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NASA NTRS2013

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗
NASA NTRS2022

Aboveground biomass density models for NASA’s Global Ecosystem Dynamics Investigation (GEDI) lidar mission

NASA’s Global Ecosystem Dynamics Investigation (GEDI) is collecting spaceborne full waveform lidar data with a primary science goal of producing accurate estimates of forest aboveground biomass density (AGBD). This paper presents the development of the models used to create GEDI’s footprint-level (~25 m) AGBD (GEDI04_A) product, including a description of the datasets used and the procedure for final model selection. The data used to fit our models are from a compilation of globally distributed spatially and temporally coincident field and airborne lidar datasets, whereby we simulated GEDI-like waveforms from airborne lidar to build a calibration database. We used this database to expand the geographic extent of past waveform lidar studies, and divided the globe into four broad strata by Plant Functional Type (PFT) and six geographic regions. GEDI’s waveform-to-biomass models take the form of parametric Ordinary Least Squares (OLS) models with simulated Relative Height (RH) metrics as predictor variables. From an exhaustive set of candidate models, we selected the best input predictor variables, and data transformations for each geographic stratum in the GEDI domain to produce a set of comprehensive predictive footprint-level models. We found that model selection frequently favored combinations of RH metrics at the 98th, 90th, 50th, and 10th height above ground-level percentiles (RH98, RH90, RH50, and RH10, respectively), but that inclusion of lower RH metrics (e.g. RH10) did not markedly improve model performance. Second, forced inclusion of RH98 in all models was important and did not degrade model performance, and the best performing models were parsimonious, typically having only 1-3 predictors. Third, stratification by geographic domain (PFT, geographic region) improved model performance in comparison to global models without stratification. Fourth, for the vast majority of strata, the best performing models were fit using square root transformation of field AGBD and/or height metrics. There was considerable variability in model performance across geographic strata, and areas with sparse training data and/or high AGBD values had the poorest performance. These models are used to produce global predictions of AGBD, but will be improved in the future as more and better training data become available.

Laura Duncanson↗
NASA NTRS2002

Basal glycogenolysis in mouse skeletal muscle: in vitro model predicts in vivo fluxes

A previously published mammalian kinetic model of skeletal muscle glycogenolysis, consisting of literature in vitro parameters, was modified by substituting mouse specific Vmax values. The model demonstrates that glycogen breakdown to lactate is under ATPase control. Our criteria to test whether in vitro parameters could reproduce in vivo dynamics was the ability of the model to fit phosphocreatine (PCr) and inorganic phosphate (Pi) dynamic NMR data from ischemic basal mouse hindlimbs and predict biochemically-assayed lactate concentrations. Fitting was accomplished by optimizing four parameters--the ATPase rate coefficient, fraction of activated glycogen phosphorylase, and the equilibrium constants of creatine kinase and adenylate kinase (due to the absence of pH in the model). The optimized parameter values were physiologically reasonable, the resultant model fit the [PCr] and [Pi] timecourses well, and the model predicted the final measured lactate concentration. This result demonstrates that additional features of in vivo enzyme binding are not necessary for quantitative description of glycogenolytic dynamics.

Non-NASA Center↗
NASA NTRS1998

Fitting a Two-Component Scattering Model to Polarimetric SAR Data

Classification, decomposition and modeling of polarimetric SAR data has received a great deal of attention in the recent literature. The objective behind these efforts is to better understand the scattering mechanisms which give rise to the polarimetric signatures seen in SAR image data. In this Paper an approach is described, which involves the fit of a combination of two simple scattering mechanisms to polarimetric SAR observations. The mechanisms am canopy scatter from a cloud of randomly oriented oblate spheroids, and a ground scatter term, which can represent double-bounce scatter from a pair of orthogonal surfaces with different dielectric constants or Bragg scatter from a moderately rough surface, seen through a layer of vertically oriented scatterers. An advantage of this model fit approach is that the scattering contributions from the two basic scattering mechanisms can be estimated for clusters of pixels in polarimetric SAR images. The solution involves the estimation of four parameters from four separate equations. The model fit can be applied to polarimetric AIRSAR data at C-, L- and P-Band.

Freeman, A.↗
NASA NTRS2003

First Year Wilkinson Microwave Anisotropy Probe (WMAP)Observations: Preliminary Maps and Basic Results

We present full sky microwave maps in five frequency bands (23 to 94 GHz) from the WMAP first year sky survey. Calibration errors are less than 0.5% and the low systematic error level is well specified. The cosmic microwave background (CMB) is separated from the foregrounds using multifrequency data. The sky maps are consistent with the 7 in. full-width at half-maximum (FWHM) Cosmic Background Explorer (COBE) maps. We report more precise, but consistent, dipole and quadrupole values. The CMB anisotropy obeys Gaussian statistics with -58 less than f(sub NL) less than 134 (95% CL). The 2 less than or = l less than or = 900 anisotropy power spectrum is cosmic variance limited for l less than 354 with a signal-to-noise ratio greater than 1 per mode to l = 658. The temperature-polarization cross-power spectrum reveals both acoustic features and a large angle correlation from reionization. The optical depth of reionization is tau = 0.17 +/- 0.04, which implies a reionization epoch of t(sub r) = 180(sup +220, sub -80) Myr (95% CL) after the Big Bang at a redshift of z(sub r) = 20(sup +10, sub -9) (95% CL) for a range of ionization scenarios. This early reionization is incompatible with the presence of a significant warm dark matter density. A best-fit cosmological model to the CMB and other measures of large scale structure works remarkably well with only a few parameters. The age of the best-fit universe is t(sub 0) = 13.7 +/- 0.2 Gyr old. Decoupling was t(sub dec) = 379(sup +8, sub -7)kyr after the Big Bang at a redshift of z(sub dec) = 1089 +/- 1. The thickness of the decoupling surface was Delta(sub z(sub dec)) = 195 +/- 2. The matter density of the universe is Omega(sub m)h(sup 2) = 0.135(sup +0.008, sub -0.009) the baryon density is Omega(sub b)h(sup 2) = 0.0224 +/- 0.0009, and the total mass-energy of the universe is Omega(sub tot) = 1.02 +/- 0.02. There is progressively less fluctuation power on smaller scales, from WMAP to fine scale CMB measurements to galaxies and finally to the Ly-alpha forest. This is accounted for with a running spectral index, significant at the approx. 2(sigma) level. The spectral index of scalar fluctuations is fit as n(sub s) = 0.93 +/-0.03 at wavenumber k(sub o) = 0.05/Mpc ((sub eff) approx. = 700), with a slope of dn(sub s)/d I(sub nk) = -0.031(sup + 0.016, sub -0.018) in the best-fit model.

Bennett, C. L.↗
NASA NTRS2014

The Rise and Fall of the Type Ib Supernova iPTF13bvn Not a Massive Wolf-Rayet Star

Context. We investigate iPTF13bvn, a core-collapse (CC) supernova (SN) in the nearby spiral galaxy NGC 5806. This object was discovered by the intermediate Palomar Transient Factory (iPTF) very close to the estimated explosion date and was classified as a stripped-envelope CC SN, likely of Type Ib. Furthermore, a possible progenitor detection in pre-explosion Hubble Space Telescope (HST) images was reported, making this the only SN Ib with such an identification. Based on the luminosity and color of the progenitor candidate, as well as on early-time spectra and photometry of the SN, it was argued that the progenitor candidate is consistent with a single, massive Wolf-Rayet (WR) star. Aims. We aim to confirm the progenitor detection, to robustly classify the SN using additional spectroscopy, and to investigate if our follow-up photometric and spectroscopic data on iPTF13bvn are consistent with a single-star WR progenitor scenario. Methods. We present a large set of observational data, consisting of multi-band light curves (UBVRI, g′r′i′z′) and optical spectra. We perform standard spectral line analysis to track the evolution of the SN ejecta. We also construct a bolometric light curve and perform hydrodynamical calculations to model this light curve to constrain the synthesized radioactive nickel mass and the total ejecta mass of the SN. Late-time photometry is analyzed to constrain the amount of oxygen. Furthermore, image registration of pre- and post-explosion HST images is performed. Results. Our HST astrometry confirms the location of the progenitor candidate of iPTF13bvn, and follow-up spectra securely classify this as a SN Ib. We use our hydrodynamical model to fit the observed bolometric light curve, estimating the total ejecta mass to be 1.9 solar mass and the radioactive nickel mass to be 0.05 solar mass. The model fit requires the nickel synthesized in the explosion to be highly mixed out in the ejecta. We also find that the late-time nebular r′-band luminosity is not consistent with predictions based on the expected oxygen nucleosynthesis in very massive stars. Conclusions. We find that our bolometric light curve of iPTF13bvn is not consistent with the previously proposed single massive WR-star progenitor scenario. The total ejecta mass and, in particular, the late-time oxygen emission are both significantly lower than what would be expected from a single WR progenitor with a main-sequence mass of at least 30 solar mass.

massive↗
NASA NTRS2010

Atmospheric and Fundamental Parameters of Stars in Hubble's Next Generation Spectral Library

Hubble's Next Generation Spectral Library (NGSL) consists of R approximately 1000 spectra of 374 stars of assorted temperature, gravity, and metallicity. We are presently working to determine the atmospheric and fundamental parameters of the stars from the NGSL spectra themselves via full-spectrum fitting of model spectra to the observed (extinction-corrected) spectrum over the full wavelength range, 0.2-1.0 micron. We use two grids of model spectra for this purpose: the very low-resolution spectral grid from Castelli-Kurucz (2004), and the grid from MARCS (2008). Both the observed spectrum and the MARCS spectra are first degraded in resolution to match the very low resolution of the Castelli-Kurucz models, so that our fitting technique is the same for both model grids. We will present our preliminary results with a comparison with those from the Sloan/Segue Stellar Parameter Pipeline, ELODIE, and MILES, etc.

Heap, Sally↗
NASA NTRS2010

Data Validation in the Kepler Science Operations Center Pipeline

We present an overview of the Data Validation (DV) software component and its context within the Kepler ScienceOperations Center (SOC) pipeline and overall Kepler Science mission. The SOC pipeline performs a transiting planetsearch on the corrected light curves for over 150,000 targets across the focal plane array. We discuss the DV strategy forautomated validation of Threshold Crossing Events (TCEs) generated in the transiting planet search. For each TCE, atransiting planet model is fitted to the target light curve. A multiple planet search is conducted by repeating the transitingplanet search on the residual light curve after the model flux has been removed; if an additional detection occurs, aplanet model is fitted to the new TCE. A suite of automated tests are performed after all planet candidates have beenidentified. We describe a centroid motion test to determine the significance of the motion of the target photocenterduring transit and to estimate the coordinates of the transit source within the photometric aperture; a series of eclipsingbinary discrimination tests on the parameters of the planet model fits to all transits and the sequences of odd and eventransits; and a statistical bootstrap to assess the likelihood that the TCE would have been generated purely by chancegiven the target light curve with all transits removed.

photometry↗
NASA NTRS2010

Data Validation in the Kepler Science Operations Center Pipeline

We present an overview of the Data Validation (DV) software component and its context within the Kepler Science Operations Center (SOC) pipeline and overall Kepler Science mission. The SOC pipeline performs a transiting planet search on the corrected light curves for over 150,000 targets across the focal plane array. We discuss the DV strategy for automated validation of Threshold Crossing Events (TCEs) generated in the transiting planet search. For each TCE, a transiting planet model is fitted to the target light curve. A multiple planet search is conducted by repeating the transiting planet search on the residual light curve after the model flux has been removed; if an additional detection occurs, a planet model is fitted to the new TCE. A suite of automated tests are performed after all planet candidates have been identified. We describe a centroid motion test to determine the significance of the motion of the target photocenter during transit and to estimate the coordinates of the transit source within the photometric aperture; a series of eclipsing binary discrimination tests on the parameters of the planet model fits to all transits and the sequences of odd and even transits; and a statistical bootstrap to assess the likelihood that the TCE would have been generated purely by chance given the target light curve with all transits removed. Keywords: photometry, data validation, Kepler, Earth-size planets

Wu, Hayley↗
NASA NTRS1989

Fitting improved accretion disk models to the multiwavelength continua of quasars and active galactic nuclei

Fits to the ultraviolet-optical-infrared spectra of 60 quasars and active galactic nuclei (AGNs) are investigated, using black hole accretion disk models. The disk is assumed to be geometrically thin and optically thick. The observed spectrum from a black hole accretion disk, rotating (Kerr) or nonrotating (Schwarzschild), is transformed by the geometric inclination effect, Doppler shifts, gravitational redshifts, and gravitational focusing. These effects alter the locally emitted fluxes and produce harder spectra for an observer at higher inclination angles. The relativistic corrections are much more significant in the Kerr geometry since the inner edge of the disk is much closer to the rotating black hole. A simple inverse relation between the inferred black hole mass and the assumed inclination angle was found in the Kerr case, while the inferred accretion rate (solar masses/yr) remains independent of the angle. In the Schwarzschild case, the ratio of the inferred accretion rate to the black hole mass remains roughly constant when the viewing angle changes. In both geometries, low-redshift Seyfert galaxies have relatively low accretion rates, only a few percent of their Eddington luminosities, while the most luminous quasars are accreting near their Eddington limits.

Sun, Wei-Hsin↗
NASA NTRS2001

Relativistic Iron Emission and Disk Reflection in Galactic Microquasar XTE J1748-288

We report evidence for an Fe K-alpha fluorescence line feature and disk reflection in the very high, high-, and low-state X-ray spectra of the Galactic microquasar XTE J1748 - 288 during its 1998 June outburst. Spectral analyses are made on data gathered throughout the outburst by the Rossi X-Ray Timing Explorer Proportional Counter Array. Gaussian line, relativistic disk emission line, and ionized disk reflection models are fitted to the data. In the very high state the line profile appears strongly redshifted, consistent with disk emission from the innermost stable orbits around a maximally rotating Kerr black hole. In the high state the line profile is less redshifted and increasingly prominent. The low-state line profile is very strong (approx. 0.5 keV equivalent width) and centered at 6.7 +/- 0.10 keV; disk line emission model fits indicate that the inner edge of the disk fluctuates between approx. 20R(sub g) and - approx. 100R(sub g) in this state. The disk reflection fraction is traced through the outburst; reflection from an ionized disk is preferred in the very high and high states, and reflection from a relatively neutral disk is preferred in the low state. We discuss the implications of our findings for the binary system dynamics and accretion flow geometry in XTE J1748 - 288.

Miller, J. M.↗
NASA NTRS2001

Relativistic Iron Emission and Disk Reflection in Galactic Microquasar XTE J1748-288

We report evidence for an Fe K(alpha) fluorescence line feature and disk reflection in the very high, high-, and low-state X-ray spectra of the Galactic microquasar XTE J1748-288 during its 1998 June outburst. Spectral analyses are made on data gathered throughout the outburst by the Rossi X-Ray Timing Explorer Proportional Counter Array. Gaussian line, relativistic disk emission line, and ionized disk reflection models are fitted to the data. In the very high state the line profile appears strongly redshifted, consistent with disk emission from the innermost stable orbits around a maximally rotating Kerr black hole. In the high state the line profile is less redshifted and increasingly prominent. The low-state line profile is very strong (approx. 0.5 keV equivalent width) and centered at 6.7 +/- 0.10 keV; disk line emission model fits indicate that the inner edge of the disk fluctuates between approx. 20Rg and approx. 100Rg in this state. The disk reflection fraction is traced through the outburst; reflection from an ionized disk is preferred in the very high and high states, and reflection from a relatively neutral disk is preferred in the low state. We discuss the implications of our findings for the binary system dynamics and accretion flow geometry in XTE J1748-288.

Miller, J. M.↗
NASA NTRS1985

The energy spectra of solar flare electrons

A survey of 50 electron energy spectra from .1 to 100 MeV originating from solar flares was made by the combination of data from two spectrometers onboard the International Sun Earth Explorer-3 spacecraft. The observed spectral shapes of flare events can be divided into two classes through the criteria of fit to an acceleration model. This standard two step acceleration model, which fits the spectral shape of the first class of flares, involves an impulsive step that accelerates particles up to 100 keV and a second step that further accelerates these particles up to 100 MeV by a single shock. This fit fails for the second class of flares that can be characterized as having excessively hard spectra above 1 MeV relative to the predictions of the model. Correlations with soft X-ray and meter radio observations imply that the acceleration of the high energy particles in the second class of flares is dominated by the impulsive phase of the flares.

Evenson, P. A.↗
NASA NTRS2011

The Atacama Cosmology Telescope: Cosmological Parameters from the 2008 Power Spectrum

We present cosmological parameters derived from the angular power spectrum of the cosmic microwave background (CMB) radiation observed at 148 GHz and 218 GHz over 296 deg(exp 2) with the Atacama Cosmology Telescope (ACT) during its 2008 season. ACT measures fluctuations at scales 500 < l < 10,000. We fit a model for the lensed CMB, Sunyaev-Zel'dovich (SZ), and foreground contribution to the 148 GHz and 218 GHz power spectra, including thermal and kinetic SZ, Poisson power from radio and infrared point sources, and clustered power from infrared point sources. At l = 3000, about half the power at 148 GHz comes from primary CMB after masking bright radio sources. The power from thermal and kinetic SZ is estimated to be Beta(sub 3000) is identical to 6.8 +/- 2.9 mu K (exp 2), where Beta (sub l) is identical to l(l + 1) C(sub l)/2pi. The IR Poisson power at 148 GHz is Bewta(sub 3000) 7.8 +/- 0.7 muK(exp 2) (C(sub l) = 5.5 +/- 0.5 nK(exp 2)), and a clustered IR component is required with Beta (sub 3000) = 4.6 +/- 0.9 muK(exp 2), assuming an analytic model for its power spectrum shape. At 218 GHz only about 15% of the power, approximately 27 mu K(exp 2), is CMB anisotropy at l = 3000. The remaining 85% is attributed to IR sources (approximately 50% Poisson and 35% clustered), with spectral index alpha = 3.69 +/- 0.14 for flux scaling as S(nu) varies as nu(sup alpha). We estimate primary cosmological parameters from the less contaminated 148 GHz spectrum, marginalizing over SZ and source power. The ACDM cosmological model is a good fit to the data (chi square/dof = 29/46), and ACDM parameters estimated from ACT+Wilkinson Microwave Anisotropy Probe (WMAP) are consistent with the seven-year WMAP limits, with scale invariant n(sub s) = 1 excluded at 99.7% confidence level (CL) (3 sigma). A model with no CMB lensing is disfavored at 2.8 sigma. By measuring the third to seventh acoustic peaks, and probing the Silk damping regime, the ACT data improve limits on cosmological parameters that affect the small-scale CMB power. The ACT data combined with WMAP give a 6 sigma detection of primordial helium, with Y(sub p) = 0.313 +/- 0.044, and a 4 sigma detection of relativistic species, assumed to be neutrinos, with N(sub eff) = 5.3 +/- 1.3 (4.6 +/- 0.8 with BAO+H(sub 0) data). From the CMB alone the running of the spectral index is constrained to be d(sub s) / d ln k = -0,034 +/- 0,018, the limit on the tensor-to-scalar ratio is r < 0,25 (95% CL), and the possible contribution of Nambu cosmic strings to the power spectrum is constrained to string tension G(sub mu) < 1.6 x 10(exp -7) (95% CL),

Dunkley, J.↗
NASA NTRS1999

Backus Effect on a Perpendicular Errors in Harmonic Models of Real vs. Synthetic Data

Measurements of geomagnetic scalar intensity on a thin spherical shell alone are not enough to separate internal from external source fields; moreover, such scalar data are not enough for accurate modeling of the vector field from internal sources because of unmodeled fields and small data errors. Spherical harmonic models of the geomagnetic potential fitted to scalar data alone therefore suffer from well-understood Backus effect and perpendicular errors. Curiously, errors in some models of simulated 'data' are very much less than those in models of real data. We analyze select Magsat vector and scalar measurements separately to illustrate Backus effect and perpendicular errors in models of real scalar data. By using a model to synthesize 'data' at the observation points, and by adding various types of 'noise', we illustrate such errors in models of synthetic 'data'. Perpendicular errors prove quite sensitive to the maximum degree in the spherical harmonic expansion of the potential field model fitted to the scalar data. Small errors in models of synthetic 'data' are found to be an artifact of matched truncation levels. For example, consider scalar synthetic 'data' computed from a degree 14 model. A degree 14 model fitted to such synthetic 'data' yields negligible error, but amplifies 4 nT (rmss) added noise into a 60 nT error (rmss); however, a degree 12 model fitted to the noisy 'data' suffers a 492 nT error (rmms through degree 12). Geomagnetic measurements remain unaware of model truncation, so the small errors indicated by some simulations cannot be realized in practice. Errors in models fitted to scalar data alone approach 1000 nT (rmss) and several thousand nT (maximum).

Voorhies, C. V.↗
NASA NTRS1974

The magnetic anomaly of the Ivreazone

A magnetic field survey was made in the Ivreazone in 1969/70. The results were: significant anomaly of the vertical intensity is found. It follows the basic main part of the Ivrea-Verbano zone and continues to the south. The width of the anomaly is about 10 km, the maximum measures about +800 gamma. The model interpretation shows that possibly the anomaly belongs to an amphibolitic body, which in connection with the Ivrea-body was found by deep seismic sounding. Therefore, the magnetic anomaly provides further evidence for the conception that the Ivrea-body has to be regarded as a chip of earthmantle material pushed upward by tectonic processes.

Vertical Intensity of Magnetic Field↗
NASA NTRS1985

Images of the earth's aurora and geocorona from the Dynamics Explorer mission

Several series of auroral and geocoronal images from th Dynamics Explorer Mission are presented and analyzed. It is found that the motion of the transpolar arc of a theta aurora is correlated with the y-component of the IMF; the arc motion is in the general direction of the y-component. In addition, a sequence of global images of a small auroral substorm shows the initial development of intense luminosities in a relatively small spatial region or 'bright spot' in the premidnight sector of the auroral oval and a subsequent appearance of an expanding area of lesser intensities at low latitudes and contiguous to the midnight boundary of the bright spot. Finally, a series of images of the geocorona in scattered solar Ly-alpha emissions is used to obtain a best-fit spherical model of atomic hydrogen densities in the earth's exosphere; a Chamberlain model provides an adequate fit to radial distances of 4.5 earth-radii, beyond which an exponential fit is used. The geocoronal tail is detected as an asymmetric increase in scattered Ly-alpha intensities in the antisolar direction.

Frank, L. A.↗
NASA NTRS1989

Protein crystal nucleation kinetics using relative light-scattering techniques: Center director's discretionary fund

Light-scattering intensity measurements are a sensitive method for following changes in the hydrodynamic radius of particles in solution. The approach used in this report utilizes the light-scattering intensity ratios of a polydisperse to a monodisperse system. By numerically modeling the process, and fitting the model curves to the data, estimates have been obtained for the dimerization equilibrium constant, the dimer + dimer yields tetramer equilibrium constant, and the association rate constant for the dimerization process.

Pusey, Marc Lee↗