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pro vyhledávání: '"Beaton, Nicholas R"'
We consider partially directed walks crossing a $L\times L$ square weighted according to their length by a fugacity $t$. The exact solution of this model is computed in three different ways, depending on whether $t$ is less than, equal to or greater
Externí odkaz:
http://arxiv.org/abs/2212.09200
Autor:
Beaton, Nicholas R., Holmes, Mark
We give an explicit formula for the mean square displacement of the random walk on the $d$-dimensional Manhattan lattice after $n$ steps, for all $n$ and all dimensions $d \geq 2$.
Externí odkaz:
http://arxiv.org/abs/2206.12999
Autor:
Beaton, Nicholas R., Ishihara, Kai, Atapour, Mahshid, Eng, Jeremy W., Vazquez, Mariel, Shimokawa, Koya, Soteros, Christine E.
It has been conjectured that the exponential growth rate of the number of lattice polygons with knot-type $K$ is the same as that for unknot polygons, and that the entropic critical exponent increases by one for each prime knot in the knot decomposit
Externí odkaz:
http://arxiv.org/abs/2204.06186
Autor:
Beaton, Nicholas R.
We consider walks on the edges of the square lattice $\mathbb Z^2$ which obey \emph{two-step rules,} which allow (or forbid) steps in a given direction to be followed by steps in another direction. We classify these rules according to a number of cri
Externí odkaz:
http://arxiv.org/abs/2010.06955
We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pairs of directed lattice paths. In three dimensions the solutions are wr
Externí odkaz:
http://arxiv.org/abs/2007.02495
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We study a model of a semiflexible long chain polymer confined to a two-dimensional slit of width $w$, and interacting with the walls of the slit. The interactions with the walls are controlled by Boltzmann weights $a$ and $b$, and the flexibility of
Externí odkaz:
http://arxiv.org/abs/1912.00151
We investigate, by series methods, the behaviour of interacting self-avoiding walks (ISAWs) on the honeycomb lattice and on the square lattice. This is the first such investigation of ISAWs on the honeycomb lattice. We have generated data for ISAWs u
Externí odkaz:
http://arxiv.org/abs/1911.05852
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site percolation on $
Externí odkaz:
http://arxiv.org/abs/1908.07203
Lattice paths in the quarter plane have led to a large and varied set of results in recent years. One major project has been the classification of step sets according to the properties of the corresponding generating functions, and this has involved
Externí odkaz:
http://arxiv.org/abs/1905.10908