Assumption Of Density Research Articles

Derivation of free energy expressions for tube models from coarse-grained slip-link models

We present the free energy of a single-chain mean-field model for polymer melt dynamics, which uses a continuous (tube-like) approximation to the discrete entanglements with surrounding chains, but, in contrast to previous tube models, includes fluctuations in the number density of Kuhn steps along the primitive path and in the degree of entanglement. The free energy is obtained from that of the slip-link model with fluctuating entanglement positions [J. D. Schieber and K. Horio, J. Chem. Phys. 132, 074905 (2010)] by taking the continuous limit of (functions of) the discrete Kuhn-step numbers and end-to-end vectors of the strands between entanglements. This coarse-graining from a more-detailed level of description has the advantage that no ad hoc arguments need to be introduced. Moreover, the thermodynamic consistency of the slip-link model [J. D. Schieber, J. Non-Equilib. Thermodyn. 28, 179 (2003)] can be preserved. Fluctuations in the positions of entanglements lead to a harmonic bending term in the free energy of the continuous chain, similar to that derived by Read et al. [Macromolecules 41, 6843 (2008)] starting from a modified GLaMM model [R. S. Graham, A. E. Likhtman, T. C. B. McLeish, and S. T. Milner, J. Rheol. 47, 1171 (2003)]. If these fluctuations are set to zero, the free energy becomes purely Gaussian and corresponds to the continuous limit of the original slip-link model, with affinely moving entanglements [J. D. Schieber, J. Chem. Phys. 118, 5162 (2003)]. The free energy reduces to that of Read et al. under their assumptions of a homogeneous Kuhn-step number density and a constant degree of entanglement. Finally, we show how a transformation of the primitive-path coordinate can be applied to make the degree of entanglement an outcome of the model instead of a variable. In summary, this paper constitutes a first step towards a unified mathematical formulation of tube models. The next step will be to formulate the dynamics of the primitive-path conformation and the entanglement density along the primitive path. Now that the free energy is known, statistical mechanics can be employed for this purpose.

The nature of the Compton-thick X-ray reprocessor in NGC 4945

We present an exhaustive methodology for fitting Compton-thick X-ray reprocessor models to obscured AGNs and for interpreting the results. We focus on the MYTORUS model but also utilize other models. We apply the techniques to Suzaku, BeppoSAX, and Swift BAT spectra of the Sy 2 galaxy NGC 4945, but the methods are applicable to other AGNs including Compton-thin sources. The models overcome a major restriction of disk-reflection models, namely the assumption of an infinite column density. Finite column-density models produce a richer variety of spectral shapes and characteristics, even for Compton-thin AGNs. Although NGC 4945 is one of the brightest AGNs above 10 keV, the models span nearly a factor of 3 in column density (~2 to 6 x 10^{24} cm^{-2}) and 2 orders of magnitude in the intrinsic 2-195 keV luminosity. Models in which the continuum above 10 keV is dominated by the direct (unscattered) continuum or Compton-scattered continuum give the highest and lowest intrinsic luminosities respectively. Variability properties favor solutions in which the unscattered continuum dominates above 10 keV. The data require that the Compton-scattered continuum and Fe Kalpha line emission come predominantly from the illuminated surfaces of the X-ray reprocessor, implying a clumpy medium with a global covering factor that is small enough that the Compton-scattered continuum does not dominate the spectrum above 10 keV. This can be identified with the ~30 pc region spatially resolved by Chandra. The implied intrinsic bolometric luminosity is close to, or greater than, the Eddington luminosity. However, a strongly beamed AGN embedded in a shell of Compton-thick (but clumpy) matter requires less fine-tuning of the covering factor. Beaming is consistent with recent radio and Fermi results. Such beamed Compton-thick AGNs would be preferentially selected in surveys over unbeamed Compton-thick AGNs.

Erratum: “A matched filter for chaos” [Chaos 20, 023123 (2010)

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Dynamics of a lightning corona sheath—A constant field approach using the generalized traveling current source return stroke model

A generalized lightning traveling current source return stroke model has been used to examine the characteristics of the lightning channel corona sheath surrounding a thin channel core. A model of the lightning channel consisting of a charged corona sheath and a narrow, highly conducting central core that conducts the main current flow is assumed. Strong electric field, with a predominant radial direction, has been created during the return stroke between the channel core and the outer channel sheath containing the negative charge. The return stroke process is modeled with the positive charge coming from the channel core discharging the negative leader charge in the corona sheath. The corona sheath model that predicts the charge motion in the sheath is used to derive the expressions of the sheath radius vs. time during the return stroke. According to the corona sheath model proposed earlier by Maslowski and Rakov (2006) and Maslowski et al. (2009), it consists of three zones, zone 1 (surrounding channel core with net positive charge), zone 2 (surrounding zone 1 with negative charge) and zone 3 (outer zone representing the virgin air without charges). We adopted the assumption of a constant electric field inside zone 1 of the corona sheath observed in the experimental research of corona discharges in a coaxial geometry by Cooray (2000). This assumption seems to be more realistic than the assumption of a uniform corona space charge density used previously in the study of Maslowski and Rakov (2006), Marjanovic and Cvetic (2009), and Tausanovic et al. (2010). Applying the Gauss’ law on the infinitesimally small cylindrical section of the channel the expressions for time-dependence of the radii of zones 1 and 2 during the return stroke are derived. The calculations have shown that the overall channel dynamics concerning electrical discharge is roughly 50% slower and the maximum radius of zone 1 is about 33% smaller compared to the corresponding values calculated in the study of Tausanovic et al. (2010).

Do we have to explicitly model the ions in Brownian dynamics simulations of proteins?

Brownian dynamics (BD) is a very efficient coarse-grained simulation technique which is based on Einstein's explanation of the diffusion of colloidal particles. On these length scales well beyond the solvent granularity, a treatment of the electrostatic interactions on a Debye-Hückel (DH) level with its continuous ion densities is consistent with the implicit solvent of BD. On the other hand, since many years BD is being used as a workhorse simulation technique for the much smaller biological proteins. Here, the assumption of a continuous ion density, and therefore the validity of the DH electrostatics, becomes questionable. We therefore investigated for a few simple cases how far the efficient DH electrostatics with point charges can be used and when the ions should be included explicitly in the BD simulation. We find that for large many-protein scenarios or for binary association rates, the conventional continuum methods work well and that the ions should be included explicitly when detailed association trajectories or protein folding are investigated.

Development of sub-channel code SACoS and its application in coupled neutronics/thermal hydraulics system for SCWR

Supercritical Water Reactor (SCWR) is one of the promising reactors from the list of fourth generation of nuclear reactors. High thermal efficiency and low cost of electricity make it an attractive option in the era of growing energy demand. An almost seven fold density variation for coolant/moderator along the active height does not allow the use of constant density assumption for design calculations, as used for previous generations of reactors. The advancement in computer technology gives us the superior option of performing coupled analysis. Thermal hydraulics calculations of supercritical water systems present extra challenges as not many computational tools are available to perform that job. This paper introduces a new sub-channel code called Sub-channel Analysis Code of SCWR (SACoS) and its application in coupled analyses of High Performance Light Water Reactor (HPLWR). SACoS can compute the basic thermal hydraulic parameters needed for design studies of a supercritical water reactor. Multiple heat transfer and pressure drop correlations are incorporated in the code according to the flow regime. It has the additional capability of calculating the thermal hydraulic parameters of moderator flowing in water box and between fuel assemblies under co-current or counter current flow conditions. Using MCNP4c and SACoS, a coupled system has been developed for SCWR design analyses. The developed coupled system is verified by performing and comparing HPLWR calculations. The results were found to be in very good agreement. Significant difference between the results was seen when Doppler feedback effect was included in the coupled calculations. This difference is due to the use of different values of fuel temperature to include Doppler feedback in our and reference coupled systems. This also lays emphasis on the use of true representative values of critical parameters in the design calculations to get the real picture of conditions rather than over or under estimated values.

The effect of voxel size on high‐resolution peripheral computed tomography measurements of trabecular and cortical bone microstructure

Accurate quantification of bone microstructure plays a significant role in understanding bone mechanics and response to disease or treatment. High-resolution peripheral quantitative computed tomography (HR-pQCT) allows for the quantification of trabecular and cortical structure in vivo, with the capability of generating images at multiple voxel sizes (41, 82, and 123 μm). The aim of this study was to characterize the effect of voxel size on structural measures of trabecular and cortical bone and to determine accuracy in reference to micro-CT ([micro sign]CT), the gold standard for bone microstructure quantification. Seventeen radii from human cadaver specimens were imaged at each HR-pQCT voxel size and subsequently imaged using [micro sign]CT. Bone density and microstructural assessment was performed in both the trabecular and cortical compartments, including cortical porosity quantification. Two distinct analysis techniques were applied to the 41 μm HR-pQCT data: the standard clinical indirect analysis and a direct analysis requiring no density or structural model assumptions. Analysis parameters were adjusted to enable segmentation and structure extraction at each voxel size. For trabecular microstructural measures, the 41 μm HR-pQCT data displayed the strongest correlations and smallest errors compared to [micro sign]CT data. The direct analysis technique applied to the 41 μm data yielded an additional improvement in accuracy, especially for measures of trabecular thickness. The 123 μm data performed poorly, with all microstructural measures either having moderate or nonsignificant correlations with [micro sign]CT data. Trabecular densitometric measures showed strong correlations to [micro sign]CT data across all voxel sizes. Cortical thickness was strongly correlated with [micro sign]CT values across all HR-pQCT voxel sizes. The accuracy of cortical porosity parameters was highly dependent on voxel size; again, the 41 μm data was most strongly correlated. Measures of cortical density and pore diameter at all HR-pQCT voxel sizes had either weak or nonsignificant correlations. This study demonstrates the effect of voxel size on the accuracy of HR-pQCT measurements of trabecular and cortical microstructure and presents parameters for HR-pQCT analysis at nonstandard resolutions. For all parameters measured, correlations were strongest at 41 μm. Weak correlations for porosity measures indicate that a better understanding of pore structure and resolution dependence is needed.

On the sensor order in sequential integrated probability data association filter

The processing order of sensors with different detection probabilities and in different clutter densities in a multi-sensor system is investigated in this paper. A sequential implementation of the integrated probability data association (IPDA) algorithm under random set framework is derived. Under the assumptions of different detection probabilities and different clutter densities of individual sensor in a multi-sensor system, we reach the conclusion that the sequential IPDA filter depends on the order analyzing the target existence probability of varying sensor orders. Moreover, we obtain the optimal order of sensors for the sequential IPDA filter in terms of maximizing the target existence probability. The conclusions are demonstrated by simulation results.

Extensions of Lattice Set Functions to Regular Borel Measures

This paper deals with the unique extension of a finite regular set function from the $\delta$-lattice of all compact $G_\delta$-subsets of a locally compact Hausdorff space to a finite regular measure on the $\delta$-ring of all relatively compact Borel subsets of the space. This extension is a two-step method because it is performed (without density assumptions) via the $\delta$-ring of all relatively compact Baire subsets of the space.

The effects of variation in snow properties on passive microwave snow mass estimation

Estimating snow mass at continental scales is difficult, but important for understanding land-atmosphere interactions, biogeochemical cycles and the hydrology of the Northern latitudes. Remote sensing provides the only consistent global observations, but with unknown errors. We test the theoretical performance of the Chang algorithm for estimating snow mass from passive microwave measurements using the Helsinki University of Technology (HUT) snow microwave emission model. The algorithm's dependence upon assumptions of fixed and uniform snow density and grainsize is determined, and measurements of these properties made at the Cold Land Processes Experiment (CLPX) Colorado field site in 2002–2003 used to quantify the retrieval errors caused by differences between the algorithm assumptions and measurements. Deviation from the Chang algorithm snow density and grainsize assumptions gives rise to an error of a factor of between two and three in calculating snow mass. The possibility that the algorithm performs more accurately over large areas than at points is tested by simulating emission from a 25km diameter area of snow with a distribution of properties derived from the snow pit measurements, using the Chang algorithm to calculate mean snow-mass from the simulated emission. The snow mass estimation from a site exhibiting the heterogeneity of the CLPX Colorado site proves only marginally different than that from a similarly-simulated homogeneous site. The estimation accuracy predictions are tested using the CLPX field measurements of snow mass, and simultaneous SSM/I and AMSR-E measurements.

Static Hazards of the VAST

The vertical atmospheric storage tank (VAST) is a large, mechanically weak tank often used to store static accumulating flammable liquids. Explosion of a single VAST can destroy an entire tank farm via rocketing and domino effects. This article provides a new methodology for assessing electrostatic hazards. Appendix A describes flammability aspects, including a new analysis of flash point measurement errors. Appendix B discusses two recent VAST explosions. Recommendations are made for improving the safety of VAST operations. Electrostatic analysis starts with our previously published model expressing the surface potential at the center of the liquid surface “Vmax” in the form of an infinite series of Bessel and hyperbolic functions. A truncated one-term approximation with an improved scale factor “κ” is provided to facilitate spreadsheet calculation. Using at least the first three terms of the series expansion, thousands of individual calculations were made for a wide range of tank dimensions, filling rates and liquid relaxation times, to determine the maximum potential “V∗max” attained during filling, which occurs at some critical depth “Dcrit”. It’s shown there exists a critical width “wcrit”, typically 0.75-1.5 m, at which V∗max reaches a maximum for a given flow rate and relaxation time. At widths above the critical width, V∗max becomes independent of flow rate and, provided the aspect ratio (H/w) of the VAST exceeds 2/3, V∗max becomes independent of height (H) as well. The worst case for VAST filling is a width near “wcrit” plus an effective liquid relaxation time ∼30 s (measured conductivity ∼1 pS/m). We derived very simple expressions for the critical width “wcrit”, the critical liquid depth “Dcrit”, the V∗max yielded by a given charging current “IC”, and the charging current needed to yield a particular V∗max. Of particular interest were the conditions for V∗max = 25 kV, the recognized threshold for incendiary brush discharges. Assuming a worst case 30 s relaxation time and a maximum allowable V∗max of 25 kV, we examined three different expressions for the charging current “IC” and determined the minimum “vd” product (flow velocity x inlet pipe diameter) that could theoretically produce this potential. Equations and graphs are presented showing that the maximum allowable vd product increases with increased VAST width (beyond the critical width) and varies with the assumed charging equation. It’s shown that the classic “Schon” equation isn’t conservative and that charging currents are likely to be much higher than predicted, especially when the diameter of the inlet pipe is less than about 0.1 m (4-inch) and the liquid has a high charging tendency. The “vd” expressions and graphs should assist in the development of Codes of Practice. The uniform charge density assumption used in our model is most valid as conditions approach worst-case, since for widths near the critical width the jet mixing time constant at typical flow rates is small compared with the assumed “worst case” 30 s relaxation time constant. However, in practical cases, jetting from bottom side entry inlets may greatly increase charge densities at the liquid surface. This plus other non-idealities such as water and sediment in tank bottoms are discussed with reference to practical VAST operations.

희박 예혼합 가스터빈 연소기 3 차원 전산 해석 및 화학반응기 네트워크에 의한 NOx 예측

This paper presents 3D simulation by STAR-CCM+ for lean premixed combustion in a stationary gas turbine combustor with separate pilot and main nozzles. The constant for the source term in the flame area density transport equation was modified to account for a low global equivalence ratio and validated against measurement data. A Partially-premixed Coherent Flame Model(PCFM) involves propagation of a laminar premixed flame with the predicted flame surface density and equilibrium assumption in the burned gas with spatial inhomogeneity. The conditions for cooling by radiation and convection are considered for accurate determination of the heat flux on the wall. A parametric study is of the pilot-fuel-to-total-fuel-ratio is carried out. A chemical reactor network (CRN) was constructed on the basis of the 3D simulation results and compared against measurements of NOx.

Testing dasymetric techniques to spatially disaggregate the regional population forecasts for South East Queensland

This research develops methodologies to explore the future settlement patterns of the population by applying a dasymetric approach to step down the regional population forecasts to smaller geographical units. This research extends the dasymetric method beyond its current simple form to techniques that incorporate more complex density assumptions to disaggregate the spatial data. Several dasymetric techniques are evaluated to spatially disaggregate population data over the study area and to assess their relative accuracies. The outputs of the method are population forecasts across the smaller areas that can be used to derive a deeper understanding of future urban structure.

Detection of electrically charged soot particles in laminar premixed flames

A particle mass spectrometer has been used to investigate the formation of electrically charged species and soot particles in laminar premixed flames. The mass range was from 600–6 × 10 5 amu and extends from high molecular hydrocarbons to soot particles of 10 nm diameter. The flames were stabilized on cooled porous plate burners. Acetylene/oxygen flames were investigated at low pressure (30 mbar), and ethylene/air flames were investigated at atmospheric pressure. Soot particles could only be detected in flames showing yellow luminosity, i.e. above the critical C/O-ratio for soot formation. Both positively and negatively charged particles were found, the positive charge dominating in the low pressure acetylene/oxygen flames, the negative charge dominating in the atmospheric ethylene/air flames. With the assumption of spherical shape and constant density, the mass spectra were converted to size spectra. Usually, they show a multiple peak structure which is somewhat difficult to interpret. There are indications that particles may carry multiple (1–2) charges, and also that particles of different types may coexist beside polyaromatic and polyhedral species in the early stage of particle inception.

Extension of lightning corona sheath model during return stroke

A generalized lightning traveling current source return stroke model has been used to examine the characteristics of the lightning channel corona sheath. A model of lightning channel consisting of a charged corona sheath and a narrow, high conducting central core is assumed. The return stroke process is modeled with the positive charge coming from the channel core discharging the negative leader charge in the corona sheath. According to the corona sheath model proposed earlier by Maslowski and Rakov, it consists of three zones, zone 1 (inner zone containing net positive charge), zone 2 (surrounding zone 1 with negative charge and outer zone 3 without charge. We adopted the assumption of a constant electric field inside zone 1 of the corona sheath proved in the experimental research of the corona discharges in a coaxial geometry of Cooray. This assumption seems to be more realistic than the assumption of a uniform corona space charge density used previously in the study of Maslowski and Rakov, Marjanovic and Cvetic, and Tausanovic et al. Based on the measurements of the electric field performed by Miki et al, the conductivity of the channel sheath in zone 1 is calculated.

STELLAR-MASS BLACK HOLES IN YOUNG GALAXIES

We explore the potential cumulative energy production of stellar mass black holes in early galaxies. Stellar mass black holes may accrete substantially from the higher density interstellar media of primordial galaxies, and their energy release would be distributed more uniformly over the galaxy, perhaps providing a different mode of energy feedback into young galaxies than central supermassive black holes. We construct a model for the production and growth of stellar mass black holes over the first few gigayears of a young galaxy. With the simplifying assumption of a constant density of the ISM, n ~ 10^4 - 10^5 per cubic centimeter, we estimate the number of accreting stellar mass black holes to be ~ 10^6 and the potential energy production to be as high as 10^61 ergs over several billion years. For densities less than 10^5 per cubic centimeter, stellar mass black holes are unlikely to reach their Eddington limit luminosities. The framework we present could be incorporated in numerical simulations to compute the feedback from stellar-mass black holes with inhomogeneous, evolving interstellar media.

Volume and mass changes of the Greenland ice sheet inferred from ICESat and GRACE

This study examines the recent evolution of the Greenland ice sheet and its six major drainage basins. Based on laser altimetry data acquired by the Ice, Cloud and Land Elevation Satellite (ICESat), covering the period September–November 2003 to February–March 2008, ice surface height changes and their temporal variations were inferred. Our refined repeat track analysis is solely based on ICESat data and is independent of external elevation models, since it accounts for both ice height changes and the local topography. From the high resolution ice height change pattern we infer an overall mean surface height trend of −0.12±0.006myr−1. Furthermore, the largest changes could be identified at coastal margins of the ice sheet, exhibiting rates of more than −2myr−1. The total ice volume change of the entire ice sheet amounts to −205.4±10.6km3yr−1. In addition, we assessed mass changes from 78 monthly Gravity Recovery and Climate Experiment (GRACE) solutions. The Release-04 gravity field solutions of GeoForschungsZentrum Potsdam cover the period between August 2002 and June 2009. We applied an adjusted regional integration approach in order to minimize the leakage effects. Attention was paid to an optimized filtering which reduces error effects from different sources. The overall error assessment accounts for GRACE errors as well as for errors due to imperfect model reductions. In particular, errors caused by uncertainties in the glacial isostatic adjustment models could be identified as the largest source of errors. Finally, we determined both seasonal and long-term mass change rates. The latter amounts to an overall ice mass change of −191.2±20.9Gtyr−1 corresponding to 0.53±0.06mmyr−1 equivalent eustatic sea level rise. From the combination of the volume and mass change estimates we determined a mean density of the lost mass to be 930±11kgm−3. This value supports our applied density assumption 900±30kgm−3 which was used to perform the volume–mass-conversion of our ICESat results. Hence, mass change estimates from two independent observation techniques were inferred and are generally in good agreement.

Probing magnetic helicity with synchrotron radiation and Faraday rotation

We present a first application of the recently proposed LITMUS test for magnetic helicity, as well as a thorough study of its applicability under different circumstances. In order to apply this test to the galactic magnetic field, the newly developed critical filter formalism is used to produce an all-sky map of the Faraday depth. The test does not detect helicity in the galactic magnetic field. To understand the significance of this finding, we made an applicability study, showing that a definite conclusion about the absence of magnetic helicity in the galactic field has not yet been reached. This study is conducted by applying the test to simulated observational data. We consider simulations in a flat sky approximation and all-sky simulations, both with assumptions of constant electron densities and realistic distributions of thermal and cosmic ray electrons. Our results suggest that the LITMUS test does indeed perform very well in cases where constant electron densities can be assumed, both in the flat-sky limit and in the galactic setting. Non-trivial distributions of thermal and cosmic ray electrons, however, may complicate the scenario to the point where helicity in the magnetic field can escape detection.

Encoding of stoichiometric constraints in the composition depth profile reconstruction from angle resolved X‐ray photoelectron spectroscopy data

The inversion of angle resolved XPS data is a difficult problem, due to mathematical complexity of accurate model of electron transport, sensitivity to noise and small number of measured points limiting the depth resolution and the accuracy of the calculated depth profiles. Extended maximum entropy model for the calculation of apparent compositions (measured intensity ratios) is presented which allows to encode linear relationship between element concentrations. These can be used to calculate a solution with additional stoichiometric relationships and analyze, simultaneously, signals from several synthetic peak components. The synthetic peak components used in the model can represent various core level energy shifts, which are otherwise difficult to determine unambiguously from the measured signal. Element concentrations linked with stoichiometric relationships are used to identify compound materials with known density and inelastic scattering properties. The new model, thus allows self‐consistent recovery of depth profiles using maximum entropy method without the assumption of homogeneous density. The improved accuracy of the recovered depth profiles is demonstrated on the analysis of HfON/SiON overlayers. Various artefacts in the depth profiles obtained with standard maximum entropy model, which assumes constants density are identified. Copyright © 2011 John Wiley & Sons, Ltd.

IMPLICATIONS OF X-RAY LINE VARIATIONS FOR 4U1822–371

4U 1822-371 is one of the proto-type accretion disk coronal sources with an orbital period of about 5.6 hours. The binary is viewed almost edge-on at a high inclination angle of 83 degrees, which makes it a unique candidate to study binary orbital and accretion disk dynamics in high powered X-ray sources. We observed the X-ray source in 4U 1822-371 with the Chandra High Energy Transmission Grating Spectrometer (HETGS) for almost nine binary orbits. X-ray eclipse times provide an update of the orbital ephemeris. We find that our result follows the quadratic function implied by previous observations; however, it suggests a flatter trend. Detailed line dynamics also confirm a previous suggestion that the observed photo-ionized line emission originates from a confined region in the outer edge of the accretion disk near the hot spot. Line properties allow us to impose limits on the size of accretion disk, the central corona, and the emission region. The photo-ionized plasma is consistent with ionization parameters of log(xi) > 2, and when combined with disk size and reasonable assumptions for the plasma density, this suggests illuminating disk luminosities which are over an order of magnitude higher than what is actually observed. That is, we do not directly observe the central emitting X-ray source. The spectral continua are best fit by a flat power law with a high energy cut-off and partial covering absorption (N_H ranging from 5.4-6.3x10^{22} cm^{-2}) with a covering fraction of about 50%. We discuss some implications of our findings with respect to the photo-ionized line emission for the basic properties of the X-ray source.