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Relaxation dynamics of an elastic string in random media
1Department of Physics, University of Seoul, Seoul 130-743, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
The relaxation dynamics of an elastic string in random media is governed by thermal fluctuations. Its correlation length grows logarithmically with time, indicating energy barriers dictate string movement.
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Soft matter physics
Background:
- Elastic strings in random media exhibit complex dynamics influenced by thermal fluctuations.
- Understanding relaxation processes is crucial for materials science and polymer physics.
Purpose of the Study:
- To numerically investigate the relaxation dynamics of an elastic string in 2D random media.
- To characterize the time evolution of spatial fluctuations and correlation length.
- To identify the underlying mechanisms driving the relaxation process.
Main Methods:
- Numerical simulations of an elastic string in a two-dimensional random medium.
- Analysis of spatial fluctuations in the string's mean position.
- Measurement of correlation length growth over time.
Main Results:
- Correlation length grows logarithmically with time: xi approximately (ln t)1/chi.
- Relaxation dynamics are driven by thermal activations over energy barriers scaling as EB(l) approximately l;chi.
- The energy barrier exponent chi is found to be equal to the energy fluctuation exponent chi=1/3.
- A long transient regime with power-law dynamics (xi approximately t1/z) was observed.
Conclusions:
- The study reveals logarithmic growth of correlation length, characteristic of thermal activation over random energy barriers.
- Numerical evidence supports the universality of the energy barrier exponent.
- The observed transient scaling suggests complex relaxation dynamics on ramified disordered structures.
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