SOLVABLE MODEL OF THE PAIRING TRANSITION IN A TWO-DIMENSIONAL ONE-COMPONENT PLASMA/METAL INTERFACE MODEL

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 303-315 ◽  
Author(s):  
P. J. FORRESTER
Keyword(s):  
Solvable Model ◽  
Coulomb Gas ◽  
Two Dimensions ◽  
Analytic Description ◽  
Two Dimensional ◽  
Metal Interface ◽  
Exactly Solvable ◽  
Component Plasma ◽  
Two Phases ◽  
The One

An exactly solvable model of the pairing transition from a conductive to an insulator phase in a two-dimensional, log-potential Coulomb system is given. The system considered is the one-component plasma of positive particles without a neutralizing background near a metal interface, which is coupled to an external (non-Coulombic) potential. A complete analytic description of the equilibrium properties of the two phases and the transition is provided, and this is compared with the expected analytic properties of the two-component log-potential Coulomb gas in one and two-dimensions.

scholarly journals TWO-DIMENSIONAL ONE-COMPONENT PLASMA IN A QUADRUPOLAR FIELD

1996 ◽  
Vol 11 (05) ◽  
pp. 941-949 ◽  
Author(s):  
P.J. FORRESTER ◽  
B. JANCOVICI
Keyword(s):  
Correlation Function ◽  
Surface Charge ◽  
Particle System ◽  
Solvable Model ◽  
Two Dimensional ◽  
Exactly Solvable ◽  
Component Plasma ◽  
Classical Plasma ◽  
The One ◽  
Body Potential

The classical two-dimensional one-component plasma is an exactly solvable model at some special temperature even when the one-body potential acting on the particles has a quadrupolar term. As a supplement to a recent work of Di Francesco, Gaudin, Itzykson and Lesage1 about an N-particle system (N large but finite), a macroscopic argument is given for confirming that the particles form an elliptical blob, the analogy between the classical plasma and a quantum N-fermion system in a magnetic field is used for the microscopic approach, and a microscopic calculation of the surface charge–surface charge correlation function is performed; an expected universal form is shown to be realized by this correlation function.

scholarly journals Exact and Asymptotic Features of the Edge Density Profile for the One Component Plasma in Two Dimensions

2014 ◽  
Vol 158 (5) ◽  
pp. 1147-1180 ◽  
Author(s):  
T. Can ◽  
P. J. Forrester ◽  
G. Téllez ◽  
P. Wiegmann
Keyword(s):  
Density Profile ◽  
Two Dimensions ◽  
Edge Density ◽  
Component Plasma ◽  
The One

SOLVING THE TWO-DIMENSIONAL INVERSE FRACTAL PROBLEM WITH THE WAVELET TRANSFORM

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 469-475 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Scale Invariance ◽  
Wavelet Decomposition ◽  
Two Dimensions ◽  
The Self ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
One Dimensional ◽  
Affine Functions ◽  
The One

The methodology of the solution to the inverse fractal problem with the wavelet transform1,2 is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions, this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.

A Comparison of Diffusion Flame Stability in One and Two Spatial Dimensions Near Cold, Inert Surfaces

2001 ◽  
Author(s):  
Robert Vance ◽  
Indrek S. Wichman
Keyword(s):  
Two Dimensions ◽  
Low Flow ◽  
Dimensional System ◽  
Flame Stability ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Cellular Flames ◽  
The One ◽  
Inert Surfaces

Abstract A linear stability analysis is performed on two simplified models representing a one-dimensional flame between oxidizer and fuel reservoirs and a two-dimensional “edge-flame” between the same reservoirs but above a cold, inert wall. Comparison of the eigenvalue spectra for both models is performed to discern the validity of extending the results from the one-dimensional problem to the two-dimensional problem. Of primary interest is the influence on flame stability of thermal-diffusive imbalances, i.e. non-unity Lewis numbers. Flame oscillations are observed when Le > 1, and cellular flames are witnessed when Le < 1. It is found that when Le > 1 the characteristics of flame behavior are consistent between the two models. Furthermore, when Le < 1, the models are found to be in good agreement with respect to the magnitude of the critical wave numbers. Results from the coarse mesh analysis of the two-dimensional system are presented and compared to the one-dimensional eigenvalue spectra. Additionally, an examination of low reactant convection is undertaken. It is concluded that for low flow rates the behavior in one and two dimensions are similar qualitatively and quantitatively.

scholarly journals Capillary-induced deformations of a thin elastic sheet

2016 ◽  
Vol 374 (2066) ◽  
pp. 20150169 ◽  
Author(s):  
N. D. Brubaker ◽  
J. Lega
Keyword(s):  
Finite Thickness ◽  
Three Dimensional ◽  
Two Dimensions ◽  
System Of Equations ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Drop Volume ◽  
Exactly Solvable ◽  
Encapsulation Process

We develop a three-dimensional model for capillary origami systems in which a rectangular plate has finite thickness, is allowed to stretch and undergoes small deflections. This latter constraint limits our description of the encapsulation process to its initial folding phase. We first simplify the resulting system of equations to two dimensions by assuming that the plate has infinite aspect ratio, which allows us to compare our approach to known two-dimensional capillary origami models for inextensible plates. Moreover, as this two-dimensional model is exactly solvable, we give an expression for its solution in terms of its parameters. We then turn to the full three-dimensional model in the limit of small drop volume and provide numerical simulations showing how the plate and the drop deform due to the effect of capillary forces.

Two-dimensional magnetophotonic crystal: Exactly solvable model

2005 ◽  
Vol 72 (3) ◽  
Author(s):  
A. B. Khanikaev ◽  
A. V. Baryshev ◽  
M. Inoue ◽  
A. B. Granovsky ◽  
A. P. Vinogradov
Keyword(s):  
Solvable Model ◽  
Two Dimensional ◽  
Exactly Solvable Model ◽  
Exactly Solvable ◽  
Magnetophotonic Crystal

scholarly journals Classical instanton solutions in quantum field theory

2020 ◽  
pp. 78-85
Author(s):  
Roman G. Shulyakovsky ◽  
Alexander S. Gribowsky ◽  
Alexander S. Garkun ◽  
Maxim N. Nevmerzhitsky ◽  
Alexei O. Shaplov ◽  
...  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
Yang Mills ◽  
The One

Instantons are non-trivial solutions of classical Euclidean equations of motion with a finite action. They provide stationary phase points in the path integral for tunnel amplitude between two topologically distinct vacua. It make them useful in many applications of quantum theory, especially for describing the wave function of systems with a degenerate vacua in the framework of the path integrals formalism. Our goal is to introduce the current situation about research on instantons and prepare for experiments. In this paper we give a review of instanton effects in quantum theory. We find in stanton solutions in some quantum mechanical problems, namely, in the problems of the one-dimensional motion of a particle in two-well and periodic potentials. We describe known instantons in quantum field theory that arise, in particular, in the two-dimensional Abelian Higgs model and in SU(2) Yang – Mills gauge fields. We find instanton solutions of two-dimensional scalar field models with sine-Gordon and double-well potentials in a limited spatial volume. We show that accounting of instantons significantly changes the form of the Yukawa potential for the sine-Gordon model in two dimensions.

Collective phenomena in the one-dimensional three-particle model of high-energy potential scattering

1979 ◽  
Vol 57 (7) ◽  
pp. 974-980
Author(s):  
V. I. Inozemtsev
Keyword(s):  
Solvable Model ◽  
Impulse Approximation ◽  
High Energy ◽  
Potential Scattering ◽  
Particle Model ◽  
Collective Phenomena ◽  
Energy Potential ◽  
Exactly Solvable ◽  
The One ◽  
High Energy Scattering

Within the framework of an exactly solvable model of three particles interacting through zero-range forces it is shown that the high-energy scattering with high momentum transfer is due to collective phenomena. The spectrum of particles scattered through 180° is compared with the results of impulse approximation.

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