Second-order integral equations for Lennard-Jones associating fluids

1997 ◽  
Vol 93 (14) ◽  
pp. 2367-2372 ◽  
Author(s):  
Paweł Bryk ◽  
O. Pizio ◽  
Stefan Sokołowski
Keyword(s):  
Integral Equations ◽  
Second Order ◽  
Associating Fluids ◽  
Lennard Jones

scholarly journals On the theory of finite deformations of elastic crystals

1942 ◽  
Vol 180 (982) ◽  
pp. 285-304 ◽  
Keyword(s):  
Order Approximation ◽  
Finite Deformations ◽  
Second Order ◽  
Order Effects ◽  
Zero Temperature ◽  
Cubic Crystals ◽  
Special Values ◽  
Lennard Jones ◽  
Second Order Effects ◽  
Elastic Crystals

The general theory of finite deformation of cubic crystals at zero temperature is developed to a second-order approximation, and the cases of (1) a uniform hydrostatic pressure, (2) a tension in the direction of one of the axes, (3) a shear along the (0, 1, 0) planes, and (4) a shear along the (0, 1, 1) planes of the lattice, are worked out in detail. A number of ‘second-order effects’ (deviations from Hooke’s law) are predicted which in case (1) have been observed and measured by Bridgman, and in the remaining cases certainly can be detected and measured by suitable experimental arrangements. Assuming the particular force law between the particles of the lattice which was first introduced by Mie and Grüneisen, and later used in the investigations of Lennard-Jones and of Born and his collaborators, and using some of the results of the latter authors, the constants governing the above-mentioned second-order effects are expressed in terms of the constants governing the force law, and calculated numerically for a number of special values of these constants. Thus by comparing the calculated values of these constants with the results of measurements at low temperature the unknown force law could probably be determined.

scholarly journals Mean-square stability of a class of stochastic integral equations

1972 ◽  
Vol 7 (3) ◽  
pp. 337-352
Author(s):  
W.J. Padgett
Keyword(s):  
Stochastic Process ◽  
Integral Equations ◽  
Stochastic Integral ◽  
Second Order ◽  
Mean Square ◽  
Random Solution ◽  
Mean Square Stability ◽  
Stochastic Integral Equations ◽  
Exponentially Stable ◽  
Image Position

The object of this paper is to investigate under very general conditions the existence and mean-square stability of a random solution of a class of stochastic integral equations in the formfor t ≥ 0, where a random solution is a second order stochastic process {x(t; w) t ≥ 0} which satisfies the equation almost certainly. A random solution x(t; w) is defined to be stable in mean-square if E[|x(t; w)|2] ≤ p for all t ≥ 0 and some p > 0 or exponentially stable in mean-square if E[|x(t; w)|2] ≤ pe-at, t ≥ 0, for some constants ρ > 0 and α > 0.

scholarly journals A simple second order thermodynamic perturbation theory for associating fluids

2021 ◽  
Vol 24 (3) ◽  
pp. 33602
Author(s):  
B. D. Marshall
Keyword(s):  
Hydrogen Bond ◽  
Perturbation Theory ◽  
General Solution ◽  
Pure Component ◽  
Second Order ◽  
Order Effects ◽  
Thermodynamic Perturbation Theory ◽  
Associating Fluids ◽  
Hydrogen Bond Cooperativity ◽  
Second Order Perturbation Theory

An approximation within Wertheim's second order perturbation theory is proposed which allows for the development of a general solution for pure component fluids with an arbitrary number and functionality of association sites. The solution is closed, concise and general for all second order effects such as ring formation, steric hindrance and hydrogen bond cooperativity. The approach is validated by comparison to hydrogen bond structure data for liquid water.

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