlinear mode-locking in random lasers
Comments: 13 pages, 8 figures, 1 table
Subjects: Optics (physics.optics); Disordered Systems and Neural Networks (cond-mat.dis-nn); Data Analysis, Statistics and Probability (physics.data-an)
[69] arXiv:1904.00626 (cross-list from math.DS) [pdf, other]
Title: State-dependent effective interactions in oscillator networks through coupling functions with dead zones
Subjects: Dynamical Systems (math.DS); Disordered Systems and Neural Networks (cond-mat.dis-nn); Adaptation and Self-Organizing Systems (nlin.AO)
[70] arXiv:1904.01220 (cross-list from math.PR) [pdf, other]
Title: Avalanches in an excitable network
Subjects: Probability (math.PR); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[71] arXiv:1904.01820 (cross-list from math.PR) [pdf, other]
Title: Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices
Subjects: Probability (math.PR); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Statistics Theory (math.ST)
[72] arXiv:1904.02467 (cross-list from quant-ph) [pdf, other]
Title: Neural network agent playing spin Hamiltonian games on a quantum computer
Comments: Local spin correction procedure was used to compensate real device errors; comparison with variational approach was added
Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[73] arXiv:1904.02808 (cross-list from cs.IT) [pdf, other]
Title: Overlap matrix concentration in optimal Bayesian inference
Authors: Jean Barbier
Subjects: Information Theory (cs.IT); Disordered Systems and Neural Networks (cond-mat.dis-nn); Probability (math.PR)
[74] arXiv:1904.03399 (cross-list from q-bio.NC) [pdf, other]
Title: Functional Geometry of Human Connectome and Robustness of Gender Differences
Comments: 13 pages, 7 figures
Subjects: Neurons and Cognition (q-bio.NC); Disordered Systems and Neural Networks (cond-mat.dis-nn); Algebraic Topology (math.AT)
[75] arXiv:1904.03910 (cross-list from q-bio.MN) [pdf]
Title: The EntOptLayout Cytoscape plug-in for the efficient visualization of major protein complexes in protein-protein interaction and signalling networks
Journal-ref: Bioinformatics 2019 35, 4490-4492
Subjects: Molecular Networks (q-bio.MN); Disordered Systems and Neural Networks (cond-mat.dis-nn); Computer Vision and Pattern Recognition (cs.CV); Biological Physics (physics.bio-ph)
[76] arXiv:1904.04154 (cross-list from stat.ML) [pdf, other]
Title: Bayesian Neural Networks at Finite Temperature
Comments: 11 pages, 4 figures
Subjects: Machine Learning (stat.ML); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG)
[77] arXiv:1904.04544 (cross-list from q-bio.NC) [pdf, other]
Title: Predicting synchronous firing of large neural populations from sequential recordings
Subjects: Neurons and Cognition (q-bio.NC); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[78] arXiv:1904.04565 (cross-list from cs.IT) [pdf, ps, other]
Title: Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization
Comments: 5 pages; typos corrected, references added; Proceedings of the 2019 IEEE Information Theory Workshop
Subjects: Information Theory (cs.IT); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mathematical Physics (math-ph)
[79] arXiv:1904.05060 (cross-list from stat.ME) [pdf, other]
Title: Network depth: identifying median and contours in complex networks
Subjects: Methodology (stat.ME); Disordered Systems and Neural Networks (cond-mat.dis-nn); Physics and Society (physics.soc-ph)
[80] arXiv:1904.05229 (cross-list from physics.optics) [pdf, other]
Title: Shaping the Branched Flow of Light through Disordered Media
Comments: 6 pages, 5 figures, including appendix
Journal-ref: PNAS - Proc. Natl. Acad. Sci. U.S.A. 116, 13260 (2019)
Subjects: Optics (physics.optics); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Chaotic Dynamics (nlin.CD)
[81] arXiv:1904.05294 (cross-list from math.PR) [pdf, other]
Title: Hamilton-Jacobi equations for finite-rank matrix inference
Subjects: Probability (math.PR); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[82] arXiv:1904.05523 (cross-list from physics.soc-ph) [pdf, other]
Title: Relational flexibility of network elements based on inconsistent community detection
Comments: 10 pages, 5 figures, 2 tables
Journal-ref: Phys. Rev. E 100, 022311 (2019)
Subjects: Physics and Society (physics.soc-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Social and Information Networks (cs.SI)
[83] arXiv:1904.05777 (cross-list from stat.ML) [pdf, other]
Title: Compressed sensing reconstruction using Expectation Propagation
Comments: 20 pages, 6 figures
Subjects: Machine Learning (stat.ML); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); Computational Physics (physics.comp-ph)
[84] arXiv:1904.05902 (cross-list from quant-ph) [pdf, other]
Title: Experimental neural network enhanced quantum tomography
Comments: 11 pages, 3+6 figures; All data and source code are available online; RevTeX
Journal-ref: npj Quantum Information 6:20 (2020)
Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
[85] arXiv:1904.06482 (cross-list from quant-ph) [pdf, other]
Title: Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
Comments: 11 pages, 6 figures
Journal-ref: Phys. Rev. B 101, 121108 (2020)
Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Chaotic Dynamics (nlin.CD)
[86] arXiv:1904.08891 (cross-list from math.PR) [pdf, other]
Title: Breaking of 1RSB in random MAX-NAE-SAT
Subjects: Probability (math.PR); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[87] arXiv:1904.09144 (cross-list from physics.data-an) [pdf, other]
Title: The peculiar statistical mechanics of Optimal Learning Machines
Authors: Matteo Marsili
Comments: 17 pages, 4 figures
Subjects: Data Analysis, Statistics and Probability (physics.data-an); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[88] arXiv:1904.09185 (cross-list from quant-ph) [pdf]
Title: Radial basis function network using Lambert-Tsallis Wq function
Comments: 9 pages, 6 figures
Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[89] arXiv:1904.10819 (cross-list from physics.optics) [pdf, other]
Title: All Optical Neural Network with Nonlinear Activation Functions
Comments: 6 pages, 4 figures
Journal-ref: Optica 6, 1132 (2019)
Subjects: Optics (physics.optics); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[90] arXiv:1904.10996 (cross-list from cs.LG) [pdf, other]
Title: PAN: Path Integral Based Convolution for Deep Graph Neural Networks
Journal-ref: ICML 2019 Workshop on Learning and Reasoning with Graph-Structured Representations (Oral)
Subjects: Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Social and Information Networks (cs.SI); Machine Learning (stat.ML)
[91] arXiv:1904.11420 (cross-list from nlin.AO) [pdf, other]
Title: Real-time vulnerability of synchronized states
Journal-ref: Phys. Rev. E 100, 052201 (2019)
Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Disordered Systems and Neural Networks (cond-mat.dis-nn)
[92] arXiv:1904.11472 (cross-list from math.DS) [pdf, other]
Title: Koopman Operator and its Approximations for Systems with Symmetries
Subjects: Dynamical Systems (math.DS); Disordered Systems and Neural Networks (cond-mat.dis-nn); Group Theory (math.GR); Spectral Theory (math.SP)
[93] arXiv:1904.12072 (cross-list from hep-lat) [pdf, other]
Title: Flow-based generative models for Markov chain Monte Carlo in lattice field theory
Comments: 13 pages, 7 figures; corrected normalization conventions in eqns. 20 and 23
Journal-ref: Phys. Rev. D 100, 034515 (2019)
Subjects: High Energy Physics - Lattice (hep-lat); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG)
[94] arXiv:1904.12591 (cross-list from cs.DC) [pdf, other]
Title: Winner-Take-All Computation in Spiking Neural Networks
Subjects: Distributed, Parallel, and Cluster Computing (cs.DC); Disordered Systems and Neural Networks (cond-mat.dis-nn); Neural and Evolutionary Computing (cs.NE); Neurons and Cognition (q-bio.NC)
[95] arXiv:1904.12702 (cross-list from nlin.CD) [pdf, ps, other]
Title: Non-monotonic diffusion rates in atom-optics Lévy kicked rotor
Comments: 5 pages, revtex
Journal-ref: Phys. Rev. E 100, 060201 (2019)
Subjects: Chaotic Dynamics (nlin.CD); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)
[96] arXiv:1904.06632 (cross-list from stat.ME) [pdf, ps, other]
Title: Analysis of overfitting in the regularized Cox model
Subjects: Methodology (stat.ME); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)
[97] arXiv:1904.09238 (cross-list from physics.soc-ph) [pdf, other]
Title: A Model for the Influence of Media on the Ideology of Content in Online Social Networks
Subjects: Physics and Society (physics.soc-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Social and Information Networks (cs.SI)
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# Mayer, L (2009). Formation of supermassive black hole binaries and massive seed SMBHs in gas-rich mergers. In: Hunting for the Dark: the Hidden Side of Galaxy Formation, Qawra, Malta, 19 October 2009 - 23 October 2009, 181-194.
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## Abstract
We review the results of multi-scale, hydrodynamical simulations of major mergers between galaxies with or without central supermassive black holes (SMBHs) to investigate the orbital decay of SMBH pairs in galactic nuclei and the formation of massive SMBH seeds via direct gas collapse. Both SPH simulations and AMR simulations are carried out. The complex balance between heating and cooling is modeled via an effective EOS with varying adiabatic index γ apparopriate for the conditions of an intense nuclear starburst such as that expected during and after the merger. Prominent gas inflows due to tidal torques produce nuclear disks at the centers of merger remnants whose properties depend sensitively on the details of gas thermodynamics. In parsec-scale resolution simulations starting with two SMBHs originally at the centers of the two galaxies, a SMBH binary forms very rapidly, less than a million years after the merger of the two galaxies, owing to the drag exerted by the surrounding gaseous nuclear disk. Binary formation is significantly suppressed if heating, by e.g. radiative feedback from the accreting SMBHs, renders cooling negligible.
The nuclear disk rearranges its mass distribution in response to a second, internal gas inflow occurring while the binary sinks. The inflow is driven by spiral instabilities imprinted by the final collision between the two galactic cores. In simulations with 0.1 pc resolution, the gas inflow continues all the way down to the center and peaks at >104 Msolar/yr, producing a Jeans-unstable supermassive central cloud (with mass a few times 108 Msolar) only 105 yr after the merger. If the collapse continues, the cloud could form a massive black hole seed (Mseed>105 Msolar) after prior formation of a supermassive star or quasi-star. The massive SMBH seed can grow up to a billion solar masses in less than a billion years by accreting the surrounding nuclear gas. If the gas-rich merger occurs at z>8, this is then a new, attractive way to explain the rapid emergence of the bright QSOs discovered by the Sloan Digital Sky survey at z>6, which does not require the assumption of primordial gas composition in order to suppress cooling below 104 K and star formationas in models starting from unstable, isolated protogalactic disks. If there is a pre-existing pair of SMBHs their orbital decay stalls at parsec scales because, as a result of the formation of the supermassive cloud, the nuclear disk density decreases outside the cloud, yielding much weaker dynamical friction. We envision a new scenario in which direct formation of massive black hole seeds and SMBH binary formation are mutually exclusive; if a SMBH is already present in the nuclear disk it can stabilize it and weaken the secondary inflow via its energetic feedback, maintaining a high enough density where the SMBHs are located and assisting their sinking.
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http://psjd.icm.edu.pl/psjd/element/bwmeta1.element.bwnjournal-article-appv92z410kz
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## Acta Physica Polonica A
1997 | 92 | 4 | 695-698
Article title
### Two-Electron Quantum Dots in Magnetic Field
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Abstracts
EN
A theoretical description is given for electronic properties of semiconductor quantum dots in a magnetic field. A two-electron model is applied for electrons in a cylindrical quantum dot with a parabolic confinement potential. The eigenvalue problem is solved by the variational method with the trial wave function proposed in the form of linear combination of S-type and P-type Gaussians. The energy levels of singlet and triplet states with arbitrary radial and magnetic quantum numbers have been calculated as a function of the applied magnetic field. The calculated cyclotron transition energies agree well with those measured for InGaAs/GaAs quantum dots. It is shown that the electron-electron interaction has a small influence on the transition energy.
Keywords
EN
Journal
Year
Volume
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695-698
Physical description
Dates
published
1997-10
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author
• Faculty of Physics and Nuclear Techniques, Technical University (AGH), Al. Mickiewicza 30, 30-059 Kraków, Poland
author
• Faculty of Physics and Nuclear Techniques, Technical University (AGH), Al. Mickiewicza 30, 30-059 Kraków, Poland
References
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https://competitive-exam.in/questions/discuss/the-indifference-curve-technique
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# The indifference curve technique:
Helps in separating the income effect and the substitution effect
Does not help in separating the two effects
Mixed up the two effects
None of the above
Please do not use chat terms. Example: avoid using "grt" instead of "great".
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http://math.stackexchange.com/questions/292859/matrix-algebra-true-or-false
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# Matrix Algebra - True or False?
I have 5 T-F statements right here about symmetric matrices, and to the right are my attempts. I have a feeling some of them are wrong, though.
(a) Symmetric matrices must be square. (T)
There can be a rectangular matrix which is symmetrical.
(b) A scalar is symmetric. (T)
I don't know why
(c) If $A$ is symmetric, then $\alpha A$ is symmetric. (T)
What is $\alpha A$?
(d) The sum of symmetric matrices is symmetric.
I think this is false as not all sums will be symmetric.
(e) If $(A')' = A$ , then $A$ is symmetric.
I think this is true.
Could I encourage that, if you know one part of the answer, please go ahead to answer them? I know that it will be very, very hard to find one answer with all 5.
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It should not be that hard...no worries. – 1015 Feb 2 '13 at 16:01
I guess everybody here will be able to answer, but I somewhat feel that answering your question will deprive you of the chance to learn for youself. Why don't you tell us which definition you are using and what you have to check exactly for every single question. I bet you will find some answers yourself. Also: make sure you understand how you can consider a scalar as a matrix. What is $A'$ ? do you mean the transpose? – Simon Markett Feb 2 '13 at 16:06
I'll take $A=A^t$ (where $A^t$ denotes the transposed matrix) for the definition of $A$ to be symmetric.
(a) True. If $A$ is an $m\times n$ matrix and is equal to its transpose which is an $n\times m$ matrix, then $m=n$.
(b) True. A scalar is a $1\times 1$ matrix, so equal to its transpose. More generally, what is the transpose of a scalar matrix? Itself.
(c) True. Note that $\alpha A$ is the matrix obtained from $A$ by multiplying each coefficient by $\alpha$.
(d) True (symmetric matrices of same size). Essentially because $(A+B)^t=A^t+B^t$.
(e) False. It $A'$ denotes $A^t$ the transpose of $A$.... Note that $(A^t)^t=A$ for every matrix $A$. And not every matrix is symmetric.
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I Finally reviewed my notes and understand what you're talking about...thank you so much. – bryansis2010 Feb 13 '13 at 15:29
@bryansis2010 Great! You're welcome. – 1015 Feb 13 '13 at 15:31
Hints:
(a) This is true apparently directly from the very definition of symmetric matrix, but also because one the main characteristics of a symmetric matrix $\,A\,$ is that $\,A^t=A\,$ , and this equality forces $\,A\,$ .
(b) You seem to have meant "a scalar matrix is symmetric", and a scalar matrix is of the form
$$\alpha I=\begin{pmatrix}\alpha&0&0&...&0\\0&\alpha&0&...&0\\...&...&...&...&...\\0&0&0&...&\alpha\end{pmatrix}$$
So what say you? Is that symmetric or not?
(c) $\,A=(a_{ij})\,$ is symmetric iff $\,a_{ij}=a_{ji}\,\,\forall\,i\neq j\,$ , and $\,\alpha A=(\alpha a_{ij})\,$ ...
(d) This now follows at once from the above, and about (e) I'm not sure what you mean by $\,A'\,$...
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+1. Don. I have learned much from your answers here. – S. Snape Feb 4 '13 at 9:19
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https://www.physicsforums.com/threads/arrow-of-time-entropy-probability.119086/
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Arrow of time/ entropy probability
1. Apr 28, 2006
Tsunami
In Popper's autobiography, published in his contribution of Library of Philosophers, I read the following, after Popper's presentation of Boltzmann's ideas about entropy:
A bit further this is formulated as such:
Is this all accepted? Any additional comments? (The arrow of time always sounded valid to me.)
2. Apr 28, 2006
Tsunami
edit: via search functions I did find the two pages of that paper.
It seems to me though as if Prigogine seems to discard Popper's point. What Popper tried to show, was that states of more entropy are more likely, regardless of the direction of time. If you imagine a curve of entropy states in function of time, it is easy to imagine a state of low entropy being surrounded by states of higher entropy... thus, you get a sort of gaussian curve with the most optimal result in the center. (It doesn't have to be gaussian, just an high medium which is lower in both directions starting from this point.)
Popper's idea is, I suppose, that if we could track what happens to this situation of entropy states when it moves from low entropy to high entropy, then this situation could be reversed by backtracking everything that happens.
One should note that Popper also refused the idea of having information as a counter-force against entropy. (If people want to use the information argument to tackle Popper's point, I'll look up his ideas regarding this so this can be tackled as well if necessary)
Last edited: Apr 28, 2006
3. Apr 28, 2006
Andrew Mason
I have no idea what the scientific basis for this could be. I am not aware of a principle of physics that:
Not only that, I think it is an incorrect statement. A gas that expands from a smaller to larger space will not compress by itself back to the smaller space. Nor will the forces of nature suddenly combine (eventually) to compress it.
Now, this does not necessarily mean that the conclusion (that the arrow of time is not the result of ever-increasing entropy) is incorrect. Popper was certainly at the top of his field in philosophy, but he was not a scientist. Philosophy should not be confused with science.
It seems to me that the arrow of time is partly about probability (of the universe self-organizing itself to a precise state that existed). Entropy is partly about probability. To say there is no connection seems to be more than a little presumptuous.
I would say that the arrow of time is simply the result of logic. Time can only go in one direction by definition. If the universe is in a certain state, changes and then returns to the precise previous state, the initial state is still in the past.
AM
4. Apr 28, 2006
Physics Monkey
The theorem being referred to is a famous one by Poincare called the Poincare Recurrence Theorem which roughly states that an isolated and bounded mechanical system will eventually return arbitrarily close to any initial state. This theorem does quite explicitly state that if you had a perfectly isolated classical gas in which the gas started in one side of the container, you would find at a later time that the gas was again all in one side of the container. There is no conflict with the laws of thermodynamics since such a recurrence would take far too long to occur even if one had happened to have on hand a perfectly isolated classical gas.
5. Apr 28, 2006
Physics Monkey
And to address Tsunami's original question
Yes, this stuff, by which I mean the reconciliation of the reversible laws of mechanics with the apparent irreversability of thermodynamics, is all pretty much accepted. One particular interesting and transparent test of these ideas is to look at "gases" of cellular automata that have reversible dynamics. One can watch these purely reversible systems start in one side of the container, expand, and eventually fill the whole container. With a sufficiently large number of the little guys running around, you never see them all return to one side of the container. In short, the laws of thermodynamics appear to hold good. However, if you go and perfectly reverse all the velocities, sure enough, the gas goes dutifully right back into one side of the container.
6. Apr 29, 2006
SizarieldoR
Hay, physics isn't the only science (although it is the basic natural science), if memory serves, philosophy can be called a science as well.
Does entropy decrease with the action of forces? I mean, does the entropy in a given amount of lava decrease, when the lava crystallizes?
Also, thermal energy is the vibration of atoms/molecules hitting each other (correct me if i'm wrong). So, if we can calculate how two billiard balls hit each other (and the change in their momentums), we should be able to calculate how two atoms/molecules hit each other as well in the limits of the uncertainty principle. Of course, we will need some freakin-powerful supercomputers and stuff, not to mention taking the London dispersion force into account, but doesn't that mean that entropy isn't an increase in disorder?
7. Apr 29, 2006
vanesch
Staff Emeritus
There is some controversy over this, but the most "down to earth" view is this: the arrow of time (= the increase in entropy) comes about from the special initial condition (low-entropy state of the early universe).
In fact, the initial state of the universe (just after the big bang) is a *highly peculiar state* of very low entropy, and we're still evolving towards equilibrium in this view.
The asymmetry is not in the time symmetric evolution laws (which, to our knowledge, are time reversible), but in the initial condition.
This displaces the question of course to why there was this special initial condition :-)
Now, to come back to Poincare recurrence, this comes in fact down to saying that in a closed classical system, motion is "essentially" periodic ; however, this period is extremely long! If you take any initial state, you will have the motion essentially divided in 3 parts:
a part where there is "increase in entropy" ; a part where there is "decrease in entropy" and a VERY LONG PART where there is equilibrium ; this then cycles on and on, and depending on where you are on this trajectory, you observe increase, decrease, or equilibrium.
In the first case, the "special state" is closer in the past than in the future. In the last case, the "special state" is closer in the future than in the past (just before a "big crunch" ?). And in between there is an extremely long part of equilibrium.
Now, it seems that we are now in a phase of "increase of entropy", because the big bang (special state) is closer to us in the past than in the future.
Now, you could even say that even if it were different, and the special state were closer to us in the "future" than the past, we would probably EXPERIENCE time in the other sense, and call this future the past, and vice versa. But that's less of a standard view. But fun to think about.
However, one thing is sure: entropy changes can only occur in "the neighbourhood" of a special (initial or final) state. If not, you are in equilibrium, which is by far the state that prevails during the longest time. At least in a purely classical system.
8. Apr 29, 2006
Tsunami
Ok, that makes sense.
I still want to solve one question though (just trying to get my fundamentals straight ):
If, in principle, we can move to a state of lower entropy by reversing all velocities, why don't we?
I can see how this can be tackled by saying that we lack sufficient information to know the exact reversal of motion, but that doesn't satisfy me. Surely, the second law must be stronger than that?
9. Apr 29, 2006
Andrew Mason
Entropy of any system can increase or decrease in a process. But the entropy of the universe will always increase in the process.
Entropy is not really about disorder.
The second law of thermodynamics simply says that the energy of the universe flows in a way that makes it more disperse.
Entropy is really about energy dispersion and probability. Consider the break in game of pool (assume a frictionless surface, perfectly elastic collisions and rebounds from the cushions). The relatively high energy of the cue ball is dispersed into all 16 balls, with each ball having a portion of that original energy. The probability that the balls will all collide with the cue ball in such a way that they all stop and the cue ball regains its original energy is very low. It would not violate the laws of physics. It would just be extremely improbable.
AM
10. Apr 29, 2006
Andrew Mason
"In science there is only physics; all the rest is stamp collecting."
Ernest Rutherford (before he won the Nobel Prize for Chemistry)
AM
11. Apr 30, 2006
Andrew Mason
Poincaré Recurrence Theorem - Zeno's Paradox in reverse
The Poincaré Recurrence theorem states that any possible event, no matter how improbable, will occur in a time interval $\Delta t$ if we make $\Delta t$ arbitrarily large.
Zeno's paradox says that two objects separated by a distance s and approaching at a fixed speed v will never hit each other in an infinite number of time intervals $\Delta t_i$ if we make the time intervals arbitrarily small (so that $\sum \Delta t_i$ < s/v).
It seems to me that both are correct mathematically. But both have nothing to do with the real world.
Similarly Quantum Mechanics has nothing to do with the lunar orbit. There is a finite probability that the moon will stop obeying Newton's laws of motion and pass through the earth and out the otherside. This would violate Newton's laws of motion but would not violate QM. It is just that the probability of this happening is very small - so small that it will not likely happen in 10^10^10^10^10^10^10^10^10 lifetimes of the universe. This does not invalidate Newton's laws of motion.
So to the suggestion that the Poincaré Recurrence theorem shows that entropy of the universe can and will decrease spontaneously, I say: 'not in this universe'.
AM
Last edited: Apr 30, 2006
12. May 3, 2006
Tsunami
However, you can make an adjusted Zeno's paradox that suits the real world: you can place a finite lower boundary on the amount of divisions you make, something like "the turtle cannot walk half a distance if this half is smaller than one of his feet"
Anyway, doing the same for Poincare probably means saying : the finite upper boundary we can think of is the duration of conscious life in the universe, so it doesn't matter.
So considering practically everything can be explained using an infinite duration of time and any improbable probability : I get your point.
13. May 15, 2006
vanesch
Staff Emeritus
As we don't know the laws of this universe (but only some aspects of it), we can't tell but you're probably right. The point was not this, the point was that even in a classical MODEL where Poincare recurrence holds, and where the microdynamics is time-reversible, a second law can hold during a time lapse which is "shortly" after a special initial condition.
And now when you look at where, in this world, we DO get our second law from, then this clearly points out to a similar reason: we get our entropy increase potential essentially from the influx of low-entropy radiation from the sun, and the outflux of high-entropy radiation into the blackness of space. Both are related to the state of the early universe and its expansion. If the universe were in thermodynamic equilibrium, then we wouldn't observe a second law (we wouldn't be there either).
Now whether there is some cyclic equivalent of the Poincare recurrence theorem or not for the "real" laws of this universe I don't know of course, but that was not the point. The point was that the apparent paradox between reversible microlaws and the second law can be solved by considering that you are evolving away from a special initial state. It might turn out that microlaws are, in the end, not time-reversible, who knows. But this is not necessary to explain the second law.
14. May 16, 2006
Andrew Mason
I don't follow you there. What do you mean by "where the microdynamics is time-reversible"?
But the universe would only move into thermodynamic equilibrium because of the second law: the state of equilibrium being the most probable state.
As a great politician once observed, there are many ways to change but only one way to remain the same. That, in a nutshell, sums up the second law.
AM
Last edited: May 16, 2006
15. May 16, 2006
vanesch
Staff Emeritus
That the dynamical laws are time-symmetric (that there is a symmetry when replacing t -> -t in the dynamical laws of classical mechanics).
Well, the point was, that this "evolution towards a more probable state" (= second law) comes about only, because we come from a state which is NOT very probable (probable in the sense of Boltzmann entropy, where the available phase space is chunked up in boxes of "equivalent macrostates", where we don't care for high-order correlations), and that there is no specific conservation law which keeps us in the small, =unprobable, box. So the time evolution of the classical state will wander from small boxes into big boxes, most of the time, because there is no specific relationship between the delimitation of the boxes, and the time evolution of the microstate. Given this a priori independence, a stochastical argument can do. It can happen that it wanders from a big box into a small box, but that is a highly peculiar happening (which happens nevertheless, due to Poincare recurrence, at the end of a "cycle"), because the size of the boxes, and the time evolution, are not really related. All this in a classical MODEL universe.
The point is simply that the timescales on which this could happen (Poincare recurrence time) is vastly longer than the time since a fixed initial condition, so the "slope of increase of box size" is still very steep, hence a clearly defined second law.
That's a nice quote :-).
However, "staying the same" is microscopically as involved as "changing". It is only that the low-order correlation functions (like matter densities and so on) do not change anymore in what we call 'equilibrium'. The high-order correlation functions change as much during "equilibrium" as during "irreversible evolution" in a classical universe.
16. May 17, 2006
Farsight
Doublepost deleted.
Last edited: May 17, 2006
17. May 17, 2006
Farsight
Time is to do with motion over a distance. The direction doesn't matter, so changing the direction won't reverse the arrow of time. What you need for that, is a negative distance. There's one in here, thankyou google. But apologies if it's bunk, I haven't read it through.
http://www.comcity.com/distance-time/Photon%20Kinematics.html [Broken]
Last edited by a moderator: May 2, 2017
18. May 17, 2006
lalbatros
Tsunami,
Already in 70's some people made computer simulations showing that entropy can decrease (close to its original value) after a long time. This is just unavoidable when the microscopic laws are reversible. Such simulations of course need to consider a small number of particles. The "recurrence time" that can simulated in this way increases very fast with the number of particles. This recurrence time also increases -of course- with the precision of the recurrence, a perfect recurrence requires generically an infinite time.
Some models can make things easier to visualise, like particles in a box with periodicity conditions: then there may even be no need to calculate the trajectories since they are analytically simple.
More obvious simulations were dealing with velocity-reversal. In such simulations, the entropy evolves exactly in the opposite directions than in the forward simulation (it decreases) until the initial condition is recovered, and thereafter the entropy increases again as usual.
Many people consider that these simulations don't represent physical reality, and that therefore something is missing in the physics to account for irreversibility. The interpretation is simple however. Preparing a system that could exhibit anti-thermodynamics behaviour is theoretically possible from the microscopic law of physics. But this preparation is extremely difficult and such systems are "fragile": they loose their exceptional properties by any small perturbation.
That's an interresting and fundamental topic. But I have not seen that it delivered any real progress in physics, till now.
Similar Discussions: Arrow of time/ entropy probability
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http://math.stackexchange.com/questions/43380/piecewise-smooth-non-orientable-closed-surface-a-contradiction-in-terms-or-a
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# Piecewise smooth, non-orientable, closed-surface: a contradiction in terms, or am I going mad?
We had a lecture a few weeks back, looking at Gauss' divergence theorem, and in the definition of the theorem, it specified that the boundary of the volume under consideration, S, had to be a 'piecewise smooth, orientable, closed surface'.
What bothers/intrigues me is that I cannot understand how a closed surface in 3D space CANNOT be orientable. Surely every closed surface is orientable!
My highly non-rigorous, intuitive argument runs as follows:
1) As the surface is closed, we can define two regions, one inside the surface, and one outside
2) We can construct a normal to the surface at any point P that is pointing towards the inside region. Thus the direction of the normal is defined for every point.
3) As the surface is piecewise continuous, this normal will vary continuously.
4) Coupling (2) (defined direction of normal) with (3) (continuously changing normal) gives us an orientation for the closed surface.
5) Therefore every closed surface is orientable.
But of course, the precise wording of the statement for Gauss' Law strongly suggests that people far smarter than me have discovered some exotic non-orientable, closed surface. Is this true?
When I asked my lecturer about this, he just smiled and said he didn't know any examples, but that they do exist, and then said something even more tantalising about 'reflections of higher dimensional objects'
I would love it if anyone could shed some light on my situation.
Thanks
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The Klein bottle en.wikipedia.org/wiki/Klein_bottle is an example. You cannot embed it in $\mathbb{R}^3$ though. – Thomas Rot Jun 5 '11 at 12:40
I think you interpret 'closed' incorrectly. I don't quite understand your reasoning in (1) that a surface being topologically closed implies it has an 'inside' and 'outside'. – wildildildlife Jun 5 '11 at 13:35
@wildildildlife: In differential geometry, a closed surface is one which is compact and without boundary. It's an unfortunate coincidence of terminology. – Zhen Lin Jun 5 '11 at 15:08
@wildildildlife Mmm, no you're exactly right. I suppose it's because all of the basic applications for closed surfaces (Gauss' Divergence theorem, the relevant Maxwell equations, etc.) all talk about closed surfaces CONTAINING stuff, it's easy to ignore these special cases. But now I see that closed surfaces need not divide 3D space (unlike closed curves in the 2D plane I suppose) – tom Jun 6 '11 at 9:45
## 1 Answer
You're right that if the surface has to fit into 3D, and if it is non-self-intersecting, then it has to be orientable.
But if you allow the 2D surface to self-intersect or go to the 4th dimension, there are many counterexamples. Klein Bottle is the simplest one.
Take a bottle, heat it up, and push the throat through the body, to connect it with a hole that you prepared at the bottom of the bottle. This manifold is equivalent to a $Z_2$ orbifold of a torus - where the $Z_2$ generator shifts by half a period in one direction of the torus and reflects the other direction of the torus.
Your rule (1) fails because there is no well-defined interior and exterior. Indeed, if you make trips around the Klein bottle that reverse the orientation, it inevitably exchanges the interior with the exterior as well. Note that if you enter the hole at the bottom of the bottle (see the picture), you're still outside, but as you travel through the throat, it becomes clear that you have gotten inside the "object" as well, so there's no distinction between the exterior and interior.
The Klein bottle is self-intersecting if embedded into three dimensions. Alternatively, you may avoid the intersections if one of the pieces of the surface that would intersect each other are shifted in a new, fourth dimension of space.
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Wow, thankyou so much for that, that's a fantastic little surface. It's funny, running the normal around it in your head, to see it change orientation, feels just like with a mobius strip. – tom Jun 5 '11 at 12:46
Dear @Tom, it was a pleasure. The Möbius strip is nothing else than a properly chosen one half of the Klein Bottle. Place a topologically nontrivial circle in the Klein bottle - for example, run from the bottom of the bottle along the throat to the left, and return to the same place. And then cut it along this circle by scissors. You will get an unorientable surface with one boundary - the circle - and it's the Mobius strip. It's safer to cut a strip along the circle I just mentioned, this one is manifestly a Mobius strip. Unlike the Klein bottle, the Mobius strip has a boundary. – Luboš Motl Jun 5 '11 at 13:20
Haha, you're exactly right :) Takes a bit to visualise though. I also see what you mean about this being related to a torus. If you were to cut a circle around a torus as you did for this, you'd just get circular stip without the half-turn. BTW, would this be (very) basic Topology, looking at questions like this? – tom Jun 6 '11 at 9:49
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https://www.cut-the-knot.org/Curriculum/Geometry/GeoGebra/FlankTriangles4.shtml
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# Two Properties of Flank Triangles - A Proof with Complex Numbers
Bottema's configuration of two squares that share a vertex is naturally embedded into Vecten's configuration of three squares erected on the sides of a triangle. The latter generalizes the first of Euclid's proofs of the Pythagorean theorem, so it rightfully refers to the Bride's Chair.
In the discussion of Vecten's configuration, we proved inter alia two properties of flank triangles that are a part of Bottema's configuration.
1. If $AM$ is a median in $\triangle ABC$, $AH$ is an altitude in $\triangle AEG$, then $M$, $A$, $H$ are collinear.
2. $EG = 2\cdot AM$.
### Proof
In geometric problems, synthetic solutions are usually valued more than algebraic or trigonometric. However, complex numbers have a simple geometric meaning. In particular, multiplication by $i$ is equivalent to a counterclockwise rotation by $90^{\circ}$ whereas multiplication by $-i$ is equivalent to a clockwise rotation. Bearing this in mind, the proof appears to truly need no further explanation.
[Honsberger] credits the proof to Boris Pritsker of New York. It appeared in the now defunct journal Quantum (May/June 1996, p. 44).
### References
1. R. Honsberger, Mathematical Diamonds, MAA, 2003, 63-64
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https://www.tutorialspoint.com/how-can-tensorflow-be-used-to-standardize-the-flower-dataset
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# How can Tensorflow be used to standardize the flower dataset?
PythonServer Side ProgrammingProgrammingTensorflow
Data standardization refers to the act of scaling the dataset to a level so that all the features can be represented using equivalent units. The rescaling layer is built using the ‘Rescaling’ method which is present in Keras module. The layer is applied to the entire dataset using the ‘map’ method.
We will be using the flowers dataset, which contains images of several thousands of flowers. It contains 5 sub-directories, and there is one sub-directory for every class.
We are using the Google Colaboratory to run the below code. Google Colab or Colaboratory helps run Python code over the browser and requires zero configuration and free access to GPUs (Graphical Processing Units). Colaboratory has been built on top of Jupyter Notebook.
from tensorflow.keras import layers
print("Standardizing the data using a rescaling layer")
normalization_layer = tf.keras.layers.experimental.preprocessing.Rescaling(1./255)
print("This layer can be applied by calling the map function on the dataset")
normalized_ds = train_ds.map(lambda x, y: (normalization_layer(x), y))
image_batch, labels_batch = next(iter(normalized_ds))
first_image = image_batch[0]
print(np.min(first_image), np.max(first_image))
## Output
Standardizing the data using a rescaling layer
This layer can be applied by calling the map function on the dataset
0.0 0.96902645
## Explanation
• The RGB channel values are in the range of 0 and 255.
• This isn't good for a neural network.
• The idea is to make the input data as small as possible.
• The values in the image are standardized, to be in thenage of 0 and 1.
• This is done with the help of a rescaling layer.
• Alternative is to include this rescaling layer in the definition of model, which would simplify the deployment.
Updated on 19-Feb-2021 17:31:27
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https://lukasatkinson.de/2013/transforming-syntax/?utm_medium=rss&utm_source=rss&utm_campaign=2020-12-26
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# Transforming Syntax
## Or: how to write the easy part of a compiler
A Stack Overflow question asked how to translate a VB-like conditional into a C-like ternary. The other answers suggested regexes or treating it as Perl code *shudder*. But transpiling code to another language can be done correctly.
This post aims to cover:
• parsing with Marpa::R2,
• AST manipulation,
• optimization passes,
• compilation, and
• Perl OO.
In the end, we’ll be able to do all that in only 200 lines of code!
Since this post is already rather long, we will not discuss parsing theory. You are expected to be familiar with EBNF grammar notation.
Note: All runnable code snippets should be prefixed by
use strict;
use warnings;
use 5.010;
Contents:
## Problem statement: How to translate an expression into a C-like language
This tutorial was prompted by a question on Stack Overflow by user2516265. Here it is, slightly edited:
I am writing a script to read an Excel file translate the text into C programing syntax.
So in the Excel sheet I have string like this:
If ((Myvalue.xyz == 1) Or (Frame_1.signal_1 == 1))
Then a = 1 Else a = 0;
I am trying to create this output:
a = (((Myvalue.xyz == 1) || (Frame_1.signal_1 == 1)) ? 1 : 0)
How this can be handled in Perl?
## Short introduction to Marpa
Various parser exists for Perl. Some of these are ancient tech, some are solid but slow, some are awesome. My favourite parsers are:
Regexp::Grammars
Provides many powerful and expressive tools. Retains the full power of Perl regexes. The downside: now everything is one huge regex.
Parser::MGC
Makes it trivial to write an object oriented top-down parser. However, the resulting code is unneccessarily verbose.
Recursive Descent
It is often best to write a RecDesc parser by hand. This affords a lot of flexibility, but can get tedious.
Marpa::R2
This is a wrapper around libmarpa. It is written in C, and uses Early parsing instead of top-down techniques. This makes it fairly easy to write arbitrary BNF, which Marpa will happily use. While it is strictly less powerful than regexes, Marpa provides excellent interfaces and good debugging help that often makes it worth the extra code.
(If you want to learn more about how the Marpa algorithm compares against other parsing algorithm, you can read my Overview of the Marpa Parser.)
Here, we will use the Scanless Interface for Marpa, which adds lexing capabilities to the BNF. To create a new grammar, we have to say:
$grammar = Marpa::R2::Scanless::G->new({ %options }) One of these options is the BNF source, which has to be passed as a reference. ### Writing the BNF We want to write a grammar that is able to correctly parse the example data If ((Myvalue.xyz == 1) Or (Frame_1.signal_1 == 1)) Then a = 1 Else a = 0; We see that the program is made from statements that are separated by semicolons. We can express this with the BNF rule StatementList ::= Expression+ separator => SEMICOLON SEMICOLON ~ ';' # Tokens are declared with '~' An expression can be an If/Then/Else, a parenthesized expression, a binary operator, an identifier, or a numeric literal. We should choose a sensible precedence for all these possibilities. E.g. parenthesization and literals should have very high precedence. The conditional should be lower so that it can include other expressions. For the binary operators, I have chosen the precedence order: 1. == equality test 2. = assignment 3. Or logical operator Marpa Scanless allows us to write simple alternatives with |, and || to provide prioritized rules. The Marpa || works roughly like | in regexes with respect to backtracking, i.e. the first alternative is tried “first.” The BNF for the expression would be: Expression ::= ('(') Expression (')') assoc => group | NUMBER || IDENT || Expression ('==') Expression || Expression ('=') Expression || Expression ('Or') Expression || Conditional Tokens enclosed in parenthesis like ('...') are matched, but their value is discarded in the AST. If the rule we are defining appears within an alternative, then we can specify the associativity of that grammar production. The parens (...) should use group associativity because it can contain expressions with lower precedence. Left associativity is the default, so a Or b Or c will be parsed as (a Or b) Or c. The other referenced rules are: Conditional ::= ('If') Expression ('Then') Expression | ('If') Expression ('Then') Expression ('Else') Expression IDENT ~ ident NUMBER ~ <number int> | <number rat> word ~ [\w]+ # Perl charclasses can be used for tokens ident ~ word | ident '.' word # allow complex identifiers <number int> ~ [\d]+ <number rat> ~ <number int> '.' <number int> As a naming convention, I use: • CamelCase names for main grammar rules (declared with ::=), • UPPERCASE for tokens (declared with ~ but used in top-level rules), and • lowercase for subtokens (declared with ~ but used in tokens or subtokens). The Marpa lingo, those correspond to: • non-terminal symbols in the G1 grammar, • terminal symbols in the G1 grammar, which are top-level non-terminal symbols of the L0 grammar, and • other non-terminal symbols in the L0 grammar. We can instruct Marpa to start matching at the “top” with the pseudorule :start ::= StatementList, and can allow the lexer to skip whitespace between tokens via :discard ~ ws ws ~ [\s]+ In the next section, we take a short look at Object Oriented Programming with Perl and will then circle back to see how Marpa interacts with that. ### Intermission: Perl OO An object is a thingy which we can ask to do something for us. Depending on what we are asking it to do, it will either throw an error or fulfill our request. This can simplify code because we don’t care how the object works on the inside, or where it knows from how to perform the task. Perl uses class-based OO. We can declare a class with the package keyword. All subs in that package can then be used as methods. We can inherit methods from another package via use parent 'Parent::Class'. When a sub is used as a method, the object it was invoked on is passed as the first argument. This invocant is usually called $self in proud Smalltalk tradition. The invocant may also be a string that holds the name of the package. That is, Perl makes no distinction between class methods and instance methods.
We can create a new instance of a class by blessing a reference into that class. Any reference will do. Usually, hash references are used where each hash entry is a field of the object. But here we will focus on array references that contain a collection of data.
For demonstration purposes, here is a small example to show blessing and inheritance. The below classes allow us to calculate the statistical mean and variance of a data set.
# Call the new method on class Data::Variance:
my $object = Data::Variance->new(1.1, 1.9, 2.1); # Call the variance method on the object: say "Var: ",$object->variance;
# Call the inherited mean method on the object:
say "Mean:", $object->mean; # Define the Data::Mean class which provides the mean method BEGIN { package Data::Mean; sub new { # The invocant for new should be the class name my ($class, @data) = @_;
# bless a reference to the data into the provided class
my $self = bless \@data =>$class;
# return the freshly baked object
return $self; } # calculate the mean sub mean { my ($self) = @_;
my $sum = 0;$sum += $_ for @$self;
return $sum / @$self;
}
}
# Define the Data::Variance class which inherits from Data::Mean:
BEGIN {
package Data::Variance;
# Specify inheritance of base classes.
# The -norequire option is used because the parent is in the same file.
use parent -norequire, 'Data::Mean';
# new is inherited
# mean is inherited
# calculate the variance, bootstrapping it with the mean
sub variance {
my ($self) = @_; my$mean = $self->mean; return Data::Mean->new(map { ($_ - $mean)**2 } @$self)->mean; # nifty math
}
}
Output:
Var: 0.186666666666667
Mean:1.7
In that example, the reference is blessed in the new method (the constructor). This is considered good style, but we can bless any reference anywhere into any class (the class doesn’t even have to exist). This is what we’ll let Marpa do in the next step.
### Marpa’s bless adverb
We can let Marpa take the array of matched values, and bless them into a class of our choosing. We can do so by augmenting a rule with the bless adverb, e.g.
StatementList ::= Expression+ separator => SEMICOLON bless => Block
But we also have to specify how these values are obtained. We can do so by setting default attributes like
:default ::= action => [values]
We could have also written an action ourselves that takes the matched values as arguments and returns some data structure. The above default action is similar to:
sub { return [@_] }
We can specify a class root for the bless adverb. If we construct the grammar with the bless_package option, e.g. bless_package => 'Ast', then the StatementList would not be blessed into the Block class but into Ast::Block.
Similar classes are added to the other rules.
In some cases of our grammar, we do not want to use the [values] action. For example, the Expression production to Conditional just delegates to another rule. Similarly, the rule for parenthesized expressions just recurses into the Expression rule. In these cases, we will use the built-in action ::first:
Expression ::=
('(') Expression (')') assoc => group action => ::first
...
|| Conditional action => ::first
### Obtaining a parse
This is the general workflow to obtain a parse from a Marpa::R2::Scannless::G Grammar object:
1. Create a recognizer for that grammar:
my $recce = Marpa::R2::Scanless::R->new({ grammar =>$grammar });
$recce->read(\$input);
3. Look at the value of the parse. The parse failed if it is undef. Otherwise, it is a reference to our AST:
my $value =$recce->value;
defined $value or die "Parse failed"; my$ast = value;
The downloadable module Parser.pm implements the above grammar. The dump-ast.pl script uses that module to parse the example input, and prints out the resulting data structure.
Here is the output of the AST using Data::Dump:
bless([
bless([
bless([
bless([
bless(["Myvalue.xyz"], "Ast::Var"),
bless([1], "Ast::Literal"),
], "Ast::Equals"),
bless([
bless(["Frame_1.signal_1"], "Ast::Var"),
bless([1], "Ast::Literal"),
], "Ast::Equals"),
], "Ast::Or"),
bless([bless(["a"], "Ast::Var"), bless([1], "Ast::Literal")], "Ast::Assign"),
bless([bless(["a"], "Ast::Var"), bless([0], "Ast::Literal")], "Ast::Assign"),
], "Ast::Cond"),
], "Ast::Block")
Here is the output using Data::TreeDumper:
ast blessed in 'Ast::Block'
- 0 = blessed in 'Ast::Cond'
|- 0 = blessed in 'Ast::Or'
| |- 0 = blessed in 'Ast::Equals'
| | |- 0 = blessed in 'Ast::Var'
| | | - 0 = 'Myvalue.xyz'
| | - 1 = blessed in 'Ast::Literal'
| | - 0 = '1'
| - 1 = blessed in 'Ast::Equals'
| |- 0 = blessed in 'Ast::Var'
| | - 0 = 'Frame_1.signal_1'
| - 1 = blessed in 'Ast::Literal'
| - 0 = '1'
|- 1 = blessed in 'Ast::Assign'
| |- 0 = blessed in 'Ast::Var'
| | - 0 = 'a'
| - 1 = blessed in 'Ast::Literal'
| - 0 = '1'
- 2 = blessed in 'Ast::Assign'
|- 0 = blessed in 'Ast::Var'
| - 0 = 'a'
- 1 = blessed in 'Ast::Literal'
- 0 = '0'
And here is the AST illustrated as a sideways tree (written manually with Unicode box drawing characters):
┌╴Var╶╴'Myvalue.xyz'
┌╴Binop╶┼╴'=='
│ └╴Literal╶╴'1'
┌╴Binop╶┼╴'Or'
│ │ ┌╴Var╶╴'Frame_1.signal_1'
│ └╴Binop╶┼╴'=='
│ └╴Literal╶╴'1'
│
│ ┌╴Var╶╴'a'
Block╶╴Cond╶┼╴Binop╶┼╴'='
│ └╴Literal╶╴'1'
│
│ ┌╴Var╶╴'a'
└╴Binop╶┼╴'='
└╴Literal╶╴'0'
We can see that the Data::Dump output is much harder to read than the tree. This is mainly because it contains too much superfluous information, and presents the information in a weird order. In a moment, we will try to create our own output for AST debugging.
## Working with the AST
Before we can start working with the syntax tree Marpa creates for us, we should take a moment to create our AST classes, and write a few accessor method so that we don’t have to hardcode indices of the underlying arrayrefs. This is fairly boring:
package Ast; # a parent class to define common methods
# a constructor for convenience.
# Marpa won't use this but rather bless directly
sub new {
my ($class, @args) = @_; bless \@args =>$class;
}
package Ast::Binop; # convenience base for all binary operators
use parent -norequire, 'Ast';
sub l { shift()->[0] }
sub r { shift()->[1] }
package Ast::Equals;
use parent -norequire, 'Ast::Binop';
package Ast::Assign;
use parent -norequire, 'Ast::Binop';
package Ast::Or;
use parent -norequire, 'Ast::Binop';
package Ast::Var;
use parent -norequire, 'Ast';
sub name { shift()->[0] }
package Ast::Cond;
use parent -norequire, 'Ast';
sub cond { shift()->[0] }
sub then { shift()->[1] }
sub else { shift()->[2] }
package Ast::Block;
use parent -norequire, 'Ast';
package Ast::Literal;
use parent -norequire, 'Ast';
sub val { shift()->[0] }
We will now look at a few ways to transform the AST.
### Transformation: cloning
It can sometimes be useful to make a deep copy of a data structure. This is fairly easy for each AST node. To copy an AST node, it
1. clones all child nodes, or copies the values if they aren’t a regular node (we call such nodes a terminal node).
2. blesses an array reference containing those copies into the correct class.
To determine whether a given child node is a terminal node, we ask it if it can perform the clone method. We can do so with the universal can method. I.e. $node->can('clone') does this check. However, it is a fatal error to call a method on an unblessed reference (something that isn’t an object). Therefore, we first do a check whether the $node is an object at all. The blessed method from Scalar::Util comes in handy here.
Therefore, we can perform cloning like:
package Ast;
use Scalar::Util qw/blessed/;
...
sub clone {
my ($self) = @_; my @childs = map { _clone_if_possible($_) } @$self; return ref($self)->new(@childs);
# ref $self is the class of$self.
}
sub _clone_if_possible {
my ($maybe_ast) = @_; if (blessed($maybe_ast) and $maybe_ast->can('clone')) { return$maybe_ast->clone;
}
return $maybe_ast; } Note: This technique assumes that the given data structure is a tree alright, and doesn’t contain loops (that would be a cyclic graph, not a tree). I have prepared a script that clones an AST tree. ### Transformation: AST dump (aka. compilation) As mentioned above, the Data::Dump output is hard to read. Therefore, we will create a method that pretty-prints a part of the AST. The output will generally look like: Ast::Something( childnode_A( ... ) 'some literal'${a.variable} )
Our prettyprint() method will take an optional argument that indicates the indentation level. First, we add the general implementation:
package Ast;
...
sub prettyprint {
my ($self,$indent) = @_;
$indent //= 0; # initialize$indent if no value passed
$indent++; # increment indent level my$items = join "\n", # concatenate items with newline
map { " "x$indent .$_ } # pad with intendation
map { _prettyprint_if_possible($_,$indent) }
@$self; my$type = ref $self; return "$type(\n$items )"; } sub _prettyprint_if_possible { my ($maybe_ast, $indent) = @_; if (blessed($maybe_ast) and $maybe_ast->can('prettyprint')) { return$maybe_ast->prettyprint($indent); } return$maybe_ast;
}
For Ast::Literal and Ast::Var, we provide special implementations:
package Ast::Literal;
...
sub prettyprint {
my ($self) = @_; return q(") .$self->val . q(");
}
package Ast::Var;
...
sub prettyprint {
my ($self) = @_; return '${' . $self->name . '}'; } I have made a script that adds prettyprinting. When the prettyprint method is called on the dumped AST, we get the output: Ast::Block( Ast::Cond( Ast::Or( Ast::Equals(${Myvalue.xyz}
"1" )
Ast::Equals(
${Frame_1.signal_1} "1" ) ) Ast::Assign(${a}
"1" )
Ast::Assign(
${a} "0" ) ) ) But what does that have to do with compilation? What I have done here was defining an output language, and then compiling the AST to that language. I can easily add further implementations that change how the AST is compiled. E.g, we could add an if-then-else for the conditional like package Ast::Cond; ... sub prettyprint { my ($self, $indent) = @_;$indent //= 0;
my ($cond,$then, $else) = map {$_->prettyprint($indent) } @$self;
return "if $cond\n" . " "x$indent . "then $then\n" . " "x$indent . "else $else"; } This would produce the output Ast::Block( if Ast::Or( Ast::Equals(${Myvalue.xyz}
"1" )
Ast::Equals(
${Frame_1.signal_1} "1" ) ) then Ast::Assign(${a}
"1" )
else Ast::Assign(
${a} "0" ) ) The output format need not be a pretty-printed output for debugging, but it can also be another target language, such as C. Because the details depend on what kind of input you are dealing with and other constraints, I’m leaving that as an exercise for the reader. But the principle is the same: you would define a method that performs the correct transformation of your AST nodes, and then you transform your tree recursively, from the bottom up. Here, the conditional might be translated to a C ternary conditional like this: package Ast::Cond; ... sub compile_c_expression { my ($self) = @_;
my ($cond,$then, $else) = map {$_->compile_c_expression } @$self; return "($cond ? $then :$else)";
}
So the method looks very similar. In fact, this C transpiler looks even simpler because it doesn’t track the correct indentation level.
### Transformation: AST modification (aka. optimization)
Arguably more difficult than flattening the AST to some representation is modifying the structure of the syntax tree. This is due mostly to Perl’s type system which doesn’t lend itself to these tasks. (Generally, strongly typed functional languages like Ocaml or Haskell tend to excel here due to very expressive pattern matching.)
In the original Stack Overflow question, a part of the problem was factoring the assignment from a common variable out of the conditional branches.
We have to match this schema:
(cond) ? a = 1 : a = 0
And turn it into this format:
a = (cond) ? 1 : 0
To do that, we have to assert:
1. That both branches are assignments. In our model, that means they are Ast::Assign instances.
2. That the lvalue of both assignments is a variable (Ast::Var instance).
3. That this variable has the same name.
Then we can factor out the assignment, and will assign the result of the conditional. Expressed as Perl code, given a branch $branch, we want this condition to be true: $branch->isa("Ast::Assign") && $branch->l->isa("Ast::Var") After that has been checked, the last condition can be expressed as $then->l->name eq $else->l->name. The complete simplify method for Ast::Cond would then be: package Ast::Cond; ... sub simplify { my$self = shift;
my ($cond,$then, $else) = map {$_->simplify } @$self; if ($then->isa('Ast::Assign') and $then->l->isa('Ast::Var') and$else->isa('Ast::Assign') and $else->l->isa('Ast::Var') and$then->l->name eq $else->l->name ) { return Ast::Assign->new($then->l,
Ast::Cond->new($cond,$then->r, $else->r), ); } # else: just do what would have been done by default return$self->SUPER::simplify;
}
All other nodes inherit a simplify from Ast that does
sub simplify {
my $self = shift; my @childs = map { blessed($_) && $_->can('simplify') ?$_->simplify : $_ } @$self;
return ref($self)->new(@childs); } In other words, a simplify() on an AST that does not contain a conditional where the common subexpression is found has the same result as a clone on the AST. I implemented this in another script. If the simplify() method is invoked on our AST, we get the following output: Ast::Block( Ast::Assign(${a}
if Ast::Or(
Ast::Equals(
${Myvalue.xyz} "1" ) Ast::Equals(${Frame_1.signal_1}
"1" ) )
then "1"
else "0" ) )
## Closing remarks
Creating an AST and compiling it down to some representation may seem somewhat hard, but it isn’t rocket science either.
In the above examples, simplicity and code size were a constraint. In a real-world application, the grammar would usually be more extensive. Here, the grammar was tailored to parse the example input, but not much more. For more complicated grammars the AST Marpa gives us and the AST we want might be slightly different. That can be fixed with custom actions.
And the AST classes would be more feature-rich. In particular, the abstract classes like Ast or Ast::Binop would refuse to be instantiated directly.
There are also some fine points when compiling to a C-like language that are not discussed in this post.
• The AST is unambiguous and has no concept of precedence. When emitting output code, it may be helpful to surround every expression with parentheses even when a human programmer knows they are unnecessary.
• Here we assume the conditional only contains expressions, but a conditional might also contain statements. In C, statements and expressions are very distinct, and (aside from a GCC extension) it is not possible to put statements inside expressions, like do {...}` allows in Perl.
• It is also sometimes necessary to extract an expression as a separate statement. That usually requires a variable name to be generated.
• These generated symbols must not clash with other variables, so now we need some function to generate unique variable names.
• If our C code uses pointers, a direct translation from the source language may be unsafe because it may assume a garbage-collected runtime.
The semantic mismatch between two languages is usually much deeper than syntactic differences. Parsing and AST manipulations are comparatively simple, especially with great tools like Marpa. That is why transforming syntax is the easy part of a compiler. The difficult part is translating semantics from the input language to the target language.
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