A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Thermodynamic consistency of the ternary functions

A ternary thermodynamic function has been developed based on statistico-thermodynamic considerations, with a particular emphasis on the higher-order terms indicating the effects of truncation at the various stages of the treatment. Although the truncation of a series involved in the equation introduces inconsistency, the latter may be removed by imposing various thermodynamic boundary conditions. These conditions are discussed in the paper. The present equation with higher-order terms shows that the α function of a component reduces to a quadratic function of composition at constant compositional paths involving the other two components in the system. The form of the function has been found to be representative of various experimental observations.

Thermodynamic consistency of the interaction parameter formalism

The apparent contradiction between the exact nature of the interaction parameter formalism as presented by Lupis and Elliott and the inconsistencies discussed recently by Pelton and Bale arise from the truncation of the Maclaurin series in the latter treatment. The truncation removes the exactness of the expression for the logarithm of the activity coefficient of a solute in a multi-component system. The integrals are therefore path dependent. Formulae for integration along paths of constant Xi,or X i/Xj are presented. The expression for In γsolvent given by Pelton and Bale is valid only in the limit that the mole fraction of solvent tends to one. The truncation also destroys the general relations between interaction parameters derived by Lupis and Elliott. For each specific choice of parameters special relationships are obtained between interaction parameters.

Weak consistency of read-only transactions: A tool to improve concurrency in heterogeneous locking protocols

Three different types of consistencies, viz., semiweak, weak, and strong, of a read-only transaction in a schedule s of a set T of transactions are defined and these are compared with the existing notions of consistencies of a read-only transaction in a schedule. We present a technique that enables a user to control the consistency of a read-only transaction in heterogeneous locking protocols. Since the weak consistency of a read-only transaction improves concurrency in heterogeneous locking protocols, the users can help to improve concurrency in heterogeneous locking protocols by supplying the consistency requirements of read-only transactions. A heterogeneous locking protocol P' derived from a locking protocol P that uses exclusive mode locks only and ensures serializability need not be deadlock-free. We present a sufficient condition that ensures the deadlock-freeness of Pprime, when P is deadlock-free and all the read-only transactions in Pprime are two phase.

Consistency limits behavior of bentonites exposed to sea water

This article examines the changes in interparticle forces brought about on prolonged contact (1 year period) of a bentonite clay with artificial seawater. The study is undertaken with the purpose of identifying the physico-chemical factors that impart a nonswelling character to smectite clays deposited in marine environments. Results show that equilibration of the bentonite clay with artificial seawater (total pore salinity approximately 42 gL-1) for a 1 year period does not lead to any mineralogical changes in the clay specimens; however, their exchangeable cation positions become prominently dominated by magnesium ions. The consistency limits of the seawater-equilibrated bentonite was determined on stepwise leaching to lower salinities. The predominance of diffuse double-layer repulsion forces in the pore salt concentration range of 42 gL-1 to 1.1 gL-1 caused an increase in the liquid limits of the seawater-equilibrated bentonite specimens on reducing the salinity in the corresponding range (42 gL-1 to 1.1 gL-1). The attraction forces, however, prevail over the repulsion forces at salt concentrations <1.1 gL-1 and cause a decrease in liquid limit of the clay specimens with reduction in pore salinity, which is typical of nonswelling clays. The attraction forces cause aggregation of the clay unit layers into domains that break down on sodium saturation of the clay specimens. It is inferred that the physico-chemical factors responsible for the nonswelling character of the seawater-equilibrated bentonite specimens at pore salt concentrations below 1.1 gL-1 are inadequate to explain the nonswelling character of smectite-rich Ariake marine clays. The lower consistency limits of the Ariake marine clays in comparison to the nonswelling character, seawater-equilibrated bentonite specimens is attributed to a relative deficiency of interparticle forces in the Ariake marine clay.

Derivation and consistency of the partial functions of the ternary system involving interaction coefficients

The logarithm of activity coefficients of the components of the ternary system is derived based on the Maclaurin infinite series, which is expressed in terms of the integral property of the system and subjected to appropriate boundary conditions. The derivation of the functions involves extensive summation of various infinite series pertaining to the first-order interaction coefficients that have been shown completely to remove any truncational error. Since the conventional equations involving interaction coefficients are internally inconsistent, a consistent form of the partial functions is developed in the article using the technique just described. The thermodynamic consistency of the functions based on the Maxwell and the Gibbs-Duhem relations has been established. The derived values of the logarithmic activity coefficients of the components have been found to be in agreement with the thermodynamic data of the Fe-Cr-Ni system at 1873 K and have been found to be independent of the compositional paths.

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

Ampcalculator (AMPC) is a Mathematica (c) based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O(p(4))) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G(27). Another illustrative set of amplitudes at tree level we provide is in the context of tau-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.

Improving the Rigor and Consistency of the Thermodynamic Theory for Clathrate Hydrates through Incorporation of Movement of Water Molecules of Hydrate Lattice

Current applications of statistical thermodynamic theories for clathrate hydrates do not incorporate the translational and rotational movement of water molecules of the hydrate lattice,in a rigorous manner. Previous studies have shown that the movement of water molecules has a significant effect on the properties of clathrate hydrates. In this Article, a method is presented to incorporate the effect of water movement with as much rigor as possible. This method is then used to calculate the Langmuir constant of the guest species in a clathrate hydrate. Unlike previous studies on modeling of clathrate hydrate thermodynamics, the method presented in this paper does not regress either the intermolecular potentials or the properties of the empty hydrate from clathrate phase equilibria data. Also the properties of empty hydrate used in the theory do not depend on the nature and composition of the guest molecules. The predicted phase equilibria from the resulting theory are shown to be highly accurate and thermodynamically consistent by comparing them with the phase equilibria computed directly from molecular simulations.

Fatigue Laws Via Functional Equations

In routine industrial design, fatigue life estimation is largely based on S-N curves and ad hoc cycle counting algorithms used with Miner's rule for predicting life under complex loading. However, there are well known deficiencies of the conventional approach. Of the many cumulative damage rules that have been proposed, Manson's Double Linear Damage Rule (DLDR) has been the most successful. Here we follow up, through comparisons with experimental data from many sources, on a new approach to empirical fatigue life estimation (A Constructive Empirical Theory for Metal Fatigue Under Block Cyclic Loading', Proceedings of the Royal Society A, in press). The basic modeling approach is first described: it depends on enforcing mathematical consistency between predictions of simple empirical models that include indeterminate functional forms, and published fatigue data from handbooks. This consistency is enforced through setting up and (with luck) solving a functional equation with three independent variables and six unknown functions. The model, after eliminating or identifying various parameters, retains three fitted parameters; for the experimental data available, one of these may be set to zero. On comparison against data from several different sources, with two fitted parameters, we find that our model works about as well as the DLDR and much better than Miner's rule. We finally discuss some ways in which the model might be used, beyond the scope of the DLDR.

CCD: Connected Component Descriptor for Robust Mosaicing of Camera-Captured Document Images

We propose a robust method for mosaicing of document images using features derived from connected components. Each connected component is described using the Angular Radial Tran. form (ART). To ensure geometric consistency during feature matching, the ART coefficients of a connected component are augmented with those of its two nearest neighbors. The proposed method addresses two critical issues often encountered in correspondence matching: (i) The stability of features and (ii) Robustness against false matches due to the multiple instances of characters in a document image. The use of connected components guarantees a stable localization across images. The augmented features ensure a successful correspondence matching even in the presence of multiple similar regions within the page. We illustrate the effectiveness of the proposed method on camera captured document images exhibiting large variations in viewpoint, illumination and scale.

Reliable estimation via simulation

Let a and s denote the inter arrival times and service times in a GI/GI/1 queue. Let a (n), s (n) be the r.v.s, with distributions as the estimated distributions of a and s from iid samples of a and s of sizes n. Let w be a r.v. with the stationary distribution lr of the waiting times of the queue with input (a, s). We consider the problem of estimating E [w~], tx > 0 and 7r via simulations when (a (n), s (n)) are used as input. Conditions for the accuracy of the asymptotic estimate, continuity of the asymptotic variance and uniformity in the rate of convergence to the estimate are obtained. We also obtain rates of convergence for sample moments, the empirical process and the quantile process for the regenerative processes. Robust estimates are also obtained when an outlier contaminated sample of a and s is provided. In the process we obtain consistency, continuity and asymptotic normality of M-estimators for stationary sequences. Some robustness results for Markov processes are included.

Gamma-ray luminosity function of gamma-ray bright AGNs

Detection of gamma-ray emissions from a class of active galactic nuclei (viz blazars), has been one of the important findings from the Compton Gamma-Ray Observatory (CGRO). However, their gamma-ray luminosity function has not-been well determined. Few attempts have been made in earlier works, where BL Lacs and Flat Spectrum Radio Quasars (FSRQs) have been considered as a single source class. In this paper, we investigated the evolution and gamma-ray luminosity function of FSRQs and BL Lacs separately. Our investigation indicates no evolution for BL Lacs, however FSRQs show significant evolution. Pure luminosity evolution is assumed for FSRQs and exponential and power law evolution models are examined. Due to the small number of sources, the low luminosity end index of the luminosity function for FSRQs is constrained with an upper limit. BL Lac luminosity function shows no signature of break. As a consistency check, the model source distributions derived from these luminosity functions show no significant departure from the observed source distributions.