scholarly journals The interaction of atoms and molecules with solid surfaces XII—Critical phenomena in a two-dimensional gas

1937 ◽  
Vol 163 (912) ◽  
pp. 132-138 ◽  
Keyword(s):  
Critical Temperature ◽  
Equation Of State ◽  
Critical Phenomena ◽  
Three Dimensional ◽  
Inert Gases ◽  
Two Dimensional ◽  
Lennard Jones ◽  
Low Concentrations ◽  
High Concentrations ◽  
The Right

In a paper recently published by Professor Lennard-Jones and the author (Lennard-Jones and Devonshire 1937) the equation of state of a gas at high concentrations has been calculated in terms of the interatomic fields. The equation found had the right kind of properties and, in particular, using the interatomic fields previously determined from the observed equation of state at low concentrations (Lennard-Jones 1931), the critical temperature was given correctly to within a few degrees for the inert gases. In this paper we shall apply the same method to determine the equation of state of a two-dimensional gas. Although such a gas cannot strictly be obtained in practice, an inert gas adsorbed on a surface (or in fact any gas held by van der Waals’ forces only) would probably behave very much like one, the fluctuations of the potential field over the surface not being of much importance. In confirmation of this it may be noted that the specific heat of argon adsorbed on charcoal was found by Simon (Simon 1935) to be equal to that of a perfect two-dimensional gas down to 60° K. A gas adsorbed on a liquid would be an even better representation of a two-dimensional one. Some measurements on the adsorption of krypton and xenon on liquid mercury have been made by Cassel and Neugebauer (Cassel and Neugebauer 1936), and they found no trace of any critical phenomena though they worked at temperatures considerably below the critical temperature of xenon. Our results are in agreement with this, for they show that the critical temperature of a two-dimensional gas should be about half that of the corresponding three-dimensional one.

scholarly journals Anharmonic Self-Consistent Theory of Crystals. II. The 2d and 3d Quartic Crystal Models

1994 ◽  
Vol 49 (6) ◽  
pp. 663-670
Author(s):  
S. Sh. Soulayman ◽  
C. Ch. Marti ◽  
Ch. Ch. Guilpin
Keyword(s):  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Three Dimensional ◽  
Inert Gases ◽  
Thermoelastic Properties ◽  
Consistent Theory ◽  
Jones Potential ◽  
Lennard Jones ◽  
2D And 3D ◽  
Strong Anharmonicity

Abstract In this paper we apply the method developed in part I for describing the crystalline state of two and three dimensional inert gases. For strong anharmonicity of fourth order, the equations of state of these gases are obtained. This way we calculate the thermoelastic properties of two and three dimensional argon, krypton and xenon using the Lennard-Jones potential. The corrections to the Helmholtz free energy and thermodynamic properties due to quantum effects are considered. The results are compared with the available experimental data.

Separation of the 3D stress state of a loaded plate into two-dimensional tasks: bending and symmetric compression of the plate

2021 ◽  
Vol 103 (3) ◽  
pp. 53-62
Author(s):  
Victor Revenko ◽  
Andrian Revenko
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Partial Solution ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Equilibrium Equations ◽  
Dimensional Boundary ◽  
The Right

The three-dimensional stress-strain state of an isotropic plate loaded on all its surfaces is considered in the article. The initial problem is divided into two ones: symmetrical bending of the plate and a symmetrical compression of the plate, by specified loads. It is shown that the plane problem of the theory of elasticity is a special case of the second task. To solve the second task, the symmetry of normal stresses is used. Boundary conditions on plane surfaces are satisfied and harmonic conditions are obtained for some functions. Expressions of effort were found after integrating three-dimensional stresses that satisfy three equilibrium equations. For a thin plate, a closed system of equations was obtained to determine the harmonic functions. Displacements and stresses in the plate were expressed in two two-dimensional harmonic functions and a partial solution of the Laplace equation with the right-hand side, which is determined by the end loads. Three-dimensional boundary conditions were reduced to two-dimensional ones. The formula was found for experimental determination of the sum of normal stresses via the displacements of the surface of the plate.

scholarly journals Making Anaglyphs in Photoshop

2005 ◽  
Vol 13 (3) ◽  
pp. 36-39 ◽  
Author(s):  
Jerry Sedgewick
Keyword(s):  
Imaging System ◽  
Three Dimensional ◽  
Ct Scans ◽  
Two Dimensional ◽  
The Right ◽  
Two Dimensional Images

In order to achieve a three dimensional appearance to a pair of two dimensional images, two off-axis images can be produced and colorized. These can be overlayed slightly apart and then viewed through glasses with two differently colored sides, one color for the left eye and another for the right eye in combinations containing red, green or blue colors. These off-axis and colorized images are referred to as anaglyphs.Off-axis images can be achieved through the use of a tilting stage on a microscope, by physically changing the position of a camera in relation to a still object, or through changing the axis of an optical stack of sections, such as what is created by confocal/CT scans. Some images lend themselves more to a 3D look both by virtue of inherent three dimensionality limited by the resolution of the imaging system.

Percus–Yevick equation of state for the two‐dimensional Lennard‐Jones fluid

1977 ◽  
Vol 66 (10) ◽  
pp. 4503-4508 ◽  
Author(s):  
Eduardo D. Glandt ◽  
Donald D. Fitts
Keyword(s):  
Equation Of State ◽  
Two Dimensional ◽  
Lennard Jones

Action potential morphology heterogeneity in the atrium and its effect on atrial reentry: a two-dimensional and quasi-three-dimensional study

2006 ◽  
Vol 364 (1843) ◽  
pp. 1349-1366 ◽  
Author(s):  
Samuel R Kuo ◽  
Natalia A Trayanova
Keyword(s):  
Action Potential ◽  
Action Potentials ◽  
Three Dimensional ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Crista Terminalis ◽  
Wave Dynamics ◽  
Continuous Surface ◽  
The Right

Atrial fibrillation (AF) is believed to be perpetuated by recirculating spiral waves. Atrial structures are often characterized with action potentials of varying morphologies; however, the role of the structure-dependent atrial electrophysiological heterogeneity in spiral wave behaviour is not well understood. The purpose of this study is to determine the effect of action potential morphology heterogeneity associated with the major atrial structures in spiral wave maintenance. The present study also focuses on how this effect is further modulated by the presence of the inherent periodicity in atrial structure. The goals of the study are achieved through the simulation of electrical behaviour in a two-dimensional atrial tissue model that incorporates the representation of action potentials in various structurally distinct regions in the right atrium. Periodic boundary conditions are then imposed to form a cylinder (quasi three-dimensional), thus allowing exploration of the additional effect of structure periodicity on spiral wave behaviour. Transmembrane potential maps and phase singularity traces are analysed to determine effects on spiral wave behaviour. Results demonstrate that the prolonged refractoriness of the crista terminalis (CT) affects the pattern of spiral wave reentry, while the variation in action potential morphology of the other structures does not. The CT anchors the spiral waves, preventing them from drifting away. Spiral wave dynamics is altered when the ends of the sheet are spliced together to form a cylinder. The main effect of the continuous surface is the generation of secondary spiral waves which influences the primary rotors. The interaction of the primary and secondary spiral waves decreased as cylinder diameter increased.

scholarly journals Multigrain indexing of unknown multiphase materials

2016 ◽  
Vol 49 (2) ◽  
pp. 616-621 ◽  
Author(s):  
Christian Wejdemann ◽  
Henning Friis Poulsen
Keyword(s):  
A Priori ◽  
Computing Time ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Complex Samples ◽  
Multiphase Materials ◽  
Mineral Phases ◽  
Dirac Comb ◽  
Crystallographic Planes ◽  
The Right

A multigrain indexing algorithm for use with samples comprising an arbitrary number of known or unknown phases is presented. No a priori crystallographic knowledge is required. The algorithm applies to data acquired with a monochromatic beam and a conventional two-dimensional detector for diffraction. Initially, candidate grains are found by searching for crystallographic planes, using a Dirac comb convoluted with a box function as a filter. Next, candidate grains are validated and the unit cell is optimized. The algorithm is validated by simulations. Simulations of 500 cementite grains and ∼100 reflections per grain resulted in 99.2% of all grains being indexed correctly and 99.5% of the reflections becoming associated with the right grain. Simulations with 200 grains associated with four mineral phases and 50–700 reflections per grain resulted in 99.9% of all grains being indexed correctly and 99.9% of the reflections becoming associated with the right grain. The main limitation is in terms of overlap of diffraction spots and computing time. Potential areas of use include three-dimensional grain mapping, structural solution and refinement studies of complex samples, and studies of dilute phases.

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