Estimation of the Thermodynamic Properties for Branched Hydrocarbons

1999 ◽  
Author(s):  
Hui He ◽  
Mohamad Metghalchi ◽  
James C. Keck
Keyword(s):  
Thermodynamic Properties ◽  
Degrees Of Freedom ◽  
Statistical Thermodynamic ◽  
Motion Modes ◽  
Branched Alkanes ◽  
Branched Hydrocarbons ◽  
Wide Range ◽  
On Line ◽  
Kinetic Calculations ◽  
Good Agreement

Abstract A simple model has been developed to estimate the sensible thermodynamic properties such as Gibbs free energy, enthalpy, heat capacity, and entropy of hydrocarbons over a wide range of temperatures with special attention to the branched molecules. The model is based on statistical thermodynamic expressions incorporating translational, rotational and vibrational motions of the atoms. A method to determine the number of degrees of freedom for different motion modes (bending and torsion) has been established. Branched rotational groups, such as CH3 and OH, have been considered. A modification of the characteristic temperatures for different motion mode has been made which improves the agreement with the exact values for simple cases. The properties of branched alkanes up to 2,3,4-Trimthylpentane have been calculated and the results are in good agreement with the experimental data. A relatively small number of parameters are needed in this model to estimate the sensible thermodynamic properties of a wide range of species. The model may also be used to estimate the properties of molecules and their isomers, which have not been measured, and is simple enough to be easily programmed as a subroutine for on-line kinetic calculations.

Estimation of the Thermodynamic Properties of Branched Hydrocarbons

2000 ◽  
Vol 122 (3) ◽  
pp. 147-152 ◽  
Author(s):  
Hui He ◽  
Mohamad Metghalchi ◽  
James C. Keck
Keyword(s):  
Thermodynamic Properties ◽  
Degrees Of Freedom ◽  
Statistical Thermodynamic ◽  
Motion Modes ◽  
Branched Alkanes ◽  
Branched Hydrocarbons ◽  
Wide Range ◽  
On Line ◽  
Kinetic Calculations ◽  
Good Agreement

A simple model has been developed to estimate the sensible thermodynamic properties such as Gibbs free energy, enthalpy, heat capacity, and entropy of hydrocarbons over a wide range of temperatures with special attention to the branched molecules. The model is based on statistical thermodynamic expressions incorporating translational, rotational and vibrational motions of the atoms. A method to determine the number of degrees of freedom for different motion modes (bending and torsion) has been established. Branched rotational groups, such as CH3 and OH, have been considered. A modification of the characteristic temperatures for different motion mode has been made which improves the agreement with the exact values for simple cases. The properties of branched alkanes up to 2,3,4,-trimthylpentane have been calculated and the results are in good agreement with the experimental data. A relatively small number of parameters are needed in this model to estimate the sensible thermodynamic properties of a wide range of species. The model may also be used to estimate the properties of molecules and their isomers, which have not been measured, and is simple enough to be easily programmed as a subroutine for on-line kinetic calculations. [S0195-0738(00)00902-X]

Estimation of the Thermodynamic Properties of Unbranched Hydrocarbons

1999 ◽  
Vol 121 (1) ◽  
pp. 45-50 ◽  
Author(s):  
H. He ◽  
M. Metghalchi ◽  
J. C. Keck
Keyword(s):  
Experimental Data ◽  
Heat Capacity ◽  
Free Energy ◽  
Simple Model ◽  
Thermodynamic Properties ◽  
Statistical Thermodynamic ◽  
Wide Range ◽  
On Line ◽  
Kinetic Calculations ◽  
Good Agreement

A simple model has been developed to estimate the sensible thermodynamic properties such as Gibbs free energy, enthalpy, heat capacity, and entropy of unbranched hydrocarbons over a wide range of temperatures. The model is based on statistical thermodynamic expressions incorporating translational, rotational, and vibrational motions of the atoms. A relatively small number of parameters are needed to calculate the thermodynamic properties of a wide range of molecules. The calculated results are in good agreement with the available experimental data for unbranched hydrocarbons. The model can be used to make estimates for molecules whose properties have not been measured and is simple enough to be easily programmed as a subroutine for on-line kinetic calculations.

Thermodynamic Properties of Pure and Mixed Thermal Plasmas Over a Wide Range of Temperature and Pressure

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Omid Askari
Keyword(s):  
Thermodynamic Properties ◽  
Specific Heat ◽  
Fluid Dynamic ◽  
Thermal Plasmas ◽  
Statistical Thermodynamic ◽  
Reference Source ◽  
Degree Of Ionization ◽  
Wide Range ◽  
Self Consistent ◽  
Temperature And Pressure

Chemical composition and thermodynamics properties of different thermal plasmas are calculated in a wide range of temperatures (300–100,000 K) and pressures (10−6–100 atm). The calculation is performed in dissociation and ionization temperature ranges using statistical thermodynamic modeling. The thermodynamic properties considered in this study are enthalpy, entropy, Gibbs free energy, specific heat at constant pressure, specific heat ratio, speed of sound, mean molar mass, and degree of ionization. The calculations have been done for seven pure plasmas such as hydrogen, helium, carbon, nitrogen, oxygen, neon, and argon. In this study, the Debye–Huckel cutoff criterion in conjunction with the Griem’s self-consistent model is applied for terminating the electronic partition function series and to calculate the reduction of the ionization potential. The Rydberg and Ritz extrapolation laws have been used for energy levels which are not observed in tabulated data. Two different methods called complete chemical equilibrium and progressive methods are presented to find the composition of available species. The calculated pure plasma properties are then presented as functions of temperature and pressure, in terms of a new set of thermodynamically self-consistent correlations for efficient use in computational fluid dynamic (CFD) simulations. The results have been shown excellent agreement with literature. The results from pure plasmas as a reliable reference source in conjunction with an alternative method are then used to calculate the thermodynamic properties of any arbitrary plasma mixtures (mixed plasmas) having elemental atoms of H, He, C, N, O, Ne, and Ar in their chemical structure.

scholarly journals Theoretical Determination of Porpoising Instability of High-Speed Planing Boats

1978 ◽  
Vol 22 (01) ◽  
pp. 32-53 ◽  
Author(s):  
Milton Martin
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Method ◽  
Theoretical Determination ◽  
Damping Characteristics ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Good Agreement

A theoretical method is derived for predicting trim angle and speed coefficient at the inception of propoising of prismatic planing hulls. Although equations are derived for the surge, pitch, and heave degrees of freedom, it is seen that the effect of surge is small at ordinary operating trim angles. Comparisons of theoretical predictions with existing experimental data on coupled pitch and heave porpoising show reasonably good agreement for a wide range of speed coefficients, load coefficients, and deadrise angles. The theory may also be used for estimating the natural frequencies and damping characteristics of prismatic hulls in the stable, high-speed planing range.

Recent Progress and Plans in Computer-Controlled High Resolution Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 154-155
Author(s):  
W.J. de Ruijter ◽  
Peter Rez ◽  
David J. Smith
Keyword(s):  
Electron Microscopy ◽  
Digital Processing ◽  
High Resolution Electron Microscopy ◽  
Objective Lens ◽  
Linear Filter ◽  
Contrast Transfer Function ◽  
Image Displacement ◽  
Spatially Resolved ◽  
Wide Range ◽  
On Line

Digital computers are becoming widely recognized as standard accessories for electron microscopy. Due to instrumental innovations the emphasis in digital processing is shifting from off-line manipulation of electron micrographs to on-line image acquisition, analysis and microscope control. An on-line computer leads to better utilization of the instrument and, moreover, the flexibility of software control creates the possibility of a wide range of novel experiments, for example, based on temporal and spatially resolved acquisition of images or microdiffraction patterns. The instrumental resolution in electron microscopy is often restricted by a combination of specimen movement, radiation damage and improper microscope adjustment (where the settings of focus, objective lens stigmatism and especially beam alignment are most critical). We are investigating the possibility of proper microscope alignment based on computer induced tilt of the electron beam. Image details corresponding to specimen spacings larger than ∼20Å are produced mainly through amplitude contrast; an analysis based on geometric optics indicates that beam tilt causes a simple image displacement. Higher resolution detail is characterized by wave propagation through the optical system of the microscope and we find that beam tilt results in a dispersive image displacement, i.e. the displacement varies with spacing. This approach is valid for weak phase objects (such as amorphous thin films), where transfer is simply described by a linear filter (phase contrast transfer function) and for crystalline materials, where imaging is described in terms of dynamical scattering and non-linear imaging theory. In both cases beam tilt introduces image artefacts.

Understanding Conformational Entropy in Small Molecules

2020 ◽  
Author(s):  
Lucian Chan ◽  
Garrett Morris ◽  
Geoffrey Hutchison
Keyword(s):  
Small Molecules ◽  
Degrees Of Freedom ◽  
Absolute Error ◽  
Low Energy ◽  
Standard Entropy ◽  
Free Energies ◽  
Conformational Entropy ◽  
Wide Range ◽  
High Degree ◽  
Empirical Corrections

The calculation of the entropy of flexible molecules can be challenging, since the number of possible conformers grows exponentially with molecule size and many low-energy conformers may be thermally accessible. Different methods have been proposed to approximate the contribution of conformational entropy to the molecular standard entropy, including performing thermochemistry calculations with all possible stable conformations, and developing empirical corrections from experimental data. We have performed conformer sampling on over 120,000 small molecules generating some 12 million conformers, to develop models to predict conformational entropy across a wide range of molecules. Using insight into the nature of conformational disorder, our cross-validated physically-motivated statistical model can outperform common machine learning and deep learning methods, with a mean absolute error ≈4.8 J/mol•K, or under 0.4 kcal/mol at 300 K. Beyond predicting molecular entropies and free energies, the model implies a high degree of correlation between torsions in most molecules, often as- sumed to be independent. While individual dihedral rotations may have low energetic barriers, the shape and chemical functionality of most molecules necessarily correlate their torsional degrees of freedom, and hence restrict the number of low-energy conformations immensely. Our simple models capture these correlations, and advance our understanding of small molecule conformational entropy.

scholarly journals Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

2020 ◽  
Vol 499 (3) ◽  
pp. 4418-4431 ◽  
Author(s):  
Sujatha Ramakrishnan ◽  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
High Precision ◽  
Gaussian Distribution ◽  
Initial Perturbation ◽  
Analytical Framework ◽  
Web Environment ◽  
Wide Range ◽  
Galaxy Assembly ◽  
Very High ◽  
Good Agreement

ABSTRACT We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias b1 and b2 on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy α to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work that exploits the near-lognormal shape of the distribution of α and results in very high precision calibrations. We present convenient fitting functions for the dependence of b1 and b2 on α over a wide range of halo mass for redshifts 0 ≤ z ≤ 1. Our calibration of b2(α) is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results that showed that α is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of b1 and b2 on any such secondary property that has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using α as a segregating variable in multitracer analyses.

scholarly journals Quantum information probes of charge fractionalization in large-N gauge theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Brandon S. DiNunno ◽  
Niko Jokela ◽  
Juan F. Pedraza ◽  
Arttu Pönni
Keyword(s):  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
Strongly Coupled ◽  
Information Theoretic ◽  
Large N ◽  
Wide Range ◽  
Charge Fractionalization ◽  
Electric Flux

Abstract We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of large-N gauge theories. For concreteness, we focus on a simple holographic (2 + 1)-dimensional strongly coupled electron fluid whose charged states organize themselves into fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To address this deficiency, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a U(1) gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic c-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.

A Wide Range Ge Gamma-Ray Spectrometer for on-Line Measurements of Reactor Cooling Water Activity

1977 ◽  
Vol 24 (1) ◽  
pp. 673-677 ◽  
Author(s):  
J. J. Lipsett ◽  
I. L. Fowler ◽  
R. J. Dinger ◽  
H. L. Malm
Keyword(s):  
Water Activity ◽  
Gamma Ray ◽  
Cooling Water ◽  
Gamma Ray Spectrometer ◽  
Wide Range ◽  
On Line

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

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