Numerical calculations on lattice chains

An alternative approach to equation (31) is based on lattice model walks with some site potential energy to simulate chain contact repulsion. A key feature of this approach is the use of the generating functions  

For the case of fully developed excluded volume limit, the exact enumeration method consists of carrying out enumerations of the number, C , of all possible nonintersecting random walks of n steps on a lattice and the number, f (/ )A/ , of those walks whose end points lie between R and R -h A/ from the origin. Since all possible configurations are a priori equally possible 

There is an alternative method, called the Monte Carlo method, to obtain v where nonintersecting random walks are simulated on various lattices and statistical data describing the chain are accumulated. This method is restricted in accuracy by statistical fluctuations in contrast to the exact enumeration method. But long walks can be studied here. This method has been applied to understand a variety of phenomena involving polymers as reviewed in refs. 73-75. 

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