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Scaling properties of a moving polymer. (English) Zbl 1504.60102

Summary: We set up an SPDE model for a moving, weakly self-avoiding polymer with intrinsic length \(J\) taking values in \((0,\infty)\). Our main result states that the effective radius of the polymer is approximately \({J^{5/3}}\); evidently for large \(J\) the polymer undergoes stretching. This contrasts with the equilibrium situation without the time variable, where many earlier results show that the effective radius is approximately \(J\).
For such a moving polymer taking values in \({\mathbb{R}^2}\), we offer a conjecture that the effective radius is approximately \({J^{5/4}}\).

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
82D60 Statistical mechanics of polymers
60H40 White noise theory
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