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We have developed an improved algorithm that allows us to enumerate the number of site animals (polyominoes) on the square lattice up to size 46. Analysis of the resulting series yields an improved estimate, τ = 4.062570(8), for the growth constant of lattice animals and confirms to a very high degree of certainty that the generating function has a… (More)

We have developed an improved algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 90. Analysis of the resulting series yields very accurate estimates of the connective constant µ = 2.63815852927(1) (biased) and the critical exponent α = 0.5000005(10) (unbiased). The critical point is… (More)

- Iwan Jensen
- 2004

We calculate improved lower bounds for the connective constants for self-avoiding walks on the square, hexagonal, triangular, (4.8 2), and (3.12 2) lattices. The bound is found by Kesten's method of irreducible bridges. This involves using transfer-matrix techniques to exactly enumerate the number of bridges of a given span to very many steps. Upper bounds… (More)

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation… (More)

- Iwan Jensen
- 2001

We have developed an improved algorithm that allows us to enumerate the number of site animals on the square lattice up to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyration of both lattice animals and trees up to size 42. Analysis of the resulting series yields an improved estimate, λ = 4.062570(8), for the… (More)

The input from serotonin-containing nerve fibres to rabbit sympathetic preganglionic neurons projecting to either the superior cervical ganglion or the adrenal medulla was investigated by combining retrograde tracing with the B subunit of cholera toxin and immunocytochemistry for serotonin. There were pronounced rostrocaudal variations in the density of… (More)

The exact enumeration of most interesting combinatorial problems has exponential computational complexity. The finite-lattice method reduces this complexity for most two-dimensional problems. The basic idea is to enumerate the problem on small finite lattices using a transfer-matrix formalism. Systematically grow the size of the lattices and combine the… (More)

- Iwan Jensen
- 2000

A closed plane meander of order n is a closed self-avoiding curve intersecting an infinite line 2n times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on transfer matrix methods, for the enumeration of plane meanders. While the algorithm has exponential complexity, its… (More)

- Iwan Jensen
- 2004

We calculate improved lower bounds for the connective constants for self-avoiding walks on the square, hexagonal, triangular, (4.8 2), and (3.12 2) lattices. The bound is found by Kesten's method of irreducible bridges. This involves using transfer-matrix techniques to exactly enumerate the number of bridges of a given span to very many steps. Upper bounds… (More)

- Iwan Jensen
- 2008

A new algorithm for the derivation of low-density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems. Numerical evidence shows that the computational complexity grows exponentially, but with a growth factor λ < 8 √ 2, which is much smaller than the growth factor λ = 4 √ 2 of the previous best… (More)