Two-dimensional random walk and loop factor in helix-coil transition theory of DNA

2011 ◽  
Vol 46 (5) ◽  
pp. 242-246 ◽  
Author(s):  
G. N. Hayrapetyan ◽  
Y. Sh. Mamasakhlisov ◽  
V. F. Morozov ◽  
Vl. V. Papoyan ◽  
V. B. Priezzhev
Keyword(s):  
Random Walk ◽  
Transition Theory ◽  
Two Dimensional ◽  
Coil Transition

THE HELIX-COIL TRANSITION IN A DOUBLE-STRANDED POLYNUCLEOTIDE AND THE TWO-DIMENSIONAL RANDOM WALK

2012 ◽  
Vol 26 (13) ◽  
pp. 1250083
Author(s):  
G. N. HAYRAPETYAN ◽  
V. F. MOROZOV ◽  
V. V. PAPOYAN ◽  
S. S. POGHOSYAN ◽  
V. B. PRIEZZHEV
Keyword(s):  
Random Walk ◽  
Hydrogen Bonds ◽  
Polymer Chains ◽  
Square Lattice ◽  
Two Dimensional ◽  
Competing Interactions ◽  
New Approach ◽  
Rich Phase ◽  
Coil Transition ◽  
The Rich

The helix-coil transition in a double-stranded homopolynucleotide is considered. The new approach to the melted loops account is proposed. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of hydrogen bonds between complementary units. To take into account the interaction of monomers inside the chains, we consider various regimes of return to the origin. One of them involves two competing interactions and demonstrates a nontrivial sharp denaturation transition. The rich phase behavior of the double-stranded homopolynucleotide is discussed in terms of the proposed approach.

A non-Wiener random walk in a two-dimensional Bernoulli environment

1988 ◽  
Vol 50 (3-4) ◽  
pp. 599-609
Author(s):  
A. Kr�mli ◽  
P. Luk�cs ◽  
D. Sz�sz
Keyword(s):  
Random Walk ◽  
Two Dimensional

scholarly journals Quantum walks and elliptic integrals

2010 ◽  
Vol 20 (6) ◽  
pp. 1091-1098 ◽  
Author(s):  
NORIO KONNO
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Elliptic Integral ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Elliptic Integrals ◽  
Two Dimensional ◽  
One Dimensional ◽  
Similar Expression ◽  
Return Probability

Pólya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional quantum walk.

scholarly journals Two-dimensional Quantum Random Walk

2010 ◽  
Vol 142 (1) ◽  
pp. 78-107 ◽  
Author(s):  
Yuliy Baryshnikov ◽  
Wil Brady ◽  
Andrew Bressler ◽  
Robin Pemantle
Keyword(s):  
Random Walk ◽  
Two Dimensional ◽  
Quantum Random Walk

Magnetic Breakdown in a dislocated lattice

1965 ◽  
Vol 287 (1409) ◽  
pp. 165-182 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Random Walk ◽  
Dislocation Density ◽  
Network Model ◽  
Random Phase ◽  
Two Dimensional ◽  
Magnetic Breakdown ◽  
Low Dislocation Density ◽  
Electron Orbit ◽  
Straight Lines

The network model of electron orbits coupled by magnetic breakdown is extended to a two dimensional metal containing dislocations. It is shown that the network is still likely to be a valid representation, but the phase lengths of the arms are altered, and a very low dislocation density (about one per electron orbit) is enough to produce almost complete randomization. The Bloch-like quasi-particles that can travel in straight lines on a perfect network are now heavily scattered, and it is preferable to think of electrons performing a random walk on the arms of the network, although the justification for this procedure is somewhat doubtful. A simpler alternative to Falicov & Sievert’s method is presented for calculating the electrical conductivity of a random-phase network, and is extended to cases where randomness affects only some of the phases, as is believed to be the situation in real metals like zinc and magnesium.

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