Effects of substrate heterogeneity on adsorption isotherms near a two-dimensional gas-liquid critical point

1986 ◽  
Vol 33 (3) ◽  
pp. 1746-1751 ◽  
Author(s):  
Robert E. Ecke ◽  
Jian Ma ◽  
Aldo D. Migone ◽  
Timothy S. Sullivan
Keyword(s):  
Critical Point ◽  
Adsorption Isotherms ◽  
Two Dimensional ◽  
Substrate Heterogeneity

scholarly journals Universality class of the motility-induced critical point in large scale off-lattice simulations of active particles.

Soft Matter ◽  
2021 ◽  
Author(s):  
Claudio Maggi ◽  
Matteo Paoluzzi ◽  
Andrea Crisanti ◽  
Emanuela Zaccarelli ◽  
Nicoletta Gnan
Keyword(s):  
Phase Separation ◽  
Critical Point ◽  
Computer Simulations ◽  
Large Scale ◽  
Universality Class ◽  
Critical Behaviour ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Active Particles ◽  
Two Dimensional Model

We perform large-scale computer simulations of an off-lattice two-dimensional model of active particles undergoing a motility-induced phase separation (MIPS) to investigate the systems critical behaviour close to the critical point...

On the critical behaviour of the two dimensional spin XY model

1982 ◽  
Vol 60 (3) ◽  
pp. 368-372 ◽  
Author(s):  
Jos Rogiers
Keyword(s):  
Critical Point ◽  
Triangular Lattice ◽  
Second Order ◽  
Critical Behaviour ◽  
Transverse Magnetization ◽  
Xy Model ◽  
Two Dimensional ◽  
Exponential Behaviour ◽  
Transformation Methods

Transformation methods are used to analyse the series for the second order fluctuation of the transverse magnetization for the triangular and square lattices. For the triangular lattice some evidence is found for an exponential behaviour of this quantity near the critical point with a tentative estimate for the exponent [Formula: see text].

Transfer Matrix of the Two-dimensional Ising Model

2020 ◽  
pp. 211-234
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Critical Point ◽  
Transfer Matrix ◽  
Functional Equations ◽  
Baxter Equation ◽  
Matrix Formalism ◽  
Two Dimensional ◽  
R Matrix ◽  
Transfer Matrix Formalism ◽  
Lowest Eigenvalue

This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative properties of the transfer matrices, which lead to a functional equation for their eigenvalues. The exact free energy of the Ising model and its critical point can be identified by means of the lowest eigenvalue. The chapter covers Baxter's approach, the Yang–Baxter equation and its relation to the Boltzmann weights, the R-matrix, and discusses activity away from the critical point, the six-vertex model, as well as functional equations and symmetries.

Mode Analysis on Onset of Turing Instability in Time-Fractional Reaction-Subdiffusion Equations by Two-Dimensional Numerical Simulations

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Masataka Fukunaga
Keyword(s):  
Critical Point ◽  
Fractional Order ◽  
Time Derivative ◽  
Turing Instability ◽  
Reaction Diffusion Equations ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Linearized Equations ◽  
Special Cases ◽  
Fractional Reaction

There are two types of time-fractional reaction-subdiffusion equations for two species. One of them generalizes the time derivative of species to fractional order, while in the other type, the diffusion term is differentiated with respect to time of fractional order. In the latter equation, the Turing instability appears as oscillation of concentration of species. In this paper, it is shown by the mode analysis that the critical point for the Turing instability is the standing oscillation of the concentrations of the species that does neither decays nor increases with time. In special cases in which the fractional order is a rational number, the critical point is derived analytically by mode analysis of linearized equations. However, in most cases, the critical point is derived numerically by the linearized equations and two-dimensional (2D) simulations. As a by-product of mode analysis, a method of checking the accuracy of numerical fractional reaction-subdiffusion equation is found. The solutions of the linearized equation at the critical points are used to check accuracy of discretized model of one-dimensional (1D) and 2D fractional reaction–diffusion equations.

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