Diffusion dépolarisée Rayleigh par des molécules anisotropes: calcul analytique des contributions propres, collisionnelles et croisées pour divers potentiels

1989 ◽  
Vol 67 (5) ◽  
pp. 525-531 ◽  
Author(s):  
B. Dumon ◽  
J. Berrue ◽  
A. Chave ◽  
A. Barreau
Keyword(s):  
Pair Correlation ◽  
Analytical Calculation ◽  
Preceding Paper ◽  
Dipole Approximation ◽  
Intermolecular Potential ◽  
Polarizability Tensor ◽  
Cross Term ◽  
Quadrupolar Moment ◽  
Induced Dipole ◽  
The Cross

In a preceding paper, a new analytical calculation of the integrated Rayleigh light scattered intensities, taking into account the permanent anisotropy in the collisionnal polarizability tensor, has been developped. The contributions of orientational pair correlation collision induced light scattering and the cross term have been evaluated in the first order dipole induced dipole approximation, at low density in the center–center polarizability scheme. In this article, from these analytical expansions, we calculate contribution values in N2, CO2, Cl2, and O2 to the scattered intensities. The intermolecular potential is represented by a two (or three)-site Lennard–Jones model without (or with) a quadrupolar moment. We show that these new analytical calculations lead to important corrections of up to 30% for the cross term in O2, and that the potential choice plays an essential role. These results are compared with experimental data and to other studies.

Basic Statistical Mechanics

1984 ◽  
Author(s):  
C. G. Gray ◽  
K. E. Gubbins
Keyword(s):  
Potential Energy ◽  
Pair Correlation ◽  
Complete Information ◽  
Distribution Functions ◽  
Uniform Electric Field ◽  
Intermolecular Potential ◽  
Molecular Fluids ◽  
Rigid Molecule ◽  
General Potential ◽  
Simple Molecules

In this chapter we introduce distribution functions for molecular momenta and positions. All equilibrium properties of the system can be calculated if both the intermolecular potential energy and the distribution functions are known. Throughout, we shall make use of the ‘rigid molecule’ and classical approximations. In the rigid molecule approximation the system intermolecular potential energy u(rNωN ) depends only on the positions of the centres of mass rN ≡ r1 . . . rN for the N molecules and on their molecular orientations ωN ≡ ω1 . . . ωN; any dependence on vibrational or internal rotational coordinates is neglected. In the classical approximation the translational and rotational motions of the molecules are assumed to be classical. These assumptions should be quite realistic for many fluids composed of simple molecules, e.g. N2 , CO, CO2 , SO2 CF4 , etc. They are discussed in detail in §§ 1.2.1 and 1.2.2; quantum corrections to the partition function are discussed in §§ 1.2.2 and 6.9, and in Appendix 3D. In considering fluids in equilibrium we can distinguish three principal cases: (a) isotropic, homogeneous fluids (e.g. liquid or compressed gas states of N2 , O2 , etc. in the absence of an external field), (b) anisotropic, homogeneous fluids (e.g. a polyatomic fluid in the presence of a uniform electric field, nematic liquid crystals), and (c) inhomogeneous fluids (e.g. the interfacial region). These fluid states have been listed in order of increasing complexity; thus, more independent variables are involved in cases (b) and (c), and consequently the evaluation of the necessary distribution functions is more difficult. For molecular fluids it is convenient to introduce several types of distribution functions, correlation functions, and related quantities: (a) The angular pair correlation function g(r1r2 ω1 ω2). This gives complete information about the pair of molecules, and arises in expressions for the equilibrium properties for a general potential.

scholarly journals Computation of Thin-Walled Cross-Section Resistance to Local Buckling with the Use of the Critical Plate Method

2016 ◽  
Vol 62 (2) ◽  
pp. 229-264 ◽  
Author(s):  
A. Szychowski
Keyword(s):  
Cross Section ◽  
Critical Stress ◽  
Analytical Calculation ◽  
Local Buckling ◽  
Stability Loss ◽  
Longitudinal Stress ◽  
Plate Method ◽  
Thin Walled ◽  
The Cross ◽  
Elastically Restrained

Abstract Thin-walled bars currently applied in metal construction engineering belong to a group of members, the cross-section res i stance of which is affected by the phenomena of local or distortional stability loss. This results from the fact that the cross-section of such a bar consists of slender-plate elements. The study presents the method of calculating the resistance of the cross-section susceptible to local buckling which is based on the loss of stability of the weakest plate (wall). The “Critical Plate” (CP) was identified by comparing critical stress in cross-section component plates under a given stress condition. Then, the CP showing the lowest critical stress was modelled, depending on boundary conditions, as an internal or cantilever element elastically restrained in the restraining plate (RP). Longitudinal stress distribution was accounted for by means of a constant, linear or non-linear (acc. the second degree parabola) function. For the critical buckling stress, as calculated above, the local critical resistance of the cross-section was determined, which sets a limit on the validity of the Vlasov theory. In order to determine the design ultimate resistance of the cross-section, the effective width theory was applied, while taking into consideration the assumptions specified in the study. The application of the Critical Plate Method (CPM) was presented in the examples. Analytical calculation results were compared with selected experimental findings. It was demonstrated that taking into consideration the CP elastic restraint and longitudinal stress variation results in a more accurate representation of thin-walled element behaviour in the engineering computational model.

scholarly journals Second-order properties and central limit theory for the vertex process of iteration infinitely divisible and iteration stable random tessellations in the plane

2010 ◽  
Vol 42 (4) ◽  
pp. 913-935 ◽  
Author(s):  
Tomasz Schreiber ◽  
Christoph Thäle
Keyword(s):  
Correlation Function ◽  
Point Process ◽  
Central Limit ◽  
Pair Correlation ◽  
Density Parameter ◽  
Infinitely Divisible ◽  
Limit Theory ◽  
Vertex Point ◽  
Cross Covariance ◽  
The Cross

The point process of vertices of an iteration infinitely divisible or, more specifically, of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation function, as well as the cross-covariance measure and the cross-correlation function of the vertex point process and the random length measure in the general nonstationary regime. We also give special formulae in the stationary and isotropic setting. Exact formulae are given for vertex count variances in compact and convex sampling windows, and asymptotic relations are derived. Our results are then compared with those for a Poisson line tessellation having the same length density parameter. Moreover, a functional central limit theorem for the joint process of suitably rescaled total edge counts and edge lengths is established with the process (ξ, tξ), t > 0, arising in the limit, where ξ is a centered Gaussian variable with explicitly known variance.

Spectral lineshapes of collision-induced absorption (CIA) using isotropic intermolecular potential for N2-CH4

2021 ◽  
Vol 21 (4) ◽  
pp. 1063-1078
Author(s):  
M.S.A. El-Kader ◽  
G. Maroulis ◽  
T. Bancewicz
Keyword(s):  
Potential Model ◽  
Dipole Moments ◽  
Molecular Nitrogen ◽  
Intermolecular Potential ◽  
Gaseous Mixtures ◽  
Induced Absorption ◽  
Induced Dipole ◽  
Different Temperatures ◽  
Experimental Absorption ◽  
Good Agreement

Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures are computed for gaseous mixtures of molecular nitrogen and methane using theoretical values for the induced dipole moments and intermolecular potential as input. Comparison with theoretical absorption spectra shows satisfactory agreement. An empirical model of the dipole moment which reproduces the experimental spectra and the first three spectral moments more closely than the fundamental theory, is also presented. Good agreement between computed and experimental absorption lineshapes is obtained when a potential model which is constructed from the thermophysical and transport properties is used.

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