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In polymer physics, random walk describes an ideal chain. It is the simplest model to study polymers. [37] In other fields of mathematics, random walk is used to calculate solutions to Laplace's equation, to estimate the harmonic measure, and for various constructions in analysis and combinatorics.
The simplest formulation of excluded volume is the self-avoiding random walk, a random walk that cannot repeat its previous path. A path of this walk of N steps in three dimensions represents a conformation of a polymer with excluded volume interaction. Because of the self-avoiding nature of this model, the number of possible conformations is ...
A topological problem in polymer physics: configurational and mechanical properties of a random walk enclosing a constant are; D. Shortle and M. Ackerman, Persistence of native-like topology in a denatured protein in 8 M urea, Science 293 (2001), pp. 487–489
An ideal chain (or freely-jointed chain) is the simplest model in polymer chemistry to describe polymers, such as nucleic acids and proteins.It assumes that the monomers in a polymer are located at the steps of a hypothetical random walker that does not remember its previous steps.
The pivot algorithm works by taking a self-avoiding walk and randomly choosing a point on this walk, and then applying symmetrical transformations (rotations and reflections) on the walk after the n th step to create a new walk. Calculating the number of self-avoiding walks in any given lattice is a common computational problem. There is ...
The polymer chain will behave exactly as predicted by the random walk or ideal chain model. This makes experimental determination of important quantities such as the root mean square end-to-end distance or the radius of gyration much simpler. Additionally, the theta condition is also satisfied in the bulk amorphous polymer phase. Thus, the ...
The free energy change per volume is just: = = (+ +) where is the number of strands in network, the subscript "def" means "deformation", = /, which is the number density per volume of polymer chains, = / which is the ratio between the end-to-end distance of the chain and the theoretical distance that obey random walk statistics.
Short random chain. One extremely naive yet fruitful approach to quantitatively analyze the spatial structure and configuration of a polymer is the free random walk model. . The polymer is depicted as a chain of point like unit molecules which are strongly bound by chemical bonds and hence the mutual distance between successive units can be approximated to be const