Mutual Consistency Research Articles

Mutually consistent thermodynamic potentials for fluid water, ice and seawater: a new standard for oceanography

Abstract. A new seawater standard for oceanographic and engineering applications has been developed that consists of three independent thermodynamic potential functions, derived from extensive distinct sets of very accurate experimental data. The results have been formulated as Releases of the International Association for the Properties of Water and Steam, IAPWS (1996, 2006, 2008) and are expected to be adopted internationally by other organizations in subsequent years. In order to successfully perform computations such as phase equilibria from combinations of these potential functions, mutual compatibility and consistency of these independent mathematical functions must be ensured. In this article, a brief review of their separate development and ranges of validity is given. We analyse background details on the conditions specified at their reference states, the triple point and the standard ocean state, to ensure the mutual consistency of the different formulations, and the necessity and possibility of numerically evaluating metastable states of liquid water. Computed from this formulation in quadruple precision (128-bit floating point numbers), tables of numerical reference values are provided as anchor points for the consistent incorporation of additional potential functions in the future, and as unambiguous benchmarks to be used in the determination of numerical uncertainty estimates of double-precision implementations on different platforms that may be customized for special purposes.

Effects of Multiple Scattering on Attenuation-Based Retrievals of Stratiform Rainfall from CloudSat

Abstract An attenuation-based method to retrieve vertical profiles of rainfall rates from height derivatives/gradients of CloudSat nadir-pointing W-band reflectivity measurements is discussed. This method takes advantage of the high attenuation of W-band frequency signals in rain and the low variability of nonattenuated reflectivity due to strong non-Rayleigh scattering from rain drops. The retrieval uncertainties could reach 40%–50%. The suggested method is generally applicable to rainfall rates (R) in an approximate range from about 2–3 to about 20–25 mm h−1. Multiple scattering noticeably affects the gradients of CloudSat measurements for R values greater than about 5 mm h−1. To avoid a retrieval bias caused by multiple-scattering effects, a special correction for retrievals is introduced. For rainfall rates greater than about 25 mm h−1, the influence of multiple scattering gets overwhelming, and the retrievals become problematic, especially for rainfalls with higher freezing-level altitudes. The attenuation-based retrieval method was applied to experimental data from CloudSat covering the range of rainfall rates. CloudSat retrievals were compared to the rainfall estimates available from a National Weather Service ground-based scanning precipitation radar operating at S band. Comparisons between spaceborne and conventional radar rainfall retrievals were generally in good agreement and indicated the mutual consistency of both quantitative precipitation estimate types. The suggested CloudSat rainfall retrieval method is immune to the absolute calibration of the radar and to attenuation caused by the melting layer and snow regions. Since it does not require surface returns, it is applicable to measurements above both land and water surfaces.

Crystal structure and magnetic properties of the solid-solution phase Ca 3Co 2–vMn vO 6

The homogeneity range of the Ca 3Co 2– v Mn v O 6 solid-solution phase covers the entire composition interval from v=0 to 1. A systematic powder X-ray and neutron diffraction, magnetic susceptibility, and magnetization study has been carried out to investigate effects of the Mn-for-Co substitution on structural and magnetic properties. The Mn substitution concerns primarily only the octahedral Co1 site of the Ca 3Co1Co2O 6 crystal structure, whereas the trigonal-prismatic Co2 site structurally is left essentially unaffected. The Ca 3Co 2– v Mn v O 6 crystal structure belongs to space group R 3 ¯ c with unit-cell dimensions (in hexagonal setting) 9.084⩽ a⩽9.134 Å and 10.448⩽ c⩽10.583 Å. A cut through the magnetic phase diagram at 10 K shows a ferrimagnetic domain for 0⩽ v<∼0.3 and an antiferromagnetic domain for ∼0.50< v<∼1. The magnetic ordering temperatures are quite low (<∼25/18 K), and even so further magnetic transitions appear to take place at still lower temperature. The legitimity and reliability of the different indicators used to establish the magnetic transitions, their individual accuracy, and mutual consistency are briefly discussed. Variable parameters of the crystal and magnetic structures of Ca 3Co1 1– v Mn v Co2O 6 are determined and their variation with v is briefly discussed in relation to chemical bonding. The magnetic structure in the ferrimagnetic region is essentially the same as that of the pristine v=0 phase, but since the moments at the Co2 site decrease and those at the (Co1,Mn) site increase with increasing v; characteristic traits of ferrimagnetism in magnetic susceptibility and magnetization gradually disappear. The magnetic arrangement in the antiferromagnetic region is characterized by differently sized moments at the (Co1,Mn) and Co2 sites, moments at adjacent sites in each of these sublattices being oppositely oriented along [001].

A scenario-based approach to modeling development: A prototype model of C. elegans vulval fate specification

Studies of developmental biology are often facilitated by diagram “models” that summarize the current understanding of underlying mechanisms. The increasing complexity of our understanding of development necessitates computational models that can extend these representations to include their dynamic behavior. Here we present a prototype model of Caenorhabditis elegans vulval precursor cell fate specification that represents many processes crucial for this developmental event but that are hard to integrate using other modeling methodologies. We demonstrate the integrative capabilities of our methodology by comprehensively incorporating the contents of three seminal papers, showing that this methodology can lead to comprehensive models of developmental biology. The prototype computational model was built and is run using a language (Live Sequence Charts) and tool (the Play-Engine) that facilitate the same conceptual processes biologists use to construct and probe diagram-type models. We demonstrate that this modeling approach permits rigorous tests of mutual consistency between experimental data and mechanistic hypotheses and can identify specific conflicting results, providing a useful approach to probe developmental systems.

Diurnal variations in the photosynthesis-respiration activity of a cyanobacterial bloom in a freshwater dam reservoir: an isotopic study†

The stable isotopic analyses of molecular oxygen dissolved in water (δ18O(DO)) and dissolved inorganic carbon (δ13C(DIC)), supplemented with basic chemical measurements, have been carried out on a diurnal basis to better understand the dynamics of photosynthesis and respiration in freshwater systems. Our observations have been carried out in a lowland dam reservoir, the Sulejów Lake (central Poland), during the summer cyanobacterial bloom. All data obtained, isotopic, hydrochemical, and biological, show a high mutual consistency. Namely, the lowest δ18O(DO) values, obtained at 10:00 and 14:00 (16.0 and 15.5‰, respectively), correspond to the highest amount of cyanobacterial cells observed (66 and 63 mg dm−3, respectively), whereas the minimum δ13C(DIC) (−10.6‰) obtained at 22:00 corresponds to the maximum content of organic matter (110 mg dm−3). This evidence suggests that isotopic assays of δ18O(DO) and δ13C(DIC) are a reliable tool for the quantitative study of biochemical processes in freshwater systems. † Revised version of a paper presented at the 9th. Symposium of the European Society for Isotope Research (ESIR), 23 to28 June 2007, Cluj-Napoca, Romania.

Optical second‐harmonic and reflectance‐anisotropy spectroscopy of molecular adsorption at Si(001) step‐edges

AbstractReflectance‐anisotropy spectroscopy (RAS) and spectroscopic second harmonic generation (SHG) are used to probe a single‐domain reconstructed stepped Si(001) surface offcut 6° toward [110] before and after dissociative adsorption of H2 at the DB step edges. Preliminary analysis with a simplified bond hyperpolarizability model supports the mutual consistency of RA and SHG spectra and suggests that hydrogen termination redistributes oscillator strength from the chemically active step dangling bond into the step back bonds. The data provide a benchmark for first‐principles calculations of the optical response of stepped Si surfaces to step edge molecular adsorption. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Consistency of the spatial autocorrelation method with seismic interferometry and its consequence

ABSTRACTWe have cross‐checked the conventional theory of the spatial autocorrelation method and the consequence of seismic interferometry: the retrieval of the elastodynamic Green's function. Their mutual consistency is almost complete. The basic formulas of the conventional spatial autocorrelation theory can be derived by an alternative approach based on the retrieval of the elastodynamic Green's function. The only discrepancy is found with the average of the complex coherence function over azimuth in a wavefield dependent on azimuth. It is hypothesized, in discussion, that this discrepancy is due to the way of representing the wavefield in the background theory of seismic interferometry that can produce only wavefields moderately dependent on azimuth and that the mentioned consequence of seismic interferometry can also only make sense in a wavefield moderately dependent on azimuth.Our field experiment with a wavefield dependent on azimuth showed that the consequence of seismic interferometry in the logical framework of the conventional spatial autocorrelation theory is appropriate under such degrees of approximation as the measure proposed in this study, i.e., the deviation of the total dispersion curves is between about 10 and 16 per cent at the maximum from those averaged over azimuth.The acceptance of the retrieval of Green's function gives a proper physical meaning to the complex coherence function: the real part of the elastodynamic Green's function normalized by its zero‐offset version. This makes it possible to take a deterministic approach rather than the statistical one on which the conventional spatial autocorrelation method is based and gives fruitful new aspects and perspectives. For example, the formula for the multi‐mode case is given and the possibility of exploration of two or three dimensional velocity structures is suggested.

MMV: A Metamodeling Based Microprocessor Validation Environment

With increasing levels of integration of multiple processing cores and new features to support software functionality, recent generations of microprocessors face difficult validation challenges. The systematic validation approach starts with defining the correct behaviors of the hardware and software components and their interactions. This requires new modeling paradigms that support multiple levels of abstraction. Mutual consistency of models at adjacent levels of abstraction is crucial for manual refinement of models from the full chip level to production register transfer level, which is likely to remain the dominant design methodology of complex microprocessors in the near future. In this paper, we present microprocessor modeling and validation environment (MMV), a validation environment based on metamodeling, that can be used to create models at various abstraction levels and to generate most of the important validation collaterals, viz., simulators, checkers, coverage, and test generation tools. We illustrate the functionalities in MMV by modeling a 32-bit reduced instruction set computer processor at the system, instruction set architecture, and microarchitecture levels. We show by examples how consistency across levels is enforced during modeling and also how to generate constraints for automatic test generation.

Observed Inconsistencies between Snow Extent and Snow Depth Variability at Regional/Continental Scales

Abstract Snow extent and snow depth are two related characteristics of a snowpack, but they do not need to be mutually consistent. Differences between these two variables at local scales are readily apparent. However, at larger scales, which interact with atmospheric circulation and climate, snow extent is the primary variable considered, owing largely to the scarcity of snow depth data. In this study, three regional-/continental-scale gridded snow depth/snow water equivalent (SWE) datasets, derived from station observations or passive microwave satellite sensors, are utilized to quantitatively evaluate the relationship between snow extent and snow depth/SWE over North America. Various statistical methods are used to ensure the robustness of the results, including correlations, composites, and singular value decomposition analyses. Results indicate that continental-scale snow depth variations are substantial in their own right and that depth and extent anomalies are largely unrelated over broad high-latitude regions north of the snow line. Snow extent and snow depth vary more consistently in the vicinity of the snow line, especially in autumn and spring, during which precipitation and ablation can affect both variables. It is also found that deeper (shallower) winter snow translates into larger (smaller) snow-covered areas in the following spring/summer season, and also a longer (shorter) snow season, but only in specific regions. These results suggest a possible influence of snow depth on spring and summer climate. Overall, the observed lack of mutual consistency between these two snowpack variables at continental/regional scales suggests that snow depth variations may be of sufficiently large magnitude, spatial scope, and temporal duration to interact with regional–hemispheric climate, in a manner unrelated to the more extensively studied snow extent variations.

Stored polarized beams: M iles, L imes, S mile, sine-Bessels and S odom2 too

The fundamental theory underlying several computational algorithms for the spin dynamics of stored polarized beams is analyzed. Particular attention is paid to the consequences of the use of finite-dimensional matrices and/or Fourier series. The single resonance model with a pair of diametrically opposed nonorthogonal pointlike Siberian Snakes is analyzed in detail to clarify several points pertaining to the above algorithms, and more generally to the spin dynamics of stored polarized beams in rings with Snakes. New analytical results are also presented, e.g. for the spin tune shift in the nonorthogonal Snakes model, and the sine-Bessel functions for the orthogonal Snakes model. Many results are derived using multiple algorithms, which serves as a check on their mutual consistency.

Deming least-squares fit to multiple hyperplanes

A method is derived to fit a set of multidimensional experimental data points having a priori uncertainties and possibly also covariances in all coordinates to a straight line, plane, or hyperplane of any dimensionality less than the number of coordinates. The least-squares formulation used is that of Deming, which treats all coordinates on an equal basis. Experimentalists needing to fit a linear model to data of this kind have usually performed multiple independent fits in subspaces of the full data space such that each fit has only one dependent coordinate. That procedure does not guarantee mutual consistency of the fits. The present method can be thought of as providing multiple such hyperplane fits in a single simultaneous and therefore consistent solution. As examples, the method is applied to a straight-line fit in three dimensions to synthetic data and to an analysis of xenon isotopes in a lunar rock.

On the relation between mechanisms for single-transverse-spin asymmetries

Recent studies have shown that two widely-used mechanisms for single-transverse-spin asymmetries based on either twist-three contributions or on transverse-momentum-dependent (Sivers) parton distributions become identical in a kinematical regime of overlap. This was demonstrated for the so-called soft-gluon-pole and hard-pole contributions to the asymmetry associated with a particular quark–gluon correlation function in the nucleon. In this Letter, using semi-inclusive deep inelastic scattering as an example, we extend the study to the contributions by soft-fermion poles and by another independent twist-three correlation function. We find that these additional terms organize themselves in such a way as to maintain the mutual consistency of the two mechanisms for single-spin asymmetries.

Analysis of the consistency of kaon photoproduction data with Λ in the final state

The recent CLAS 2005, SAPHIR 2003, LEPS, and the old, pre-1972, data on ${K}^{+}\ensuremath{\Lambda}$ photoproduction are compared with theoretical calculations in the energy region of ${E}_{\ensuremath{\gamma}}^{\mathrm{lab}}&lt;2.6$ GeV in order to learn about their mutual consistency. The isobaric models Kaon-Maid and Saclay-Lyon, along with new fits to the CLAS data, are utilized in this analysis. The SAPHIR 2003 data are shown to be coherently shifted down with respect to the CLAS, LEPS, and pre-1972 data, especially at forward kaon angles. The CLAS, LEPS, and pre-1972 data in the forward hemisphere can be described satisfactorily by using the isobaric model without hadronic form factors. The inclusion of the hadronic form factors yields a strong suppression of the cross sections at small kaon angles and c.m. energies larger than 1.9 GeV, which is not observed in the existing experimental data. We demonstrate that the discrepancy between the CLAS and SAPHIR data has a significant impact on the predicted values of the mass and width of the ``missing resonance'' ${D}_{13}(1895)$ in the Kaon-Maid model.

Symplectic structure of supergravity with anomalies and Chern–Simons terms

The general actions of matter-coupled supergravity have Peccei–Quinn terms that may violate gauge and supersymmetry invariance. In addition, supergravity with vector multiplets may also contain generalized Chern–Simons terms. These have often been neglected in the literature despite their importance for gauge and supersymmetry invariance. We clarify the interplay of Peccei–Quinn terms, generalized Chern–Simons terms and quantum anomalies in the context of supergravity and exhibit conditions that have to be satisfied for their mutual consistency. This extension of the previously known matter-coupled supergravity actions follows naturally from the embedding of the gauge group into the group of symplectic duality transformations. Our results regarding this extension provide the supersymmetric framework for studies of string compactifications with axionic shift symmetries, generalized Chern–Simons terms and quantum anomalies.

A Unified Decoherence-Based Model of Microparticles in a Solution

The complex behavior of microparticles in a solution calls for different theoretical backgrounds. Here, we follow the line of two, recently developed theories on individuality, on the one hand, and conformational transitions of macromolecules in a solution, on the other. Given as separate theories, the two models may raise certain controversy in respect to their mutual consistency. Needless to say, their mutual consistency is necessary for the validity of the theories both in a general context as well as in search for a unified physico/chemical picture concerning the microparticles in a solution dynamics. We point out the consistency of these theories based on the definition of a molecule through its constituent subsystems (e.g. the center-of-mass and the “conformation” subsystems).

Coherence of climatic reconstruction from historical documents in China by different studies

AbstractMuch effort has been spent in the last few decades to reconstruct the climate over China using a variety of historical documents. However, differences in the results of reconstructions exist even when people are using similar documents. In order to address this issue, 14 published temperature series by different studies were analyzed for coherence and mutual consistency. The analyses on their temporal fluctuations indicate that for the individual time series (standardized) on the 10‐years time scales, 57 of the 91 correlation coefficients reach the significance level of 99%. The spatial patterns among the different time series also show high coherency. In addition, consistency also exhibit when comparing the reconstructions with other available natural climate change indicators. Above information was subsequently used to synthesize the temperature series for the last 500 and 1000 years. Copyright © 2007 Royal Meteorological Society

Atomic-topographic model of the electrochemical dissolution of a solid metal taking into account the effect of point lattice defects

A topokinetic model of a dissolving solid metal containing point defects, that is, either admixture atoms of a substantially more lowly or highly corrosion-resistant metal or the crystal lattice vacancies, is proposed. The model takes into account the mutual consistency of the atomic relief and the dissolution rate. Similarly to a defect-free crystal, the steady-state dissolution rate is determined by the elementary acts of transferring the base atoms to solution from step kinks whose amount substantially depends on the concentration of the point defects.

Integral Hellmann-Feynman theorem as a criterion of the quality of wave functions of atomic-molecular systems

It is proposed to use the integral Hellmann-Feynman theorem for the quality control and refinement of atomic and molecular wave functions. Its validity is verified for variational wave functions of the positronium ion e+e−e−, the negative ion of the hydrogen atom p∞+e−e− (H−), and mesomolecules μ−π+π+ and μ−p+p+. The relative violation of this theorem (10−2) is six orders of magnitude larger than the error of the energy calculation (10−8), which demonstrates its high sensitivity to the quality of wave functions. A way of refining wave functions on the basis of combination of the integral Hellmann-Feynman theorem for exactly solvable model and real atomic-molecular systems is proposed. A rule for verification of the mutual consistency of the wave functions of any three quantum-mechanical systems is formulated.

Kaon photoproduction in a multipole approach

The recently published experimental data on K{sup +}{lambda} photoproduction by the SAPHIR, CLAS, and LEPS Collaborations are analyzed by means of a multipole approach. For this purpose the background amplitudes are constructed from appropriate Feynman diagrams in a gauge-invariant and crossing-symmetric fashion. The results of our calculation emphasize the lack of mutual consistency between the SAPHIR and CLAS data previously found by several independent research groups, whereas the LEPS data are found to be more consistent with those of CLAS. The use of SAPHIR and CLAS data, individually or simultaneously, leads to quite different resonance parameters that, therefore, could lead to different conclusions on 'missing resonances'. Fitting to the SAPHIR and LEPS data simultaneously indicates that the S{sub 11}(1650),P{sub 13}(1720),D{sub 13}(1700),D{sub 13}(2080),F{sub 15}(1680), and F{sub 15}(2000) resonances are required, whereas fitting to the combination of CLAS and LEPS data leads alternatively to the P{sub 13}(1900),D{sub 13}(2080),D{sub 15}(1675),F{sub 15}(1680), and F{sub 17}(1990) resonances. Although yielding different results in most cases, both SAPHIR and CLAS data indicate that the second peak in the cross sections at W{approx}1900 MeV originates from the D{sub 13}(2080) resonance with a mass between 1911 and 1936 MeV. Furthermore, in contrast to the results of currently available modelsmore » and the Table of Particle Properties, both data sets do not exhibit the need for a P{sub 11}(1710) resonance. The few data points available for target asymmetry cannot be described by the models proposed in the present work.« less

The standard thermodynamic functions of ethyl-, formyl-, and benzoylferrocene in the ideal gas state

The standard enthalpies of formation of gaseous ethylferrocene, formylferrocene, and benzoylferrocene were calculated at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d,p) level of density functional theory using the method of isodesmic reactions. The absolute entropy, heat capacity, and enthalpy were calculated for ethylferrocene and formylferrocene by statistical thermodynamics methods over the temperature range 100–1000 K. The molecular constants necessary for calculations (structural parameters, vibrational frequencies, and internal rotation potential) were estimated at the B3LYP/6-31G(d,p) level. Empirical estimates were used to check the reliability and mutual consistency of literature experimental data on the enthalpies of formation and entropies of several ferrocene derivatives. Unreliable data were revealed and more reliable estimates of their errors were obtained.