A method for calculating the surface tension of a droplet in a lattice-gas model with long-range interaction

2000 ◽  
Vol 18 (2) ◽  
pp. 319-327 ◽  
Author(s):  
K. Ebihara ◽  
T. Watanabe
Keyword(s):  
Surface Tension ◽  
Long Range ◽  
Lattice Gas ◽  
Lattice Gas Model ◽  
Range Interaction ◽  
Long Range Interaction

Surface of Dense Phase in Lattice-Gas Fluid with Long-Range Interaction

1998 ◽  
Vol 09 (08) ◽  
pp. 1417-1427 ◽  
Author(s):  
Kenichi Ebihara ◽  
Tadashi Watanabe ◽  
Hideo Kaburaki
Keyword(s):  
Long Range ◽  
Lattice Gas ◽  
Local Density ◽  
Particle Density ◽  
Mean Free Path ◽  
Droplet Radius ◽  
Range Interaction ◽  
Long Range Interaction ◽  
Dividing Surface ◽  
Component Particle

A lattice gas with long-range interaction can simulate phase separation in the system consisting of one kind of component particle like the liquid-vapor theory of van der Waals. The generated phases are distinguished from each other by their particle density. In lattice-gas fluid with long-range interaction, the phase with high density can be observed in the phase with low density like the droplet in vapor. In this paper, the surface of the droplet in lattice-gas fluid with the long-range interaction is determined from the local density and its position is compared with that of Gibbs's dividing surface. The inside region and the outside region of the droplet are defined on the basis of the mean free path in each region. The surface tension is calculated through Laplace's formula using the droplet radius and the pressures in both regions. It is shown that the surface thickness becomes 4r where r is the distance of the long-range interaction.

DYNAMICAL PRESSURE ANISOTROPY IN LIQUID-GAS MODEL OF LATTICE-GAS

2006 ◽  
Vol 17 (01) ◽  
pp. 53-64
Author(s):  
KEN-ICHI EBIHARA
Keyword(s):  
Phase Separation ◽  
Long Range ◽  
External Force ◽  
Numerical Experiments ◽  
Lattice Gas ◽  
The Other ◽  
Dense Phase ◽  
Range Interaction ◽  
Pressure Anisotropy ◽  
Long Range Interaction

A liquid-gas model of lattice-gas is made by adding long-range interaction to lattice-gas and can simulate phase separation similar to that in the van der Waals' liquid-gas theory. This liquid-gas model can generate a circular dense-phase in the rare phase. In this paper, the deformation of the circular dense-phase by external force is simulated using the two types of liquid-gas models of lattice-gas, which are distinguished by the type of long-range interaction. It is observed that one type of model shows the valid deformation and the other shows the unphysical deformation. It is found by numerical experiments that this difference of the deformation is caused by dynamical pressure anisotropy of the liquid-gas model of lattice-gas.

Immiscible Lattice Gas with Long-Range Interaction

1997 ◽  
Vol 08 (04) ◽  
pp. 697-703
Author(s):  
Akira Tsumaya ◽  
Hirotada Ohashi
Keyword(s):  
Phase Separation ◽  
Long Range ◽  
Lattice Gas ◽  
Phase Interface ◽  
Two Phase ◽  
Range Interaction ◽  
Color Distribution ◽  
Interparticle Forces ◽  
Long Range Interaction ◽  
Two Phases

We developed a new LGA model which has the applicability for simulation of immiscible two phases with wide difference in density. We introduced long-range interparticle forces into the Rothman and Keller's ILG model to represent density difference between phases. We attempted some simulations of phase separation using our new model. Two-phase interfaces are stably made with density distribution coinciding with particle color distribution. Furthermore, the two-phase interface is clearer than that obtained by the Appert and Zaleski's LG model.

Phase transformation and Raman spectra in BaTiO3 nanocrystals

2002 ◽  
Vol 718 ◽  
Author(s):  
Jian Yu ◽  
X. J. Meng ◽  
J.L. Sun ◽  
G.S. Wang ◽  
J.H. Chu
Keyword(s):  
Particle Size ◽  
Phase Transformation ◽  
Low Temperature ◽  
Long Range ◽  
Lattice Expansion ◽  
Inversion Symmetry ◽  
Range Interaction ◽  
Cooperative Phenomena ◽  
Long Range Interaction ◽  
Hydrothermal Methods

AbstractIn this paper, size-induced ferroelectricit yweakening, phase transformation, and anomalous lattice expansion are observed in nanocrystalline BaTiO3 (nc-BaTiO3) deriv ed b y low temperature hydrothermal methods, and they are w ellunderstood using the terms of the long-range interaction and its cooperative phenomena altered by particle size in covalen t ionic nanocrystals. In cubic nc-BaTiO3, five modes centerd at 186, 254, 308, 512 and 716 cm-1 are observed Raman active in cubic nanophase, and they are attributed to local rhombohedral distortion breaking inversion-symmetry in cubic nanophase. The254 and 308 cm-1 modes are significantly affected not only by the concentration of hydroxyl defects, but also their particular configuration. And the 806 cm-1 modes found to be closely associated with OH - absorbed on grain boundaries.

scholarly journals Inverse Problem for Ising Connection Matrix with Long-Range Interaction

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1624
Author(s):  
Leonid Litinskii ◽  
Boris Kryzhanovsky
Keyword(s):  
Inverse Problem ◽  
Long Range ◽  
Random Number ◽  
Connection Matrix ◽  
Range Interaction ◽  
Connection Matrices ◽  
Ising Systems ◽  
Long Range Interaction ◽  
Matrix Spectrum ◽  
Analytical Expressions

In the present paper, we examine Ising systems on d-dimensional hypercube lattices and solve an inverse problem where we have to determine interaction constants of an Ising connection matrix when we know a spectrum of its eigenvalues. In addition, we define restrictions allowing a random number sequence to be a connection matrix spectrum. We use the previously obtained analytical expressions for the eigenvalues of Ising connection matrices accounting for an arbitrary long-range interaction and supposing periodic boundary conditions.

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