Critical Constants Research Articles

Cosmological Models with Time Dependent G and Λ Coupling Scalars

A cosmological model in which the universe has its critical density and gravitational constants generalized as coupling scalars in Einstein's theory is considered. A general method of solving the field equations is given. An exact solution for matter distribution in cosmological models satisfying G = G0(R/R0)n is presented. Corresponding physical interpretations of the cosmological solutions are also discussed.

TraPPE-UA Force Field for Acrylates and Monte Carlo Simulations for Their Mixtures with Alkanes and Alcohols

An extension of the transferable potentials for phase equilibria-united atom (TraPPE-UA) force field to acrylate and methacrylate monomers is presented. New parameters were fit to the liquid density, normal boiling point, saturated vapor pressure, and (where experimentally available) critical constants of 1,3-butadiene, isoprene, methyl acrylate, and methyl methacrylate using Gibbs ensemble Monte Carlo simulations. Excellent agreement with experiment was obtained for the parametrization compounds and seven additional acrylate and methacrylate compounds, with average errors in liquid density and normal boiling point of approximately 1%. The TraPPE-UA force field also predicts accurate heats of vaporization at 298 K. In addition, Gibbs ensemble Monte Carlo simulations of binary vapor-liquid equilibria for the mixtures methyl acrylate/1-butanol and methyl acrylate/n-decane show that the TraPPE-UA acrylate force field performs well in mixtures with both polar and nonpolar molecules. These simulations also indicate structural microheterogeneity in the liquid phase of these mixtures.

An adaptive step-down procedure with proven FDR control under independence

In this work we study an adaptive step-down procedure for testing m hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical constants iq/[(m+1−i(1−q)], i=1, …, m. Motivated by its success as a model selection procedure, as well as by its asymptotic optimality, we are interested in its false discovery rate (FDR) controlling properties for a finite number of hypotheses. We prove this step-down procedure controls the FDR at level q for independent test statistics. We then numerically compare it with two other procedures with proven FDR control under independence, both in terms of power under independence and FDR control under positive dependence.

Distribution of ratio of extreme of isotonic estimators of chi-square variables with applications

Let V 1 , … , V k be k independent chi-square variables each with ν degrees of freedom (d.f.) and let W 1 ⩽ ⋯ ⩽ W k be the corresponding isotonic estimators computed by the pool adjacent violator algorithm under simple ordering among Vs . In this paper, a recursive integration algorithm for computing the distribution function of statistic T = W k / W 1 is presented. The test statistic F max * proposed by Fujino (Biometrika 66 (1979) 133-139) to test the homogeneity of variances against ordered alternative follows same null distribution as of the statistic T. Fujino discussed the null F max * distribution of and provided critical constant only for k = 3 , … , 6 , which limited its applications. The recursive procedure given in this article can be implemented efficiently for sufficient higher value of k. Test procedures based on statistic T for testing homogeneity against simple ordered alternative of k normal variances and equality of scale parameters of k exponential distributions are discussed separately with tables of critical constants for their implementation. Correctness of the critical constants is verified through simulation study. The proposed methodology is also extended to address the problem of testing exponentiality (constant failure rate) versus increasing failure rate, using isotonic estimators of normalized spaces between consecutive order statistics, along with tables of relevant critical constants.

On Tests Based on Sample Quasi Ranges for Ordered Alternative (Scale Case of Exponential Distribution)

Consider k (k ≥ 3) treatments or competing firms such that observations from ith treatment or firm follows a two-parameter exponential probability distribution E(μ i ,θ i ), where μ i is the location parameter and θ i (θ i > 0) is the scale parameter, i = 1,…,k. Singh and Gill (2004) proposed a class of one-sided tests, based on sample quasi-ranges, for testing the null hypothesis of homogeneity against the simple ordered alternative for doubly censored data, as well as for data contaminated with outlier. In this article, a class of tests, based on sample quasi-ranges, for testing the null hypothesis H o :θ1 =···= θ k against the U-shaped alternative H u :θ1 ≥···≥ θ h ≤···≤ θ k with at least one strict inequality, a generalization of Singh and Liu's procedure is proposed. The required critical constants for the implement of the proposed procedures are computed using a recursive integration technique. A simulation study is carried to examine the robustness of our presently proposed tests based on sample quasi-ranges. An optimum selection criterion of a member from the proposed class is also considered.

Phase diagrams of grafted molecules under external fields: A mean field model

A mean field theory is extended to investigate the phase behavior of grafted molecules under external fields. In the model, each grafted molecule contains two states, similar to the Ising model, and the applied field interacts with only one of the two states. The free energy of this model is formulated as a function of composition, field strength, and a parameter to account for the intermolecular interactions of neighboring molecules. Our calculations show that uniform fields exhibit no significant effect on phase diagrams. In contrast, linear gradient fields affect critical temperature but show no direct effect on critical composition. Under external fields with quadratic spatial gradient, both critical constants become sensitive to field direction and strength. Moreover, an analysis of field dependent critical constants suggests that quadratic fields affect miscibility and critical temperature. A brief comparison of the current model and the Ising model is also given.

Novel correlations between the critical constants of the noble gases

For any particular fluid, the set of three critical constants (CC) – pressure P c, temperature T c and molar volume V c – has a central importance in defining the physical behaviour of the fluid in the gas and liquid states. However, little attention seems to have been paid in the past to the relations between the CC of different substances. In the present paper, some simple and apparently novel relations have been found between the three CC for the set of four noble gases: Ne, Ar, Kr, Xe. Defining the critical quotient Q c ≡ RT c/ P c (where R is the Gas Constant) the correlations may be summarised by the dual equation: ( V c/cm 3 mol −1) = 27 + 0.31 ( T c/K) = 3.3 + 0.280 ( Q c/cm 3 mol −1), which describes the CC data for the quartet Ne–Xe with an average uncertainty of 0.5%. Regarding the other two noble gases, the two isotopes of the lightest member, 3He and 4He, show the deviations from these relations that are expected from quantal effects and their low molar masses; while for the heaviest member, Rn, the correlations enable a value of 145(5) cm 3 mol −1 to be estimated for V c that is not otherwise well defined in the literature. By contrast, and contrary to the general assumption, the second lightest member, Ne, apparently does not show appreciable quantal effects in the area, so that Ne–Xe may be considered together as a group. These correlations are compared with the behaviour of a selection of polyatomic fluids; in these comparisons, the NG dual correlation equation provides a reference line defining the presumed simplest behaviour. This and related areas show a “Residual Volume Effect”, in that extrapolating the equivalent temperature and energy parameters to zero for the state of zero-mass point particles, referred to here as the hypothetical element zeronium (Ze), the system in each case still has a finite intercept; this intercept amounts to essentially 34% of the average volume for the present quartet Ne–Xe, rather than the zero volume expected for this condition.

A Subset Selection Procedure for Exponential Populations

SYNOPTIC ABSTRACTConsider k independent exponential populations (treatments or systems) with different scale and location (possibly unknown) parameters. The goal is to select a subset of k exponential populations which includes the “best” population, i.e. the one with the largest value of the scale parameter. The data are assumed to be: (i) complete, or (ii) incomplete with Type-II censoring. The cases of known and unknown location parameters are treated separately. Tables of critical constants which are necessary to carry out the procedure are developed. Performance of the proposed procedure in comparison to the existing procedure is assessed through simulation study. The proposed procedure is also illustrated with the help of a real life example.

Selecting the Normal Population with the Smallest Coefficient of Variation

SYNOPTIC ABSTRACTWe consider the problem of selecting the normal population with the smallest coefficient of variation, which is a natural goal when the means as well as the variances of the populations are unknown and unequal. The indifference-zone approach (Bechhofer 1954) to this problem has been previously considered by Choi, Jeon and Kim (1982). We review their selection procedure and provide tables of sample sizes for it. Next we consider the subset selection approach of Gupta (1956, 1965). We propose a natural selection procedure, derive its least favorable configuration and provide tables of critical constants. An example is given to illustrate the two procedures.

Step-Up Tests for Comparing Several Exponential Populations with Control: Location Case

SYNOPTIC ABSTRACTLet π1…, πk be k treatments/ populations which are to be compared with a control treatment π0. We assume that an observation from population πi follows exponential distribution with probability density function (pdf) , where IA(.) is an indicator function of event A, θ is the common scale parameter and μi is the location parameter, (i = 0, 1, … k. In this paper, the problem of comparing several exponential populations/treatments with a control, in terms of their location parameters, is addressed by simultaneously testing k hypotheses on differences γi = πi, i = 1, …, k by using a step-up test procedure. A method for computing exact critical constants, which control the Type-I family-wise error rate at a preassigned level α, is discussed for one-sided and two-sided testing problems. The required constants are tabulated for specific values of the Type-I family-wise error rate and application of these constants to Pareto probability model is discussed.

Vapor−Liquid Critical Properties of Elements and Compounds. 11. Organic Compounds Containing B + O; Halogens + N, + O, + O + S, + S, + Si; N + O; and O + S, + Si

This review is part 11 of a series of contributions by the critical properties group of the previous IUPAC Commission I.2 on Thermodynamics, Subcommittee on Thermodynamic Data and the present IUPAC Project #2000-026-1-100, Critical Compilation of Vapor Liquid Critical Properties, sponsored by the Physical and Biophysical Chemistry Division. It presents all known experimental data for the critical constants of organic compounds containing at least two of the following atoms: B, Halogens (counted as one), N, O, S, and Si. Recommendations are given together with uncertainties. Critical temperatures have been converted, where warranted, to the ITS-90 scale.

Nanoaggregates of Asphaltenes in a Reservoir Crude Oil and Reservoir Connectivity

Recently, asphaltenes have been shown to form nanoaggregates in toluene at very low concentrations (10−4 mass fraction). Subsequently, in situ analysis of a 3000 ft vertical column of crude oil by downhole fluid analysis (DFA) indicated that the asphaltenes in a black crude oil exhibit gravitational sedimentation according to the Boltzmann distribution and that the asphaltene colloidal size is ∼2 nm. Here, we perform a follow-up study of a reservoir black oil from a different field. The black oil in a 658 ft vertical column is analyzed by DFA and advanced laboratory analytical chemical methods. An asphaltene colloidal particle size is found to be ∼2 nm according to the Archimedes buoyancy term in the Boltzmann distribution. In addition, an equation of state (EoS) approach based on literature critical constants and molecular weights for asphaltenes gives an aggregation number of ∼8. Molecular compositional similarities between different oil samples were established with comprehensive two-dimensional gas chromatography (GC × GC). Likewise, results from electrospray ionization Fourier transform ion cyclotron resonance mass spectroscopy (ESI FT-ICR MS) of the samples are consistent with the oils being from the same equilibrium column of oil. The results herein support a growing body of literature indicating that asphaltenes in black oils form relatively tightly bonded nanoaggregates of a single size range. The similarity of results between asphaltenes in crude oil and asphaltenes in toluene points to a very limited role of resins in these nanoaggregates, in contrast to much speculation. The implications of this work on the determination of reservoir connectivity are discussed.

Solubility of Methyl Salicylate in Supercritical Carbon Dioxide at Several Temperatures

The solubility of methyl salicylate in supercritical carbon dioxide was measured in static mode at five different temperatures, (343.15, 363.15, 383.15, 403.15, and 423.15) K, at pressures up to 31 MPa. The experimental results were correlated by the Chrastil and Peng−Robinson equation of state with quadratic mixing rules. Critical constants of methyl salicylate were predicted with the Joback method and the Lee−Kesler method.

Renormalization-Group Corrections to a Perturbed-Chain Statistical Associating Fluid Theory for Pure Fluids Near to and Far from the Critical Region

A perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state has been extended to include a crossover correction, based on White’s work with renormalization-group (RG) theory, that accounts for the contributions of long-wavelength density fluctuations in the critical region. In the critical region, the improved crossover equation of state provides the correct nonclassical critical exponents. Away from the critical region, the crossover equation reduces to the original PC-SAFT equation, therefore maintaining the accuracy of PC-SAFT in this region. No modifications to the original PC-SAFT molecular parameters are necessary, therefore allowing for an accurate description of thermodynamic properties from the triple point to the critical point. Excellent agreement with vapor−liquid equilibrium experimental data for the n-alkane family is obtained inside and outside the critical region, and all critical constants Tc, Pc, and ρc are calculated within their respective experimental errors. Th...

Quantitative Structure−Property Relationships for Predicting Metal Binding by Organic Ligands

Quantitative structure-property relationships (QSPRs) are developed to predict the complexation of Al(III), Ca(II), Cd(II), Cu(II), Ni(II), Pb(II), and Zn(II) by organic ligands containing carboxylate, phenol, amine, ether, and alcoholfunctional groups. These QSPRs predict conditional stability constants (K(M') at pH 7.0 and I = 0.1) over a range of ligand types with consistent uncertainties of approximately 1 log unit without requiring any steric or connectivity information. Calibration and validation data sets were constructed using 1:1 complex formation constants from the NIST Critical Stability Constants database (version 8.0). The descriptor variables are intuitive quantities conceptually related to metal binding, such as the numbers of various ligand groups, charge density, etc. The resulting calibrations have r2 = 0.87 to 0.93 and Spred = 0.67 to 1.05 log units, with positive values for all ligand count descriptor variables. The QSPRs account for 75-95% of the variability in the validation data set with RMSE of 0.74 to 1.30 log units. These QSPRs improve upon previous work by providing a tested and mechanistically reasonable method for log K(M') prediction with uncertainties comparable to or betterthan other QSPRs calibrated with groups of diverse ligands.

Co-crystallization of Co(II) with calcite: Implications for the mobility of cobalt in aqueous environments

Two different experimental processes (precipitation and crystallization in silica gel) have been carried out to investigate the degree of non-ideality and the crystallization behavior of the calcite–sphaerocobaltite solid solution from aqueous solutions. Solid phases of different compositions were precipitated at 25 °C by mixing a Na 2CO 3 aqueous solution with solutions with different ratios of CaCl 2 and CoCl 2. The precipitates were characterized by X-ray powder diffraction (XRD) and scanning electron microscopy and microanalyses (SEM-EDS). The precipitation behavior is quite complex and involves formation of Co-bearing calcite, Co-bearing aragonite, and a Co-rich low crystallinity phase that was identified as CoCO 3 · nH 2O by Fourier Transform Infrared Spectroscopy (FTIR). The precipitates identified as Co-bearing calcites consist of virtually homogeneous (Co,Ca)CO 3 solid-solution crystals with a calcite-type structure and cobalt mole fractions ( X sph) up to 0.33. Within this range, the evolution of the unit cell parameters with composition deviates markedly from the straight line connecting the parameters of the end-members. The excess volume of mixing ( V E) of these Co-bearing calcites shows a marked positive deviation. Calcite-type solid-solution crystals grown in gels at a lower supersaturation develop in general homogeneously, with a maximum cobalt content X sph = 0.16. Occasionally, some crystals exhibit compositional zoning with a core richer in Co, but X sph never exceeds the value of 0.16. The positive excess volume of mixing and the limited incorporation of cobalt in gel-grown crystals suggest the presence of a miscibility gap and consequently a non-ideal solid solution. During precipitation, the effective distribution coefficients of cobalt between the fluid and the Co-bearing calcites vary within the range from 11 to 17, which indicates a significant preferential partitioning of cobalt towards the solid phase in spite of the high supersaturation attained in these experiments. On these bases, the degree of non-ideality of the solid solution and the equilibrium partitioning of cobalt are discussed. The study suggests that a rigorous assessment of the Co(II) behavior in aqueous environments would require a re-evaluation of the available data on both the solubility product of sphaerocobaltite and the critical stability constants of the Co-bearing aqueous species.

Formulating and implementing profiling over adaptive ranges

Modern computer systems are called on to deal with billions of events every second, whether they are executed instructions, accessed memory locations, or forwarded packets. This presents a serious challenge to those who seek to quantify, analyze, or optimize such systems, because important trends and behaviors may easily be lost in a sea of data. We present range-adaptive profiling (RAP) as a new and general-purpose profiling method capable of hierarchically efficiently classifying streams of data in hardware. Through the use of RAP, events in an input stream are dynamically classified into increasingly precise categories, based on the frequency with which they occur. The more important a class, or range of events, the more precisely it is quantified. Despite the dynamic nature of our technique, we build upon tight theoretic bounds covering both worst-case error, as well as the required memory. In the limit, it is known that error and the memory bounds can be independent of the stream size and grow only linearly with the level of precision desired. Significantly, we expose the critical constants in these algorithms and through careful engineering, algorithm redesign, and use of heuristics, we show how a high-performance profile system can be implemented for range-adaptive profiling. RAP can be used on various profiles, such as PCs, load values, and memory addresses, and has a broad range of uses, from hot-region profiling to quantifying cache miss value locality. We propose two methods of implementation of RAP, one in software and the other with specialized hardware, for which we also describe our prototype FPGA implementation. We show that with just 8KB of memory, range profiles can be gathered with an average accuracy of 98%.

Tough Fe-based bulk metallic glasses

The toughness of Fe-based bulk metallic glasses (BMGs) has been significantly improved via systematic changes in chemistry. Chemistry changes were selected based on their likely effects on critical elastic constants shown to affect plasticity/toughness in various BMGs, in addition to their recently discovered effects on chemical bonding in these Fe-based systems. The fracture energy obtained on notched toughness samples tested in mode I was correlated with chemistry-induced changes to Poisson’s ratio ν and the ratio of the elastic shear modulus μ to the bulk modulus B, as was the strain energy at fracture for smooth cylindrical compression samples that failed under mode II conditions. Fractographic observations correlate well with the observed increases in toughness.

Conserved Asp-137 Imparts Flexibility to Tropomyosin and Affects Function

Tropomyosin (Tm) is an alpha-helical coiled-coil that controls muscle contraction by sterically regulating the myosin-actin interaction. Tm moves between three states on F-actin as either a uniform or a non-uniform semi-flexible rod. Tm is stabilized by hydrophobic residues in the "a" and "d" positions of the heptad repeat. The highly conserved Asp-137 is unusual in that it introduces a negative charge on each chain in a position typically occupied by hydrophobic residues. The occurrence of two charged residues in the hydrophobic region is expected to destabilize the region and impart flexibility. To determine whether this region is unstable, we have substituted hydrophobic Leu for Asp-137 and studied changes in Tm susceptibility to limited proteolysis by trypsin and changes in regulation. We found that native and Tm controls that contain Asp-137 were readily cleaved at Arg-133 with t 1/2 of 5 min. In contrast, the Leu-137 mutant was not cleaved under the same conditions. Actin stabilized Tm, causing a 10-fold reduction in the rate of cleavage at Arg-133. The actin-myosin subfragment S1 ATPase activity was greater for the Leu mutant compared with controls in the absence of troponin and in the presence of troponin and Ca2+. We conclude that the highly conserved Asp-137 destabilizes the middle of Tm, resulting in a more flexible region that is important for the cooperative activation of the thin filament by myosin. We thus have shown a link between the dynamic properties of Tm and its function.

On optimality of the Benjamini–Hochberg procedure for the false discovery rate

The Benjamini–Hochberg step-up procedure controls the false discovery rate (FDR) provided the test statistics have a certain positive regression dependency. We show that this procedure controls the FDR under a weaker property and is optimal in the sense that its critical constants are uniformly greater than those of any step-up procedure with the FDR controlling property.