Dynamics of roughening and growth of two-dimensional self-avoiding walks

1988 ◽  
Vol 66 (2) ◽  
pp. 187-191 ◽  
Author(s):  
Dietrich Stauffer ◽  
Naeem Jan
Keyword(s):  
Critical Temperature ◽  
Critical Point ◽  
Radius Of Gyration ◽  
Small Ring ◽  
Two Dimensional ◽  
Lattice Fluid ◽  
Length Increase ◽  
The One ◽  
Self Avoiding Walks ◽  
Surface Length

The one-dimensional surface of a two-dimensional lattice fluid is simulated by a method producing self-avoiding walks of varying lengths. Below the critical temperature, the surface width varies as the square root of the surface length in equilibrium, and at the critical point it varies as (time)1/3. Above the critical temperature, the width and the length of the surface increases initially as (time)1/2, whereas finally the "surface" fills the whole lattice. If, instead, we start above the critical point from a small ring, its squared radius of gyration and its length increase initially as (time)2/3. At the critical point, this growth from a small ring gives an average radius proportional to (length)0.75, as for self-avoiding walks.

Phase Diagram of a Two-Dimensional Dilute Binary Alloy

1997 ◽  
Vol 08 (02) ◽  
pp. 139-146 ◽  
Author(s):  
G. K. Khalil ◽  
K. Yaldram ◽  
A. Sadiq
Keyword(s):  
Phase Diagram ◽  
Critical Temperature ◽  
Binary Alloy ◽  
Vacancy Concentration ◽  
Linear Trend ◽  
Nearest Neighbors ◽  
Two Dimensional ◽  
Interaction Energies ◽  
Atomic Interactions ◽  
The One

Phase diagrams of two-dimensional binary alloy with vacancies (ABV) is studied with pairwise interaction εAA, εBB, and εAB between the nearest neighbors. Attention is focussed on the case where the vacancies are annealed and εBA = ε, εAA= εBB=0. For vacancy concentrations cv<0.2, the critical temperature decreases linearly with cv. The vacancies remain randomly distributed within the A and B phase separated regions. For cv>0.2 the critical temperature no longer shows this linear trend and falls to zero very sharply at cv=0.39. This critical vacancy concentration is slightly lower than the one expected for quenched vacancies, where the percolation threshold of atomic species is 0.59 (cv=0.41). The mobility of vacancies and the nature of atomic interactions makes it energetically favorable for the vacancies to occupy the boundary layers between A and B phase separated regions, thus making the process of phase separation difficult. This lowers the critical temperature below that of the case where the vacancies are quenched. Salient features of the phase diagram are discussed by comparison with previously studied similar systems with different interaction energies.

F.VIII R:Ag in Hepatitis

1979 ◽  
Author(s):  
R. Kotitschke ◽  
J. Scharrer
Keyword(s):  
Chronic Hepatitis ◽  
Blood Donors ◽  
Blood Donation ◽  
Normal Population ◽  
Rabbit Antiserum ◽  
Two Dimensional ◽  
Plastic Plate ◽  
Significant Difference ◽  
Acute Hepatitis B ◽  
The One

F.VIII R:Ag was determined by quantitative immunelectrophoresis (I.E.) with a prefabricated system. The prefabricated system consists of a monospecific f.VIII rabbit antiserum in agarose on a plastic plate for the one and two dimensional immunelectrophoresis. The lognormal distribution of the f.VIII R:Ag concentration in the normal population was confirmed (for n=70 the f.VIII R:Ag in % of normal is = 95.4 ± 31.9). Among the normal population there was no significant difference between blood donors (one blood donation in 8 weeks; for n=43 the f.VIII R:Ag in % of normal is = 95.9 ± 34.0) and non blood donors (n=27;f.VIII R:Ag = 94.6 ± 28.4 %). The f.VIII R:Ag concentration in acute hepatitis B ranged from normal to raised values (for n=10, a factor of 1.8 times of normal was found) and was normal again after health recovery (n=10, the factor was 1.0). in chronic hepatitis the f.VIII R:Ag concentration was raised in the majority of the cases (for n=10, the factor was 3.8). Out of 22 carrier sera 20 showed reduced, 2 elevated levels of the f.VIII R:Ag concentration. in 5 sera no f.VIII R:Ag could be demonstrated. The f.VIII R:Ag concentration was normal for n=10, reduced for n=20 and elevated for n=6 in non A-non B hepatitis (n=36). Contrary to results found in the literature no difference in the electrophoretic mobility of the f.VIII R:Ag was found between hepatitis patients sera and normal sera.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

Two dimensional CrGa2Se4: A spin-gapless ferromagnetic semiconductor with inclined uniaxial anisotropy

Nanoscale ◽  
2021 ◽  
Author(s):  
Qian Chen ◽  
Ruqian Wang ◽  
Zhaocong Huang ◽  
Shijun Yuan ◽  
Haowei Wang ◽  
...  
Keyword(s):  
Critical Temperature ◽  
Material Science ◽  
2D Materials ◽  
Uniaxial Anisotropy ◽  
Magnetic Semiconductor ◽  
Ferromagnetic Semiconductor ◽  
Two Dimensional ◽  
High Critical Temperature

The magnetic semiconductor with high critical temperature has long been the focus in material science and recently is also known as one of the fundamental questions in two-dimensional (2D) materials....

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...

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals Two-dimensional self-avoiding walks on a cylinder

1999 ◽  
Vol 59 (1) ◽  
pp. R16-R19 ◽  
Author(s):  
Helge Frauenkron ◽  
Maria Serena Causo ◽  
Peter Grassberger
Keyword(s):  
Two Dimensional ◽  
Self Avoiding Walks
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