scholarly journals Corollary from the Exact Expression for Enthalpy of Vaporization

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
A. A. Sobko
Keyword(s):  
Critical Point ◽  
Thermodynamic Parameters ◽  
Exact Expression ◽  
Enthalpy Of Vaporization ◽  
Atoms And Molecules ◽  
Linear Dimensions ◽  
Accuracy Of Measurements

A problem on determining effective volumes for atoms and molecules becomes actual due to rapidly developing nanotechnologies. In the present study an exact expression for enthalpy of vaporization is obtained, from which an exact expression is derived for effective volumes of atoms and molecules, and under certain assumptions on the form of an atom (molecule) it is possible to find their linear dimensions. The accuracy is only determined by the accuracy of measurements of thermodynamic parameters at the critical point.

scholarly journals On a Form of Coordinate Percolation

2008 ◽  
Vol 17 (6) ◽  
pp. 837-845 ◽  
Author(s):  
ELIZABETH R. MOSEMAN ◽  
PETER WINKLER
Keyword(s):  
Critical Exponent ◽  
Real Number ◽  
Critical Point ◽  
Exact Expression ◽  
Unit Interval ◽  
First Derivative ◽  
Infinite Path ◽  
A Site

Let ai,bi, i = 0, 1, 2, . . . be drawn uniformly and independently from the unit interval, and let t be a fixed real number. Let a site (i, j) ∈ $\N^2$ be open if ai + bj ≤ t, and closed otherwise. We obtain a simple, exact expression for the probability Θ(t) that there is an infinite path (oriented or not) of open sites, containing the origin. Θ(t) is continuous and has continuous first derivative except at the critical point (t=1), near which it has critical exponent (3 − $\sqrt{5}$)/2.

scholarly journals DISTRIBUTION OF THERMODYNAMIC PARAMETERS IN THE DISCRETE DISORDERED POTT’S MODEL. RESULTS OF COMPUTER SIMULATION

2020 ◽  
Vol 25 (1) ◽  
pp. 7-12
Author(s):  
Albert Babaevich Babaev ◽  
Akai Kurbanovich Murtazaev
Keyword(s):  
Computer Simulation ◽  
Thermodynamic Parameters ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Spin Systems ◽  
Spin States ◽  
Spin Concentration ◽  
Disordered Spin Systems ◽  
Linear Dimensions ◽  
The Monte Carlo Method

Using the Monte Carlo method, we study the distribution of thermodynamic parameters in a strongly disordered Potts model with the number of spin states q = 4. For this model, relative dispersions of magnetization Rm and susceptibility R are calculated. It is shown that in this model, the relative dispersions of Rm and R lead to nonzero values, which in-dicates poor self-averaging for magnetization and susceptibility in a strongly diluted mod-el. Averaging the thermodynamic parameters in a strongly diluted regime over an ensem-ble of disordered spin systems with different disorder implementations requires a signifi-cant increase in the number of disordered impurity configurations. Computer simulation was performed for spin systems with periodic boundary conditions at a spin concentration of p = 0.65. Systems with linear dimensions L  L  L= N, L = 60 were investigated.

scholarly journals The probability of planarity of a random graph near the critical point

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Marc Noy ◽  
Vlady Ravelomanana ◽  
Juanjo Rué
Keyword(s):  
Critical Point ◽  
Random Graph ◽  
Random Graphs ◽  
Generating Functions ◽  
Exact Expression ◽  
Critical Window ◽  
Analytic Combinatorics ◽  
Analytic Methods ◽  
International Audience ◽  
Standing Question

International audience Erdős and Rényi conjectured in 1960 that the limiting probability $p$ that a random graph with $n$ vertices and $M=n/2$ edges is planar exists. It has been shown that indeed p exists and is a constant strictly between 0 and 1. In this paper we answer completely this long standing question by finding an exact expression for this probability, whose approximate value turns out to be $p ≈0.99780$. More generally, we compute the probability of planarity at the critical window of width $n^{2/3}$ around the critical point $M=n/2$. We extend these results to some classes of graphs closed under taking minors. As an example, we show that the probability of being series-parallel converges to 0.98003. Our proofs rely on exploiting the structure of random graphs in the critical window, obtained previously by Janson, Łuczak and Wierman, by means of generating functions and analytic methods. This is a striking example of how analytic combinatorics can be applied to classical problems on random graphs.

Large-scale Motion of Solar Filaments

2000 ◽  
Vol 179 ◽  
pp. 205-208
Author(s):  
Pavel Ambrož ◽  
Alfred Schroll
Keyword(s):  
Magnetic Flux ◽  
Proper Motion ◽  
Time Scale ◽  
Large Scale ◽  
Accuracy Of Measurements ◽  
Solar Filaments ◽  
General Movement ◽  
Scale Motion ◽  
Velocity Scatter

AbstractPrecise measurements of heliographic position of solar filaments were used for determination of the proper motion of solar filaments on the time-scale of days. The filaments have a tendency to make a shaking or waving of the external structure and to make a general movement of whole filament body, coinciding with the transport of the magnetic flux in the photosphere. The velocity scatter of individual measured points is about one order higher than the accuracy of measurements.

Models of Thermodynamic Properties of Prominences

1979 ◽  
Vol 44 ◽  
pp. 349-355
Author(s):  
R.W. Milkey
Keyword(s):  
Thermodynamic Properties ◽  
Mass Transport ◽  
Emission Spectrum ◽  
Thermodynamic Parameters ◽  
Working Group ◽  
Physical Processes ◽  
Theoretical Concepts ◽  
Group 3 ◽  
Observational Techniques

The focus of discussion in Working Group 3 was on the Thermodynamic Properties as determined spectroscopically, including the observational techniques and the theoretical modeling of physical processes responsible for the emission spectrum. Recent advances in observational techniques and theoretical concepts make this discussion particularly timely. It is wise to remember that the determination of thermodynamic parameters is not an end in itself and that these are interesting chiefly for what they can tell us about the energetics and mass transport in prominences.

The Critical Point Drying Method Applied to Scanning Electron Microscopy of L-929 Cells

1970 ◽  
Vol 28 ◽  
pp. 278-279
Author(s):  
Charles TurnbiLL ◽  
Delbert E. Philpott
Keyword(s):  
Electron Microscopy ◽  
Carbon Dioxide ◽  
Surface Tension ◽  
Critical Point ◽  
Freeze Drying ◽  
Attractive Alternative ◽  
Crystal Formation ◽  
Critical Point Drying ◽  
Time Required ◽  
Scanning Electron

The advent of the scanning electron microscope (SCEM) has renewed interest in preparing specimens by avoiding the forces of surface tension. The present method of freeze drying by Boyde and Barger (1969) and Small and Marszalek (1969) does prevent surface tension but ice crystal formation and time required for pumping out the specimen to dryness has discouraged us. We believe an attractive alternative to freeze drying is the critical point method originated by Anderson (1951; for electron microscopy. He avoided surface tension effects during drying by first exchanging the specimen water with alcohol, amy L acetate and then with carbon dioxide. He then selected a specific temperature (36.5°C) and pressure (72 Atm.) at which carbon dioxide would pass from the liquid to the gaseous phase without the effect of surface tension This combination of temperature and, pressure is known as the "critical point" of the Liquid.

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