DOCSLIB.ORG

Supplementary Information the Conversion of Monomers to Fibrils At

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Supplementary Information the Conversion of Monomers to Fibrils At Electronic Supplementary Material (ESI) for Soft Matter This journal is © The Royal Society of Chemistry 2013 Supplementary Information a 0 rpm 50 rpm 100 rpm 200 rpm 300 rpm 400 rpm 500 rpm 1000 rpm b 0 rpm 50 rpm 100 rpm 200 rpm 300 rpm 400 rpm 500 rpm 1000 rpm Supplementary Figure 1: Samples stirred at rates shown above at 70°C for 24 hours. Samples were left for 24 hours before placing between cross polarisers. a, Insulin (pH2, 2mM) shows permanent birefringence at stirring rates of 50 to 400 rpm, above this no permanent birefringence is observed. b, HEWL (pH2, 2 mM) shows strong permanent birefringence from 50 rpm to 300 rpm, which decreases at higher stir rates. The conversion of monomers to fibrils at each stirring rate for the three proteins could not be determined accurately due to the high random error associated with weighing the unaggregated protein remaining after filtering and centrifuging all solutions with a 30 kDa filter. From the technique above the measured conversion factor was between 50% to 80% 1 Electronic Supplementary Material (ESI) for Soft Matter This journal is © The Royal Society of Chemistry 2013 in no particular order for samples and therefore the minimum conversion factor of 50% (with error bars included to show the maximum possible volume fraction if the maximum conversion factor was used i.e. 80%) was used for estimating the prediction of anisotropic material using the Onsager theory. Apect ratio of fibrils from TEM images were calculated by counting the maximum number of pixels in fibril diameters and scaling by the pixel size (each pixel was approximately 5 nm, therefore only widths equal to multiple number of pixels can be given, i.e. 5, 10, 15 nm). Analysing the intensity profile perpendicular to the fibril axis would improve the measurement accuracy. However, due to the unquantified systematic errors in the focus and staining when using TEM, the pixel counting method is appropriate. Reducing the random measurement error will not give any more information. The entanglement of fibrils in all proteins at 200 rpm meant that measuring the full contour length of individual fibrils was not possible. Therefore, at 200 rpm an estimate of the lower limit contour length will be used to place a lower limit on the aspect ratio. At 500 rpm, the contour lengths of 50 fibrils (taken as a crude measure of the persistence length) were measured and averaged using the same method as before (counting and scaling pixels). The standard error in the mean contour length at 500 rpm was used where the number of fibrils, n =50. Due to upper diameter limits and lower contour length limits, the minimum aspect ratio of fibrils for each protein at 200 or 500 rpm can be predicted. This will lead to qualitative results which will allow trends to be analysed. 2 Electronic Supplementary Material (ESI) for Soft Matter This journal is © The Royal Society of Chemistry 2013 The volume fraction of monomers were calculated as follows. Under acidic conditions and elevated temperatures BLG fibrils have a line density of (i.e. monomers per unit length) 0.28nm-1 [1]. The volume of a monomer within a fibril is then: π ⋅ 22 = 45nm3 (Equation 1) 0.28 where 2 nm is the radius of a fibril [2]. To calculate the volume fraction, the number density of molecules in any BLG sample is: 2mM = 1.204×1021 molecules/L = 1.204×10−3 molecules/nm3 The volume fraction is then the volume of a monomer in a fibril, multiplied by the molecular number density given above in a 2mM sample, which is (1.204×10−3 )⋅ 45 ~ 0.05 (assuming 100% conversion). As mentioned previously, the minimum conversion factor of monomer to fibrils is used, 50 %, giving a volume fraction of 0.025. Using the aspect ratio calculated for BLG and the volume fraction calculated above, figure 2e indicates where samples stirred at 200 rpm (with liquid crystalliny) and 500 rpm (no liquid crystallinity) lie on the Onsager phase diagram. Where the area between the lines given by: 3 Electronic Supplementary Material (ESI) for Soft Matter This journal is © The Royal Society of Chemistry 2013 d d v ' = 3.340 , v '' = 4.486 p l p l is the biphasic region [3]. Anything that lies above vp” is anisotropic and anything below vp’ is isotropic. The line density for HEWL is 0.294 nm-1 [2]. As before, using equation 1, the volume of a monomer in a fibril is 42.74 nm3, multiplying this by the molecular density will give a volume fraction of 0.0257 at 50 % conversion of monomers to fibrils, which is very similar to the volume fraction of BLG due to the similar size of monomers. To calculate the volume fraction for insulin (line density of insulin is at present unknown), the volume of a free monomer rather than the volume of a monomer within a fibril was calculated and scaled using the difference in volume of a free monomer and a monomer in a fibril for BLG and HEWL. For BLG, The estimated volume of a monomer, making the assumption of a spherical shape, is: 4 π r 3 (Equation 2) 3 = 2.25×10−26 m3 = 22.5nm3 where r is monomer radius 1.75 nm [4]. The volume of a free monomer in BLG is therefore 2x smaller than a monomer in a fibril which was using equation 1, 45 nm3. The diameter of a HEWL monomer is 3.4 nm [5, 6], the volume of a free monomer using equation 2 is 20.6 nm3, which is also approximately 2x smaller than a HEWL monomer in a fibril 4 Electronic Supplementary Material (ESI) for Soft Matter This journal is © The Royal Society of Chemistry 2013 which was calculated to be is 42.74 nm3. This may seem counter intuitive that a monomer in a fibril is larger than a free monomer, however it agrees with the calculations of Aymard et al [1]. Possible explanations for this phenomenon is that when forming the β-sheet backbone to form fibrils, the native structure not involved is disrupted and cannot fold compactly. To calculate the volume fraction, the order of magnitude of the volume of monomer is the most important aspect and hence a factor of two between a free and fibril monomer will not affect the overall outcome. For insulin, the volume of a free monomer using equation 2 is 4.2 nm3; scaling this up by a factor of two which is the relationship between free monomers and monomers in a fibril for both BLG and HEWL will give a volume of 8.4 nm3. Multiplying this by the molecular density will give a volume fraction of 0.005 (50 % conversion). It should be noted that insulin is thought to have a higher conversion rate than BLG when incubated at the same quiescent conditions [7]. However, the conversion rate in this work varied considerably from 50 to 80 % with the minimum conversion rate being applied to the Onsager prediction. It is likely in practice that the conversion rate for insulin is significantly higher than 50 %. The predicted phase for either HEWL or BLG will not be affected by an increase in aspect ratio (decrease in diameter). HEWL samples at 200 and 500 rpm and BLG samples at 200 rpm will still be predicted to be anisotropic with an increase in aspect ratio (decrease in diameter). As discussed before, in order to affect the prediction of isotropic phase of BLG at 500 rpm i.e. predict anisotropic phase, the diameter of the fibril would need to be less than 2 nm which was deemed unlikely [8]. The average contour length of BLG at 500 rpm was calculated by averaging 50 fibrils and therefore will not change the aspect ratio. 5 Electronic Supplementary Material (ESI) for Soft Matter This journal is © The Royal Society of Chemistry 2013 1. Aymard, P., Durand, D., Nicolai, T., Static and Dynamic Scattering of β-Lactoglobulin Aggregates Formed after Heat-Induced Denaturation at pH 2. Macromolecules 32, 2542 (1999). 2. Humblet-Hua, N.P., Sagis, L. M. C., Van der Linden, E, Effects of Flow on Hen Egg White Lysozyme (HEWL) Fibril Formation: Length Distribution, Flexibility and Kinetics. Journal of Agricultural and Food Chemistry 56, 11875-11882 (2008). 3. Donald A. M., Windle, A., Hanna, S., Liquid Crystalline Polymers. 2nd ed, Cambridge, UK: Cambridge University Press (2006). 4. Qin, B.Y., Bewley, M.C., Creamer, L.K., Baker, H.M., Baker, E.N., Geoffrey, B., and Jameson, G.B. , Structural basis of the Tanford transition of bovine Beta-lactoglobulin. Biochemistry 37, 14014–14023 (1999) 5. Broide, M.L., Tominc, T. M., Saxowsky, M. D. , Using phase transitions to investigate the effect of salts on protein interactions. Phys. ReV. E, 53 6325 (1996). 6. Cardinaux, F., Stradner, A., Schurtenberger, P., Sciortino, F., Zaccarelli, E. , Modeling equilibrium clusters in lysozyme solution. Europhysics Letters 77, (2007). 7. Domike, K.R., Donald, A. M., Thermal Dependence of Thermally Induced Protein Spherulite Formation and Growth: Kinetics of β-lactoglobulin and Insulin. Biomacromolecules 12, 3930-3937 (2007). 8. Akkermans, C., Venema, P., Rogers, S. S., Van der Goot, A. J., . Boom, R. M., and Van der Linden, E, Shear Pulses Nucleate Fibril Aggregation. Food Biophysics 1, 1557-1858 (2006). 6 .
Load more

Recommended publications
  • Development Team
    Paper No: 16 Environmental Chemistry Module: 01 Environmental Concentration Units Development Team Prof. R.K. Kohli Principal Investigator & Prof. V.K. Garg & Prof. Ashok Dhawan Co- Principal Investigator Central University of Punjab, Bathinda Prof. K.S. Gupta Paper Coordinator University of Rajasthan, Jaipur Prof. K.S. Gupta Content Writer University of Rajasthan, Jaipur Content Reviewer Dr. V.K. Garg Central University of Punjab, Bathinda Anchor Institute Central University of Punjab 1 Environmental Chemistry Environmental Environmental Concentration Units Sciences Description of Module Subject Name Environmental Sciences Paper Name Environmental Chemistry Module Name/Title Environmental Concentration Units Module Id EVS/EC-XVI/01 Pre-requisites A basic knowledge of concentration units 1. To define exponents, prefixes and symbols based on SI units 2. To define molarity and molality 3. To define number density and mixing ratio 4. To define parts –per notation by volume Objectives 5. To define parts-per notation by mass by mass 6. To define mass by volume unit for trace gases in air 7. To define mass by volume unit for aqueous media 8. To convert one unit into another Keywords Environmental concentrations, parts- per notations, ppm, ppb, ppt, partial pressure 2 Environmental Chemistry Environmental Environmental Concentration Units Sciences Module 1: Environmental Concentration Units Contents 1. Introduction 2. Exponents 3. Environmental Concentration Units 4. Molarity, mol/L 5. Molality, mol/kg 6. Number Density (n) 7. Mixing Ratio 8. Parts-Per Notation by Volume 9. ppmv, ppbv and pptv 10. Parts-Per Notation by Mass by Mass. 11. Mass by Volume Unit for Trace Gases in Air: Microgram per Cubic Meter, µg/m3 12.
    [Show full text]
  • Supplement Of
    Supplement of Effects of Liquid–Liquid Phase Separation and Relative Humidity on the Heterogeneous OH Oxidation of Inorganic-Organic Aerosols: Insights from Methylglutaric Acid/Ammonium Sulfate Particles Hoi Ki Lam1, Rongshuang Xu1, Jack Choczynski2, James F. Davies2, Dongwan Ham3, Mijung Song3, Andreas Zuend4, Wentao Li5, Ying-Lung Steve Tse5, Man Nin Chan 1,6 1Earth System Science Programme, Faculty of Science, The Chinese University of Hong Kong, Hong Kong, China 2Department of Chemistry, University of California Riverside, Riverside, CA, USA 3Department of Earth and Environmental Sciences, Jeonbuk National University, Jeollabuk-do, Republic of Korea 4Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Québec, Canada 5Departemnt of Chemistry, The Chinese University of Hong Kong, Hong Kong, China’ 6The Institute of Environment, Energy and Sustainability, The Chinese University of Hong Kong, Hong Kong, China Corresponding author: [email protected] Table S1. Composition, viscosity, diffusion coefficient and mixing time scale of aqueous droplets containing 3-MGA and ammonium sulfate (AS) in an organic- to-inorganic dry mass ratio (OIR) = 1 at different RH predicted by the AIOMFAC-LLE. RH (%) 55 60 65 70 75 80 85 88 Salt-rich phase (Phase α) Mass fraction of 3-MGA 0.00132 0.00372 0.00904 0.0202 / / Mass fraction of AS 0.658 0.616 0.569 0.514 / / Mass fraction of H2O 0.341 0.380 0.422 0.466 / / Organic-rich phase (Phase β) Mass fraction of 3-MGA 0.612 0.596 0.574 0.546 / / Mass fraction of AS 0.218 0.209 0.199 0.190
    [Show full text]
  • Colloidal Suspensions
    Chapter 9 Colloidal suspensions 9.1 Introduction So far we have discussed the motion of one single Brownian particle in a surrounding fluid and eventually in an extaernal potential. There are many practical applications of colloidal suspensions where several interacting Brownian particles are dissolved in a fluid. Colloid science has a long history startying with the observations by Robert Brown in 1828. The colloidal state was identified by Thomas Graham in 1861. In the first decade of last century studies of colloids played a central role in the development of statistical physics. The experiments of Perrin 1910, combined with Einstein's theory of Brownian motion from 1905, not only provided a determination of Avogadro's number but also laid to rest remaining doubts about the molecular composition of matter. An important event in the development of a quantitative description of colloidal systems was the derivation of effective pair potentials of charged colloidal particles. Much subsequent work, largely in the domain of chemistry, dealt with the stability of charged colloids and their aggregation under the influence of van der Waals attractions when the Coulombic repulsion is screened strongly by the addition of electrolyte. Synthetic colloidal spheres were first made in the 1940's. In the last twenty years the availability of several such reasonably well characterised "model" colloidal systems has attracted physicists to the field once more. The study, both theoretical and experimental, of the structure and dynamics of colloidal suspensions is now a vigorous and growing subject which spans chemistry, chemical engineering and physics. A colloidal dispersion is a heterogeneous system in which particles of solid or droplets of liquid are dispersed in a liquid medium.
    [Show full text]
  • Calculation Exercises with Answers and Solutions
    Atmospheric Chemistry and Physics Calculation Exercises Contents Exercise A, chapter 1 - 3 in Jacob …………………………………………………… 2 Exercise B, chapter 4, 6 in Jacob …………………………………………………… 6 Exercise C, chapter 7, 8 in Jacob, OH on aerosols and booklet by Heintzenberg … 11 Exercise D, chapter 9 in Jacob………………………………………………………. 16 Exercise E, chapter 10 in Jacob……………………………………………………… 20 Exercise F, chapter 11 - 13 in Jacob………………………………………………… 24 Answers and solutions …………………………………………………………………. 29 Note that approximately 40% of the written exam deals with calculations. The remainder is about understanding of the theory. Exercises marked with an asterisk (*) are for the most interested students. These exercises are more comprehensive and/or difficult than questions appearing in the written exam. 1 Atmospheric Chemistry and Physics – Exercise A, chap. 1 – 3 Recommended activity before exercise: Try to solve 1:1 – 1:5, 2:1 – 2:2 and 3:1 – 3:2. Summary: Concentration Example Advantage Number density No. molecules/m3, Useful for calculations of reaction kmol/m3 rates in the gas phase Partial pressure Useful measure on the amount of a substance that easily can be converted to mixing ratio Mixing ratio ppmv can mean e.g. Concentration relative to the mole/mole or partial concentration of air molecules. Very pressure/total pressure useful because air is compressible. Ideal gas law: PV = nRT Molar mass: M = m/n Density: ρ = m/V = PM/RT; (from the two equations above) Mixing ratio (vol): Cx = nx/na = Px/Pa ≠ mx/ma Number density: Cvol = nNav/V 26 -1 Avogadro’s
    [Show full text]
  • Alkali Metal Vapor Pressures & Number Densities for Hybrid Spin Exchange Optical Pumping
    Alkali Metal Vapor Pressures & Number Densities for Hybrid Spin Exchange Optical Pumping Jaideep Singh, Peter A. M. Dolph, & William A. Tobias University of Virginia Version 1.95 April 23, 2008 Abstract Vapor pressure curves and number density formulas for the alkali metals are listed and compared from the 1995 CRC, Nesmeyanov, and Killian. Formulas to obtain the temperature, the dimer to monomer density ratio, and the pure vapor ratio given an alkali density are derived. Considerations and formulas for making a prescribed hybrid vapor ratio of alkali to Rb at a prescribed alkali density are presented. Contents 1 Vapor Pressure Curves 2 1.1TheClausius-ClapeyronEquation................................. 2 1.2NumberDensityFormulas...................................... 2 1.3Comparisonwithotherstandardformulas............................. 3 1.4AlkaliDimers............................................. 3 2 Creating Hybrid Mixes 11 2.1Predictingthehybridvaporratio.................................. 11 2.2Findingthedesiredmolefraction.................................. 11 2.3GloveboxMethod........................................... 12 2.4ReactionMethod........................................... 14 1 1 Vapor Pressure Curves 1.1 The Clausius-Clapeyron Equation The saturated vapor pressure above a liquid (solid) is described by the Clausius-Clapeyron equation. It is a consequence of the equality between the chemical potentials of the vapor and liquid (solid). The derivation can be found in any undergraduate text on thermodynamics (e.g. Kittel & Kroemer [1]): Δv · ∂P = L · ∂T/T (1) where P is the pressure, T is the temperature, L is the latent heat of vaporization (sublimation) per particle, and Δv is given by: Vv Vl(s) Δv = vv − vl(s) = − (2) Nv Nl(s) where V is the volume occupied by the particles, N is the number of particles, and the subscripts v & l(s) refer to the vapor & liquid (solid) respectively.
    [Show full text]
  • Receive! Osti
    DOE/MC/30175-5033 (DE96000569) RECEIVE! NOV 2 11995 OSTI Portable Sensor for Hazardous Waste Topical Report October 1993 - September 1994 Dr. Lawrence G. Piper October 1994 Work Performed Under Contract No.: DE-AC21-93MC30175 For U.S. Department of Energy U.S. Department of Energy Office of Environmental Management Office of Fossil Energy Office of Technology Development Morgantown Energy Technology Center Washington, DC Morgantown, West Virginia By Physical Sciences Inc. Andover, Massachusetts IAS DISTRIBUTION DP TMi.Q nnpiiycwr » I !MI IS UTT-n, S\c^ DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manu• facturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. This report has been reproduced directly from the best available copy. Available to DOE and DOE contractors from the Office of Scientific and Technical Information, 175 Oak Ridge Turnpike, Oak Ridge, TN 37831; prices available at (615) 576-8401. Available to the public from the National Technical Information Service, U.S.
    [Show full text]
  • Enter Or Copy the Title of the Article Here
    This is the author’s final, peer-reviewed manuscript as accepted for publication. The publisher-formatted version may be available through the publisher’s web site or your institution’s library. Kirkwood–Buff integrals for ideal solutions Elizabeth A. Ploetz, Nikolaos Bentenitis, Paul E. Smith. How to cite this manuscript If you make reference to this version of the manuscript, use the following information: Ploetz, E.A., Bentenitis, N., & Smith, P.E. (2010). Kirkwood–Buff integrals for ideal solutions. Retrieved from http://krex.ksu.edu Published Version Information Citation: Ploetz, E.A., Bentenitis, N., & Smith, P.E. (2010). Kirkwood–Buff integrals for ideal solutions. The journal of chemical physics, 132(16), 9. Copyright: © 2010 American Institute of Physics. Digital Object Identifier (DOI): doi:10.1063/1.3398466 Publisher’s Link: http://jcp.aip.org/resource/1/jcpsa6/v132/i16/p164501_s1 This item was retrieved from the K-State Research Exchange (K-REx), the institutional repository of Kansas State University. K-REx is available at http://krex.ksu.edu THE JOURNAL OF CHEMICAL PHYSICS 132, 164501 ͑2010͒ Kirkwood–Buff integrals for ideal solutions ͒ Elizabeth A. Ploetz,1 Nikolaos Bentenitis,2 and Paul E. Smith1,a 1Department of Chemistry, Kansas State University, Manhattan, Kansas 66506, USA 2Department of Chemistry and Biochemistry, Southwestern University, Georgetown, Texas 78626, USA ͑Received 20 May 2009; accepted 29 March 2010; published online 22 April 2010͒ The Kirkwood–Buff ͑KB͒ theory of solutions is a rigorous theory of solution mixtures which relates the molecular distributions between the solution components to the thermodynamic properties of the mixture. Ideal solutions represent a useful reference for understanding the properties of real solutions.
    [Show full text]
  • Density Lab B Test
    Northern Regional: January 19th, 2019 Density Lab B Test Name(s): _______________________________________________________________________ Team Name: ________________________________________ School Name: ________________________________________ Rank: ___________ Team Number: ___________ Score: ___________ Written Test 1) All of the below are types of densities except (5 points) a) Mass Density b) Number Density c) Area Density d) Volume Density 2) Which of the following exhibits Boyle’s Law? (5 points) a) P1V1= P2V2 b) P1/T1=P2/T2 c) PV= nRT d) V1/T1=V2/T2 3) How many atoms are in 3 moles of a substance? (5 points) 23 a) 24.023*10 atoms​ ​ 24 b) 1.81*10 ​ atoms ​ c) 23 atoms 23 d) 6.02310 atoms​ ​ 4) If the temperature of a container doubled, what would have happened to the pressure of the gas inside the container? (5 points) a) Halved b) Doubled c) Quadrupled d) Nothing 5) What factors affect density? (5 points) a) Pressure b) Temperature c) Both A and B d) None of the above 6) Water is more dense as a solid. (5 points) a) True b) False 7) Pascal is the SI Unit for pressure. (5 points) a) True b) False 8) The acceleration due to gravity on Earth is 9.8 m/s. (5 points) a) True b) False 9) Salt water is more dense than deionized water. (5 points) a) True b) False 10) By Archimedes' principle, the buoyant force is equal to the weight of fluid displaced. (5 points) a) True b) False 11) What is the Archimedes Principle? (5 points) 12) What is the molarity of a solution containing 18.9 grams of RuCl3 in enough water to ​ ​ make 1.00 L of solution?
    [Show full text]
  • Stellar Structure III
    7 – Stellar Structure III introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1 Fundamental physical constants a radiation density constant 7.55 × 10-16 J m-3 K-4 c velocity of light 3.00 × 108 m s-1 G gravitational constant 6.67 × 10-11 N m2 kg-2 h Planck’s constant 6.62 × 10-34 J s K Boltzmann’s constant 1.38 × 10-23 J K-1 -31 me mass of electron 9.11 × 10 kg -27 mH mass of hydrogen atom 1.67 × 10 kg 23 -1 NA Avogadro’s number 6.02 × 10 mol σ Stefan Boltzmann constant 5.67 × 10-8 W m-2 K-4 (σ = ac/4) R gas constant (k/mH) 8.26 × 103 J K-1 kg-1 e charge of electron 1.60 × 10-19 C 26 L¤ luminosity of Sun 3.86 × 10 W 30 M¤ mass of Sun 1.99 × 10 kg Teff¤ effective temperature of sun 5780 K 8 R¤ radius of Sun 6.96 × 10 m Parsec (unit of distance) 3.09 × 1016 m introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 2 22 7.1 - The equation of radiative transport We assume for the moment that the condition for convection is not satisfied, and we will derive an expression relating the change in temperature with radius in a star assuming all energy is transported by radiation. Hence we ignore the effects of convection and conduction. The equation of radiative transport with gas conditions is a function of only one coordinate, in this case r.
    [Show full text]
  • The Evolution of Galaxy Number Density
    Draft version October 9, 2016 A Preprint typeset using L TEX style AASTeX6 v. 1.0 THE EVOLUTION OF GALAXY NUMBER DENSITY AT Z < 8 AND ITS IMPLICATIONS Christopher J. Conselice, Aaron Wilkinson, Kenneth Duncan1, Alice Mortlock2 University of Nottingham, School of Physics & Astronomy, Nottingham, NG7 2RD UK 1Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, the Netherlands 2SUPA, Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh, EH9 3HJ ABSTRACT The evolution of the number density of galaxies in the universe, and thus also the total number of galaxies, is a fundamental question with implications for a host of astrophysical problems including galaxy evolution and cosmology. However there has never been a detailed study of this important measurement, nor a clear path to answer it. To address this we use observed galaxy stellar mass functions up to z ∼ 8 to determine how the number densities of galaxies changes as a function of time and mass limit. We show that the increase in the total number density of galaxies (φT), more massive 6 −1 than M∗ = 10 M⊙ , decreases as φT ∼ t , where t is the age of the universe. We further show 7 that this evolution turns-over and rather increases with time at higher mass lower limits of M∗ > 10 6 M⊙ . By using the M∗ = 10 M⊙ lower limit we further show that the total number of galaxies in the +0.7 12 universe up to z = 8 is 2.0−0.6 × 10 (two trillion), almost a factor of ten higher than would be seen in an all sky survey at Hubble Ultra-Deep Field depth.
    [Show full text]
  • Measurement of Particle Number Density and Volume Fraction in A
    Measurement of Particle Number Density and Volume Fraction in a Fluidized Bed using Shadow Sizing Method Seckin Gokaltun, Ph.D David Roelant, Ph.D Applied Research Center FLORIDA INTERNATIONAL UNIVERSITY Objective y 2006 Roadmap Task D1 & D2: y Detailed CFB data at ~.15m ID y Non-intrusive probes y Generate detailed experimental data to develop a new mathematical analysis procedure for defining cluster formation by utilizing granular temperature. y Measure void fraction y Obtain granular temperature y Demonstrate nonintrusive probe to collect void fraction data Granular Temperature Granular theory Kinetic theory y From the ideal gas law: y Assumptions: y Very large number of PV = NkBT particles (for valid statistical treatment) where kB is the Boltzmann y Distance among particles much larger than molecular constant and the absolute size temperature, thus: y Random particle motion with 2 constant speeds PV = NkBT = Nmvrms / 3 2 y Elastic particle-particle and T = mvrms / 3kB particle-walls collisions (no n loss of energy) v 2 = v 2 y Molecules obey Newton Laws rms ∑ i i =1 is the root-mean-square velocity Granular Temperature y From velocity 1 θ = ()σ 2 + σ 2 + σ 2 3 θ r z 2 2 where: σ z = ()u z − u y uz is particle velocity u is the average particle velocity y From voidage for dilute flows 2 3 θ ∝ ε s y From voidage for dense flows 2 θ ∝1 ε s 6 Glass beads imaged at FIU 2008 Volume Fraction y Solids volume fraction: nV ε = p s Ah y n : the number of particles y Vp : is the volume of single particle y A : the view area y h : the depth of view (Lecuona et al., Meas.
    [Show full text]
  • 1 Atmospheric Sciences 501. Course Notes Autumn 1998. 1. Ideal Gas
    1 Atmospheric Sciences 501. Course Notes Autumn 1998. 1. Ideal Gas Law and Hydrostatics. 1.1 Ideal Gas Law. Basic thermodynamic variables are: Pressure, p (N m-2; 1 N m-2 = 1 pascal (Pa) = 0.01 millibar (mb) = 0.01hectoPascals (hPa). Density, r (kgm-3) Temperature, T (K) . If the energy due to intermolecular forces is small relative to molecular kinetic energy, the ideal gas law is an excellent approximation to the equation of state relating these variables: pRT=r (1.1) R* where R = = gas constant; R* = universal gas constant = 8314J kmol-1 K-1; M = molar M weight (kg/kg-mole) and R = specific gas constant for dry air = 287 J kg-1 K-1. 1.2 Molecules and the ideal gas law, Maxwell's kinetic interpretation. Note that r=nmÃà (1.2) where nà = number density (number of molecules per unit volume m-3), and mà = molecular mass (kg). Also MmA= à (1.3) where A = Avogadro's Number = 6.022x1026 molecules per mole; note that, since SI units are used, moles here are kilogram-moles, not gram-moles. Substituting (1.2) and (1.3) into (1.1): 2 æ R* ö p = ç ÷ nTÃÃ= knT (1.4) è A ø * æ R ö -23 -1 where k = ç ÷ = 1.381x10 J K is Boltzmann's Constant. è A ø Now consider the pressure exerted by molecules of gas on a surface perpendicular to the x- axis in a Cartesian reference frame. This is the force per unit area and is equivalent to the average flux in the x-direction of molecules with x-momentum mvà , mvÃà nv x ()xx× where () represents averaging over molecular velocities.
    [Show full text]