First-order and continuous melting transitions in two-dimensional Lennard-Jones systems and repulsive disks

This work studies how morphology (i.e., the shape of a structure) and topology (i.e., how different structures are connected) influence wall adsorption and capillary condensation under tight confinement. Numerical simulations based on classical density functional theory (cDFT) are run for a wide variety of geometries using both hard-sphere and Lennard-Jones fluids. These cDFT computations are compared to results obtained using the Minkowski functionals. It is found that the Minkowski functionals can provide a good description of the behavior of Lennard-Jones fluids down to small system sizes. In addition, through decomposition of the free energy, the Minkowski functionals provide a good framework to better understand what are the dominant contributions to the phase behavior of a system. Lastly, while studying the phase envelope shift as a function of the Minkowski functionals it is found that topology has a different effect depending on whether the phase transition under consideration is a continuous or a discrete (first-order) transition.

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Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

Journal of High Energy Physics ◽

10.1007/jhep04(2021)030 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Clifford V. Johnson ◽

Felipe Rosso

Keyword(s):

Phase Structure ◽

Scalar Potential ◽

String Equation ◽

Two Dimensional ◽

Leading Order ◽

Classical Analysis ◽

First Order ◽

First Order Phase Transition ◽

Definition Of ◽

First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

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Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-1990-11-1201 ◽

1990 ◽

Vol 45 (11-12) ◽

pp. 1219-1229 ◽

Cited By ~ 1

Author(s):

D.-A. Becker ◽

E. W. Richter

Keyword(s):

Differential Equations ◽

Linear Equations ◽

Mhd Equations ◽

Two Dimensional ◽

Invariant Solutions ◽

First Order ◽

Partially Invariant Solutions ◽

Quasilinear Systems ◽

Ideal Mhd ◽

Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

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A Difference Method for Plane Problems in Magnetoelastodynamics

Journal of Applied Mechanics ◽

10.1115/1.3422774 ◽

1972 ◽

Vol 39 (3) ◽

pp. 689-695 ◽

Cited By ~ 4

Author(s):

W. W. Recker

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Numerical Method ◽

Difference Method ◽

Necessary Condition ◽

Two Dimensional ◽

Symmetric Hyperbolic System ◽

Von Neumann ◽

First Order ◽

Independent Variables

The two-dimensional equations of magnetoelastodynamics are considered as a symmetric hyperbolic system of linear first-order partial-differential equations in three independent variables. The characteristic properties of the system are determined and a numerical method for obtaining the solution to mixed initial and boundary-value problems in plane magnetoelastodynamics is presented. Results on the von Neumann necessary condition are presented. Application of the method to a problem which has a known solution provides further numerical evidence of the convergence and stability of the method.

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