Correlation Funktions of a System with Different Temperatures of the Particle Components

1964 ◽  
Vol 19 (13) ◽  
pp. 1447-1451 ◽  
Author(s):  
G. Ecker ◽  
W. Kröll
Keyword(s):  
Correlation Function ◽  
Electron Correlation ◽  
Pair Correlation ◽  
Bbgky Hierarchy ◽  
Ion Pair ◽  
Pair Correlations ◽  
The Poisson Equation ◽  
Average Potential ◽  
Different Temperatures ◽  
Dressed Particles

We consider a plasma consisting of particle components with different temperatures. The components are uniformly distributed in the configuration space and MAXWELLIAN in the velocity space. Pair correlations are assumed to be small and higher order correlations negligible. It is shown from the BBGKY-hierarchy that the influence of the electrons on the ion kinetics can be taken into account by treating the ions as dressed particles. The hierarchy for these dressed particles provides the ion-ion correlation function. The electron-ion pair correlation is calculated from the POISSON equation using the ion-ion correlation and relating the electron-ion pair distribution to the average potential. By the same procedure we derive the electron-electron correlation making use of the electron-ion correlation. The results are compared with those of other authors.

Magnetized property effect of a non-aqueous solvent upon complex formation between kryptofix 22DD with lanthanum(iii) cation: experimental aspects and molecular dynamics simulation

RSC Advances ◽  
2016 ◽  
Vol 6 (11) ◽  
pp. 9096-9105 ◽  
Author(s):  
Gholam Hossien Rounaghi ◽  
Mostafa Gholizadeh ◽  
Fatemeh Moosavi ◽  
Iman Razavipanah ◽  
Hossein Azizi-Toupkanloo ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Molecular Dynamics Simulation ◽  
Pair Correlation ◽  
Molar Conductance ◽  
Methanol Solution ◽  
Dynamics Simulation ◽  
Aqueous Solvent ◽  
Different Temperatures ◽  
Kryptofix 22Dd

The variation of molar conductance versus mole ratio for (kryptofix 22DD·La)3+ complex in methanol solution at different temperatures is in accordance with the variation of pair correlation function of oxygen atoms.

Pair correlation function in a fluid with density inhomogeneities: results of the Percus‒Yevick and hypernetted chain approximations for hard spheres near a hard wall

1986 ◽  
Vol 404 (1827) ◽  
pp. 323-337 ◽  
Keyword(s):  
Correlation Function ◽  
Pair Correlation Function ◽  
Hard Spheres ◽  
Pair Correlation ◽  
Hard Wall ◽  
Bulk Fluid ◽  
Pair Correlations ◽  
Hypernetted Chain ◽  
Density Inhomogeneities ◽  
Bulk Case

Solutions for the pair correlation function and density profile of a system of hard spheres near a hard wall are obtained by using the Percus‒Yevick and hypernetted chain approximations, generalized for inhomogeneous fluids. The Percus‒Yevick (PY) results are similar in accuracy to those obtained for the bulk fluid. The PY pair correlation function is generally too small near contact but quite good overall. The hypernetted chain (h. n. c.) results are difficult to obtain numerically and are poorer than in the bulk. Often the h. n. c. pair correlations are too small at contact, in contrast to the bulk case where they are too large, although there are configurations where the contact values of the pair correlation function are too large. Nearly always the error in the h. n. c. results is much worse than is the case for the bulk. Both approximations are qualitatively satisfactory in that they predict the correct asymmetries between the values of the pair correlation functions for pairs of hard spheres whose line of centres is parallel or normal to the surface of the wall.

Pair correlations of the leVeque sequence on the polydisc

2008 ◽  
Vol 145 (1) ◽  
pp. 197-203
Author(s):  
R. NAIR
Keyword(s):  
Correlation Function ◽  
Pair Correlation Function ◽  
Resonance Condition ◽  
Pair Correlation ◽  
Natural Numbers ◽  
Pair Correlations ◽  
The Real ◽  
Image Position

AbstractWe consider a system of “forms” defined for ẕ = (zij) on a subset of $\Bbb C^d$ by where d = d1 + ⋅ ⋅ ⋅ + dl and for each pair of integers (i,j) with 1 ≤ i ≤ l, 1 ≤ j ≤ di we denote by $(v_{ij}(k))_{k=1}^{\infty}$ a strictly increasing sequence of natural numbers. Let ${\Bbb C}_1$ = {z ∈ ${\Bbb C}$ : |z| < 1} and let ${\underline X} \ = \ \times _{i=1}^l \times _{j=1}^{d_i}X_{ij}$ where for each pair (i, j) we have Xij = ${\Bbb C}\backslash {\Bbb C}_1$. We study the distribution of the sequence on the l-polydisc $({\Bbb C}_1)^l$ defined by the coordinatewise polar fractional parts of the sequence Xk(ẕ) = (L1(ẕ)(k),. . ., Ll(ẕ)(k)) for typical ẕ in ${\underline X}$ More precisely for arcs I1, . . ., I2l in $\Bbb T$, let B = I1 × ⋅ ⋅ ⋅ × I2l be a box in $\Bbb T^{2l}$ and for each N ≥ 1 define a pair correlation function by and a discrepancy by ΔN = $\sup_{B \subset \Bbb T^{2l}}${VN(B) − N(N−1)leb(B)}, where the supremum is over all boxes in $\Bbb T^{2l}$. We show, subject to a non-resonance condition on $(v_{ij}(k))_{k=1}^{\infty}$, that given ε > 0 we have ΔN = o(N$(log N)^{l + {1\over 2}}$(log log N)1+ε) for almost every $\underline x(\underline z)\in \Bbb T^{2l}$. Similar results on extremal discrepancy are also proved. Our results complement those of I. Berkes, W. Philipp, M. Pollicott, Z. Rudnick, P. Sarnak, R Tichy and the author in the real setting.

Angular pair correlations of observed and simulated galaxy distributions

1990 ◽  
Vol 68 (9) ◽  
pp. 827-830
Author(s):  
G. Wiedenmann ◽  
H. Atmanspacher ◽  
H. Scheingraber
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Pair Correlation ◽  
Quantitative Information ◽  
Small Scale ◽  
Main Body ◽  
Pair Correlations ◽  
Large Scale Structures ◽  
Galaxy Distribution ◽  
The Galaxy

The main body of quantitative information about galaxy statistics is obtained from correlation studies. It has recently turned out that a modified correlation formalism can provide details about large-scale structure in the galaxy distribution, which are obscured by artefacts of the conventional correlation function. The modified pair correlation function, as applied to the Zwicky catalogue of galaxies, shows two distinct power-law regimes at small scales (< 1°) and large scales (around 10°). Based on the comparison of simulated bubblelike large-scale structures with the Zwicky sample, these regimes are interpreted to correspond to the distribution of galaxies within the shells of the bubbles (small scale), and the distribution of the bubbles themselves (large scale).

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