scholarly journals Minimizers for a one-dimensional interaction energy

2022 ◽  
Vol 216 ◽  
pp. 112691
Author(s):  
Rupert L. Frank
Keyword(s):  
Interaction Energy ◽  
One Dimensional ◽  
Dimensional Interaction

Statistical Thermodynamics and Surface Phase Transitions of Interacting Particles Adsorbed on One-Dimensional Channels Arranged in a Triangular Cross-Sectional Structure

2009 ◽  
Vol 150 ◽  
pp. 73-100 ◽  
Author(s):  
P.M. Pasinetti ◽  
F. Romá ◽  
J.L. Riccardo ◽  
A.J. Ramirez-Pastor
Keyword(s):  
Monte Carlo ◽  
Interaction Energy ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Single Channel ◽  
Scaling Analysis ◽  
Surface Phase ◽  
Cross Sectional ◽  
One Dimensional ◽  
Sectional Structure

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer lattice-gas, which mimics a nanoporous environment. In this model, one-dimensional chains of atoms were arranged in a triangular cross-sectional structure. Two kinds of lateral interaction energies have been considered: (1) wL, interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) wT, interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transverse interactions (wT > 0), where a rich variety of structural orderings are observed in the adlayer, depending on the value of the parameters kBT/wT (kB being the Boltzmann constant) and wL /wT. For wL /wT = 0, successive planes are uncorrelated, the system is equivalent to the triangular lattice, and the well-known [ ] ordered phase is found at low temperatures and a coverage, , of 1/3 [2/3]. In the more general case (wL /wT  0), the competition between interactions along a single channel and the transverse coupling between sites in neighboring channels leads to a three-dimensional adsorbed layer. Consequently, the and structures “propagate” along the channels and new ordered phases appear in the adlayer. The influence of each ordered phase on adsorption isotherms, differential heat of adsorption and configurational entropy of the adlayer has been analyzed and discussed in the context of the lattice-gas theory. Finally, the Monte Carlo technique was combined with the recently reported free energy minimization criterion approach (FEMCA) [F. Romá et al.: Phys. Rev. B Vol. 68 (2003), art. no. 205407] to predict the critical temperatures of the surface-phase transformations occurring in the adsorbate. The excellent qualitative agreement between simulated data and FEMCA results allows us to interpret the physical meaning of the mechanisms underlying the observed transitions.

The Theory of Adsorption of Gases on Solids when the Potential Energy Varies Continuously over the Surface

1941 ◽  
Vol 37 (1) ◽  
pp. 82-94 ◽  
Author(s):  
A. R. Miller ◽  
J. K. Roberts
Keyword(s):  
Potential Energy ◽  
Interaction Energy ◽  
Physical Model ◽  
Power Law ◽  
Repulsive Force ◽  
Inverse Power ◽  
Adsorbed Particle ◽  
One Dimensional ◽  
Inverse Power Law ◽  
Adsorption Of Gases

In developing the theory of adsorption taking into account the interaction between adsorbed particles it has been usual to use a physical model in which it is assumed that there is a fixed interaction energy between particles adsorbed on neighbouring sites on the surface. In this paper the differences between the behaviour of this model and that of actual surfaces are discussed by considering a one-dimensional film in which the potential energy of a single adsorbed particle varies continuously and periodically with its position on the surface and in which there is a repulsive force between adsorbed particles which varies with the distance between them according to an inverse power law. For such a physical model the variation of the heat of adsorption with the fraction of the sites occupied is considered in detail and it is shown in particular that there is much less difference between the behaviour of mobile and immobile films than is indicated by the earlier model in which a fixed interaction energy is assumed. These results are considered in connexion with the interpretation of experiments on the adsorption of hydrogen on tungsten.

One‐Dimensional Interaction of a Plasma with a Ruby‐Laser Beam

1971 ◽  
Vol 42 (13) ◽  
pp. 5492-5494 ◽  
Author(s):  
A. G. Engelhardt
Keyword(s):  
Laser Beam ◽  
Ruby Laser ◽  
One Dimensional ◽  
Dimensional Interaction

Spatial Aggregation in Gravity Models: 2. One-Dimensional Population Density Models

1982 ◽  
Vol 14 (4) ◽  
pp. 525-553 ◽  
Author(s):  
M Batty ◽  
P K Sikdarfl
Keyword(s):  
Population Density ◽  
Spatial Information ◽  
Interaction Model ◽  
Theoretical Models ◽  
Spatial Aggregation ◽  
Gravity Models ◽  
Model Parameters ◽  
One Dimensional ◽  
Dimensional Interaction ◽  
Population Density Model

This paper, the second of four, is concerned with applying a methodology for analysing the spatial aggregation problem in gravity models outlined in the first paper. The methodology is based on a consistent framework for linking measures of pattern in interaction data to the derivation and estimation of related interaction models using spatial information theory. In this quest, a link is forged between information in data and the parameters of an associated model, and in part 1 it was suggested that if this link could be formalised then a means would be available for predicting changes in model parameters from different aggregations of the data, prior to the actual estimation of the models themselves. This relationship can be formalised for the case of the continuous one-dimensional interaction model such as the population density model, and this paper is concerned with demonstrating such an application to aggregations of zones in the Reading region. The framework is first described and two continuous models are presented. Then, the discrete model is estimated by means both of regression and of entropy techniques applied to various aggregations of the region, and the resulting parameters are related to the predicted and observed informations. Finally, the parameters approximated from observed information by use of the theoretical models are compared with the estimated parameters, and the approximation is deemed good, thus providing some confidence in the general concepts developed to handle these types of problem.

SIMULATION OF THE DYNAMICS OF MYXOBACTERIA SWARMS BASED ON A ONE-DIMENSIONAL INTERACTION MODEL

1995 ◽  
Vol 03 (02) ◽  
pp. 579-588 ◽  
Author(s):  
BEATE PFISTNER
Keyword(s):  
Cell Density ◽  
Single Cells ◽  
Interaction Model ◽  
Time Dependent ◽  
One Dimensional ◽  
Front Tracking Method ◽  
Dimensional Interaction ◽  
Differential Integral Equation ◽  
Dependent Model ◽  
High Level

Myxobacteria have a high level of intercellular coordination. Their swarms show “streets” and “whirls” of parallel gliding cells as well as wave-like moving cell density fields, so called “rippling”. The dependence from two phenomenological parameters, gliding velocity and turning frequency, has turned out to be characteristic for cell behavior at the swarm edge. As cells at the swarm edge are mostly gliding parallel in one dimension, the behavior of single cells can be comprised in a one-dimensional model describing interactions between cells of the same species in a homogenous environment, where turning frequency determines the cell density distribution via a hyperbolic differential integral equation. After specifying the parameter functions appearing in the integral, it is examined how these parameters influence the turning behavior and therefore the edge development of swarms over time. Numerical simulations of this model are performed both for the stationary and the time dependent case. For the time dependent model a front tracking method is applied using a Lagrange interpolation at the swarm edge. The simulations show that perception of different gliding directions is significant for the dynamics of swarm expansion and retraction.

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