Homogeneous nucleation from an asymptotic point of view

2019 ◽  
Vol 33 (1) ◽  
pp. 83-106
Author(s):  
Manuel Baumgartner ◽  
Peter Spichtinger
1956 ◽  
Vol 34 (5) ◽  
pp. 473-490 ◽  
Author(s):  
K. A. Jackson ◽  
Bruce Chalmers

The kinetic theory of melting and freezing is developed from consideration of atom movements at an interface between solid and liquid. The equations developed are shown to have the same form as the corresponding thermodynamic equations. The homogeneous nucleation of a solid phase in a liquid is then considered from the point of view of this theory. Agreement with experimental observation is obtained on the following points. (1) The supercooling at which homogeneous nucleation occurs is proportional to the absolute equilibrium temperature. (2) The surface free energy per atom used in the quasi-thermodynamic treatment of nucleation should be equal to one-half the latent heat per atom. (3) The amount of liquid supercooled has a very small effect on the temperature at which homogeneous nucleation occurs.


Author(s):  
Julián Restrepo ◽  
Jose R. Simões-Moreira

Abstract One of the several challenges of the oil and natural gas offshore extraction in pre-salt reserves in Brazil, is the high content of carbon dioxide inside the wells, reaching values close to 80% in a molar fraction. This issue has a big impact on the crude extraction, due to the necessity of further expensive equipment occupying considerable deck space in platforms. Therefore, it is necessary to research and find new technologies, which allow separating high contents of carbon dioxide at low energy consumption and low maintenance. The supersonic separation concept fulfils all these requirements due to the absence of moving parts and simple operation, because its working principle is based on the strong temperature drop of gas mixtures at supersonic expansion as it occurs in de Laval nozzles. Eventually, at the right operating conditions, the mixture starts to nucleate and, therefore, it will drive the phase change. Nevertheless, the physical phenomena involved in this device is complex, because it involves phase change at supersonic speeds, which comprise compressible, multispecies, and multiphase flow. This paper analyses the threshold of the phase change at supersonic speeds. The objective of this work is to calculate the influence of operation conditions (pressure, temperature and composition) in the phase change performance in supersonic separators. The phase change was modelled using the classical theory of homogeneous nucleation. In this approach allows to estimate the phase change inside the supersonic flow for different operating conditions and allows to establish operating strategies to ensure low Mach numbers (M < 1.5) in the phase change region, allowing a further pressure recovery.


1984 ◽  
Vol 16 (03) ◽  
pp. 585-602
Author(s):  
Shigeru Mase

We consider the statistical estimation problem of potential functions of Gibbs models on the plane lattice. We assume that the area on which a random point pattern is observed is sufficiently large and take an asymptotic point of view. The main result is to show the locally asymptotic normality of the Gibbs model under certain conditions. From this result we can show the optimality of the maximum likelihood estimator employing known results about locally asymptotic normal families, though a practical computation of the maximum likelihood estimator presents difficulties. An estimation procedure based on the method of moments is also proposed.


Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 924 ◽  
Author(s):  
Alberto Lastra ◽  
Stéphane Malek

The analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain are constructed and studied from an asymptotic point of view with respect to the perturbation parameter. Two types of holomorphic solutions, the so-called inner and outer solutions, are considered. Each of them holds a particular asymptotic relation with the formal ones in terms of asymptotic expansions in the perturbation parameter. The growth rate in the asymptotics leans on the - 1 -branch of Lambert W function, which turns out to be crucial.


1984 ◽  
Vol 16 (3) ◽  
pp. 585-602 ◽  
Author(s):  
Shigeru Mase

We consider the statistical estimation problem of potential functions of Gibbs models on the plane lattice. We assume that the area on which a random point pattern is observed is sufficiently large and take an asymptotic point of view. The main result is to show the locally asymptotic normality of the Gibbs model under certain conditions. From this result we can show the optimality of the maximum likelihood estimator employing known results about locally asymptotic normal families, though a practical computation of the maximum likelihood estimator presents difficulties. An estimation procedure based on the method of moments is also proposed.


1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.


1984 ◽  
Vol 75 ◽  
pp. 331-337
Author(s):  
Richard Greenberg

ABSTRACTThe mechanism by which a shepherd satellite exerts a confining torque on a ring is considered from the point of view of a single ring particle. It is still not clear how one might most meaningfully include damping effects and other collisional processes into this type of approach to the problem.


Sign in / Sign up

Export Citation Format

Share Document