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Journal Nonlinear World №7 for 2015 г.
Article in number:
Behavior of the polymer chains and the structures under the action of random forces
Keywords: Rouse model viscoelastic properties fractal structures fluctuations. Non-Markovian process
Authors:
A.N. Morozov − Dr.Sc. (Phys.-Math.), Professor, Head of Department of Physics, Bauman Moscow State Technical University. E-mail: amor59@mail.ru A.V. Skripkin − Ph.D. (Phys.-Math.), Associate Professor, Department of Physics, Bauman Moscow Technical University. E-mail: a.skripkin@mail.ru
Abstract:
The behavior of the polymer chain and their system (fractal network) in the solution using the Rouse model is considered. It is be-lieved that the first monomer of the polymer chains is charged due to a dissociation. The solution was placed in a random electric field, so the first monomer acts a stochastic force. It is found the equation for the coordinate of the first monomer having the form of a Abel-type stochastic integral equation with index 1 − D / 2 , where D is a fractal dimension of the network of the polymer chains in the solution. Using the theory of non-Markovian processes are found characteristic functions for the coordinates of the first monomer, and then the mean and the variance for different D. In the steady state is determined the power spectral density of the fluctuations coordinates. The given density is a type of so-called colored noise. The exact nature of the noise depends on the parameter D. For example, for a purely three-dimensional network structure it refers to flicker noise.
Pages: 33-37
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