Self‐avoiding walks with span limitations. I. The mean square end‐to‐end distance

1980 ◽  
Vol 72 (4) ◽  
pp. 2702-2707 ◽  
Author(s):  
Ronnie Barr ◽  
Chava Brender ◽  
Melvin Lax
Keyword(s):  
Mean Square ◽  
End Distance ◽  
The Mean ◽  
End To End ◽  
Self Avoiding Walks

scholarly journals Semiflexible Polymer Enclosed in a 3D Compact Domain

2021 ◽  
Vol 9 ◽  
Author(s):  
Pavel Castro-Villarreal ◽  
J. E. Ramírez
Keyword(s):  
Persistence Length ◽  
Compact Domain ◽  
Mean Square ◽  
Shape Transition ◽  
Conformational States ◽  
Semiflexible Polymer ◽  
End Distance ◽  
The Mean ◽  
End To End ◽  
Polymer Shape

The conformational states of a semiflexible polymer enclosed in a volume V:=ℓ3 are studied as stochastic realizations of paths using the stochastic curvature approach developed in [Rev. E 100, 012503 (2019)], in the regime whenever 3ℓ/ℓp>1, where ℓp is the persistence length. The cases of a semiflexible polymer enclosed in a cube and sphere are considered. In these cases, we explore the Spakowitz–Wang–type polymer shape transition, where the critical persistence length distinguishes between an oscillating and a monotonic phase at the level of the mean-square end-to-end distance. This shape transition provides evidence of a universal signature of the behavior of a semiflexible polymer confined in a compact domain.

MEAN SQUARE SIZE OF POLYELECTROLYTES: ANALOGY WITH THE POLARON PROBLEM

1987 ◽  
Vol 01 (01n02) ◽  
pp. 19-25 ◽  
Author(s):  
D.C. KHANDEKAR ◽  
K.V. BHAGWAT ◽  
F.W. WIEGEL
Keyword(s):  
Electrostatic Interaction ◽  
Path Integrals ◽  
Mean Square ◽  
Polaron Theory ◽  
Polar Crystal ◽  
Formal Analogy ◽  
End Distance ◽  
The Mean ◽  
End To End

We point out that a formal analogy exists between the path integrals for the configuration sum of a polyelectrolyte and for the propagator of a polaron in a polar crystal. Using this analogy and some recent results in polaron theory we evaluate the mean square end-to-end distance <X2> of the polyelectroyte. It is shown that for large polymers the electrostatic interaction does not change the behaviour of <X2> from that of a free polymer.

SPIRAL SELF-AVOIDING WALKS AND LOOPS

1987 ◽  
Vol 01 (05n06) ◽  
pp. 1249-1264 ◽  
Author(s):  
K.Y. LIN
Keyword(s):  
Recent Progress ◽  
Square Lattice ◽  
Exact Results ◽  
End Distance ◽  
The Mean ◽  
Triangular Lattices ◽  
End To End ◽  
Self Avoiding Walks

Since the introduction of spiral self-avoiding walks on the square lattice by Privman in 1983, there has been considerable interest in this model and its generalizations. Recent progress on various models of spiral self-avoiding walks and loops is reviewed. We discuss the methods to derive exact results for (I) the number Sn and the mean end-to-end distance Rn of spiral self-avoiding walks with n steps on the square and triangular lattices, (2) the number Cn of spiral self-avoiding loops with n steps on the square and triangular lattices, (3) the number of anisotropic spiral self-avoiding loops on the square lattice.

PATH-INTEGRAL APPROACH TO A POLYMER CHAIN IN RANDOM MEDIA WITH LONG-RANGE DISORDER CORRELATIONS

2005 ◽  
Vol 19 (29) ◽  
pp. 4381-4387
Author(s):  
CHERDSAK KUNSOMBAT ◽  
VIRULH SA-YAKANIT
Keyword(s):  
Long Range ◽  
Polymer Chain ◽  
Path Integral ◽  
Random Media ◽  
Integral Approach ◽  
Mean Square ◽  
Path Integral Approach ◽  
End Distance ◽  
The Mean ◽  
End To End

In this paper we consider the model of a flexible polymer chain embedded in a quenched random medium with long-range disorder correlations. Using the Feynman path integral approach we show that for the case of long-range quadratic correlations, we obtain an analytical result. The result is [Formula: see text], where 〈R2〉 is the mean square end-to-end distance of the polymer chain, ξ is the correlation length of disorder, Δ is an unknown parameter, b is the Kuhn step length, ρ is the density of random obstacles and N is the number of links. It is shown that for a polymer chain in a random media with long-range quadratic correlations, where ρ is not too high, the behavior of the polymer chain is like that of a free chain. This result agrees with the calculation using the replica method. However, in a medium where ρ is very high, the variation of the mean square end-to-end distance with disorder and its distance depending on ρ are found in our approach.

SELF-AVOIDING WALKS ON THE 4–8 LATTICE

2002 ◽  
Vol 16 (08) ◽  
pp. 1241-1246 ◽  
Author(s):  
KEH YING LIN ◽  
CHI CHEN CHANG
Keyword(s):  
Theoretical Prediction ◽  
Radius Of Gyration ◽  
Mean Square ◽  
Amplitude Ratios ◽  
Connective Constant ◽  
End Distance ◽  
The Mean ◽  
Critical Amplitudes ◽  
Mean Square Distance ◽  
Self Avoiding Walks

We have calculated exactly the number, the mean-square end-to-end distance, the mean-square radius of gyration, and the mean-square distance of a monomer from the origin for self-avoiding walks on the 4–8 lattice up to 42 steps by computer. We estimated the connective constant and the critical amplitudes. Our numerical results are consistent with the theoretical prediction by Cardy and Saleur on the universality for certain amplitude ratios.

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