Perturbation theory and the local compressibility approximation in classical statistical mechanics

1968 ◽  
Vol 46 (15) ◽  
pp. 1725-1727 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Perturbation Theory ◽  
Statistical Mechanics ◽  
Order Term ◽  
Second Order ◽  
Three Dimensions ◽  
First Order ◽  
Classical Statistical Mechanics ◽  
Square Well ◽  
Exact Calculations

The integrals which appear in the first-order term and the local compressibility approximation to the second-order term in the Barker–Henderson perturbation theory of fluids are evaluated analytically for the square-well potential in one and three dimensions and are compared with exact calculations.

Perturbation Theory and the Triangular Well Potential

1975 ◽  
Vol 53 (1) ◽  
pp. 5-12 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Order Term ◽  
Second Order ◽  
First Order ◽  
Triangular Well Potential

Accurate calculations of the second order term in the free energy and the first order term in the radial distribution function in the Barker–Henderson (BH) perturbation theory are presented for the triangular well potential. The BH theory is found to be fully satisfactory for this system. Thus, the conclusions of Card and Walkley regarding the accuracy of the BH theory are erroneous.

A note on the perturbation theory and the triangular well potential

1977 ◽  
Vol 55 (7-8) ◽  
pp. 632-634 ◽  
Author(s):  
P. C. Wankhede ◽  
K. N. Swamy
Keyword(s):  
Monte Carlo ◽  
Perturbation Theory ◽  
Order Term ◽  
Second Order ◽  
First Order ◽  
Monte Carlo Calculations ◽  
Theory Of Liquids ◽  
Compressibility Factors ◽  
Triangular Well Potential

The integrals which appear in the first order term and the macroscopic compressibility (mc) and the local compressibility (lc) approximation for the second order term in the Barker–Henderson (BH) perturbation theory of liquids are evaluated analytically for the triangular-well potential. The compressibility factors so calculated are compared with the Monte Carlo calculations.

Neural computation of motion in the fly visual system: quadratic nonlinearity of responses induced by picrotoxin in the HS and CH cells

1995 ◽  
Vol 74 (6) ◽  
pp. 2665-2684 ◽  
Author(s):  
Y. Kondoh ◽  
Y. Hasegawa ◽  
J. Okuma ◽  
F. Takahashi
Keyword(s):  
Mean Square Error ◽  
Order Term ◽  
Mirror Image ◽  
Second Order ◽  
The Other ◽  
Linear Component ◽  
Mean Square ◽  
Nonlinear Component ◽  
First Order ◽  
Order Kernel

1. A computational model accounting for motion detection in the fly was examined by comparing responses in motion-sensitive horizontal system (HS) and centrifugal horizontal (CH) cells in the fly's lobula plate with a computer simulation implemented on a motion detector of the correlation type, the Reichardt detector. First-order (linear) and second-order (quadratic nonlinear) Wiener kernels from intracellularly recorded responses to moving patterns were computed by cross correlating with the time-dependent position of the stimulus, and were used to characterize response to motion in those cells. 2. When the fly was stimulated with moving vertical stripes with a spatial wavelength of 5-40 degrees, the HS and CH cells showed basically a biphasic first-order kernel, having an initial depolarization that was followed by hyperpolarization. The linear model matched well with the actual response, with a mean square error of 27% at best, indicating that the linear component comprises a major part of responses in these cells. The second-order nonlinearity was insignificant. When stimulated at a spatial wavelength of 2.5 degrees, the first-order kernel showed a significant decrease in amplitude, and was initially hyperpolarized; the second-order kernel was, on the other hand, well defined, having two hyperpolarizing valleys on the diagonal with two off-diagonal peaks. 3. The blockage of inhibitory interactions in the visual system by application of 10-4 M picrotoxin, however, evoked a nonlinear response that could be decomposed into the sum of the first-order (linear) and second-order (quadratic nonlinear) terms with a mean square error of 30-50%. The first-order term, comprising 10-20% of the picrotoxin-evoked response, is characterized by a differentiating first-order kernel. It thus codes the velocity of motion. The second-order term, comprising 30-40% of the response, is defined by a second-order kernel with two depolarizing peaks on the diagonal and two off-diagonal hyperpolarizing valleys, suggesting that the nonlinear component represents the power of motion. 4. Responses in the Reichardt detector, consisting of two mirror-image subunits with spatiotemporal low-pass filters followed by a multiplication stage, were computer simulated and then analyzed by the Wiener kernel method. The simulated responses were linearly related to the pattern velocity (with a mean square error of 13% for the linear model) and matched well with the observed responses in the HS and CH cells. After the multiplication stage, the linear component comprised 15-25% and the quadratic nonlinear component comprised 60-70% of the simulated response, which was similar to the picrotoxin-induced response in the HS cells. The quadratic nonlinear components were balanced between the right and left sides, and could be eliminated completely by their contralateral counterpart via a subtraction process. On the other hand, the linear component on one side was the mirror image of that on the other side, as expected from the kernel configurations. 5. These results suggest that responses to motion in the HS and CH cells depend on the multiplication process in which both the velocity and power components of motion are computed, and that a putative subtraction process selectively eliminates the nonlinear components but amplifies the linear component. The nonlinear component is directionally insensitive because of its quadratic non-linearity. Therefore the subtraction process allows the subsequent cells integrating motion (such as the HS cells) to tune the direction of motion more sharply.

scholarly journals Can We Compare Solidarity Across Europe? What, Why, When, and How to Assess Exact and Approximate Equivalence of First- and Second-Order Factor Models

2021 ◽  
Vol 3 ◽  
Author(s):  
Vera Lomazzi
Keyword(s):  
Factor Model ◽  
Second Order ◽  
Three Dimensions ◽  
Alignment Method ◽  
Cross Sectional ◽  
Political Values ◽  
First Order ◽  
Measurement Models ◽  
European Values ◽  
Order Factor

Although measurement invariance is widely considered a precondition for meaningful cross-sectional comparisons, substantive studies have often neglected evaluating this assumption, thereby risking drawing conclusions and making theoretical generalizations based on misleading results. This study offers a theoretical overview of the key issues concerning the measurement and the comparison of socio-political values and aims to answer the questions of what must be evaluated, why, when, and how to assess measurement equivalence. This paper discusses the implications of formative and reflective approaches to the measurement of socio-political values and introduces challenges in their comparison across different countries. From this perspective, exact and approximate approaches to equivalence are described as well as their empirical translation in statistical techniques, such as the multigroup confirmatory factor analysis (MGCFA) and the frequentist alignment method. To illustrate the application of these methods, the study investigates the construct of solidarity as measured by European Values Study (EVS) and using data collected in 34 countries in the last wave of the EVS (2017–2020). The concept is captured through a battery of nine items reflecting three dimensions of solidarity: social, local, and global. Two measurement models are hypothesized: a first-order factor model, in which the three independent dimensions of solidarity are correlated, and a second-order factor model, in which solidarity is conceived according to a hierarchical principle, and the construct of solidarity is reflected in the three sub-factors. In testing the equivalence of the first-order factor model, the results of the MGCFA indicated that metric invariance was achieved. The alignment method supported approximate equivalence only when the model was reduced to two factors, excluding global solidarity. The second-order factor model fit the data of only seven countries, in which this model could be used to study solidarity as a second-order concept. However, the comparison across countries resulted not appropriate at any level of invariance. Finally, the implications of these results for further substantive research are discussed.

Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid

2017 ◽  
Vol 147 (21) ◽  
pp. 214108 ◽  
Author(s):  
Luís Fernando Mercier Franco ◽  
Marcelo Castier ◽  
Ioannis G. Economou
Keyword(s):  
Perturbation Theory ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
First Order ◽  
Theory Versus ◽  
Square Well ◽  
First Order Perturbation

scholarly journals The Work Gratitude Scale: Development and Evaluation of a Multidimensional Measure

2022 ◽  
Vol 12 ◽  
Author(s):  
Carolyn M. Youssef-Morgan ◽  
Llewellyn E. van Zyl ◽  
Barbara L. Ahrens
Keyword(s):  
Measurement Invariance ◽  
Convergent Validity ◽  
Structural Equation ◽  
Discriminant Validity ◽  
The United States ◽  
Second Order ◽  
Three Dimensions ◽  
Equation Modeling ◽  
First Order ◽  
Multidimensional Measure

This study explores gratitude as a multidimensional and work-specific construct. Utilizing a sample of 625 employees from a variety of positions in a medium-sized school district in the United States, we developed and evaluated a new measure, namely the Work Gratitude Scale (WGS), which encompasses recognized conative (intentional), cognitive, affective, and social aspects of gratitude. A systematic, six-phased approach through structural equation modeling (SEM) was used to explore and confirm the factorial structure, internal consistency, measurement invariance, concurrent, convergent, and discriminant validity of the WGS. The results supported a 10-item measure with three dimensions: “grateful appraisals” (three items), “gratitude toward others” (four items), and “intentional attitude of gratitude” (three items). Thereafter, first-order, second-order, and bifactor confirmatory models were estimated and compared. Work gratitude was found to be best described by a second-order construct with three underlying first-order dimensions. Measurement invariance was supported in relation to gender. Concurrent validity was supported in relation to two existing dispositional gratitude scales, namely the Gratitude Questionnaire and the Gratitude, Resentment, and Appreciation Scale (GRAT). Convergent validity was supported in relation to the Core Self-Evaluations Scale (CSES) and the Psychological Capital Questionnaire. Discriminant validity was supported in relation to various demographic factors such as age, gender, occupation, and tenure. The findings support the WGS as a multidimensional measure that can be used in practice to measure overall work-related gratitude and to track the effectiveness of gratitude-related workplace interventions.

Analytic First-Order Derivatives of Partially Contracted N-Electron Valence State Second-Order Perturbation Theory (PC-NEVPT2)

2019 ◽  
Author(s):  
Yoshio Nishimoto
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Valence State ◽  
Second Order ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Transition Energies ◽  
First Order ◽  
Static Electron ◽  
Second Order Perturbation Theory

A balanced treatment of dynamic and static electron correlation is important in computational chemistry, and multireference perturbation theory (MRPT) is able to do this at a reasonable computational cost. In this paper, analytic first-order derivatives, speci cally gradients and dipole moments, are developed for a particular MRPT method, state-specific partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). Only one linear equation needs to be solved for the derivative calculation if the Z-vector method is employed, which facilitates the practical application of this approach. Comparison of the calculated results with experimental geometrical parameters of O<sub>3</sub> indicates excellent agreement, although the calculated results for O<sub>3</sub><sup>-</sup> are slightly outside the experimental error bars. The 0-0 transition energies of various methylpyrimidines and trans-polyacetylene are calculated by performing geometry optimizations and seminumerical second-order geometrical derivative calculations. In particular, the deviations of 0-0 transition energies of trans-polyacetylene from experimental values are consistently less than 0.1 eV with PC-NEVPT2, indicating the reliability of the method. These results demonstrate the importance of adding dynamic electron correlation on top of methods dominated by static electron correlation and of developing analytic derivatives for highly accurate methods.

The nitrous acid catalysed nitration of naphthalene. Evidence for a kinetic term that is second order with respect to the aromatic compound

1989 ◽  
Vol 67 (11) ◽  
pp. 1677-1682 ◽  
Author(s):  
J. Ramón Leis ◽  
M. Elena Pena ◽  
John H. Ridd
Keyword(s):  
Electron Transfer ◽  
Acetic Acid ◽  
Nitrous Acid ◽  
Order Term ◽  
Second Order ◽  
Rate Coefficients ◽  
Kinetic Term ◽  
Aqueous Mixtures ◽  
Electron Transfer Mechanism ◽  
First Order

The kinetic equation for the nitrous acid catalysed nitration of naphthalene in aqueous mixtures of sulphuric acid and acetic acid has at least two kinetic terms: one first order with respect to naphthalene and one second order with respect to naphthalene. The orders with respect to nitrous acid and nitric acid vary with the conditions in the way characteristic of the electron transfer mechanism of this reaction. The second-order term with respect to naphthalene is considered to derive from the formation of the dimeric radical cation (ArH)2+•. The acidity dependence of the rate coefficients and the absence of a normal isotope effect in the reaction of naphthalene-d8 are consistent with this interpretation. Keywords: naphthalene, nitration, nitrous acid.

Sign in / Sign up

Export Citation Format

Share Document