Memory effects for a trapped Brownian particle in viscoelastic shear flows
Romi Mankin1, Katrin Laas, Neeme Lumi
1Institute of Mathematics and Natural Sciences, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 16, 2013
Summary
This study investigates Brownian particle motion in a fluctuating potential under shear flow. It reveals how shear, memory, and noise induce complex behaviors like anomalous diffusion and dynamical transitions.
Area of Science:
- Statistical Mechanics
- Soft Matter Physics
- Nonlinear Dynamics
Background:
- Brownian motion is fundamental to understanding particle dynamics in complex fluids.
- Viscoelastic shear flow and fluctuating potentials significantly alter particle trajectories.
- Generalized Langevin equations model complex memory effects in particle dynamics.
Purpose of the Study:
- Investigate the long-time behavior of an underdamped Brownian particle.
- Analyze dynamics under oscillatory viscoelastic shear flow and a fluctuating harmonic potential.
- Explore the influence of multiplicative and additive noise on particle distribution.
Main Methods:
- Utilized the generalized Langevin equation with a power-law memory kernel.
- Modeled environmental fluctuations using multiplicative white noise and fractional Gaussian noise.
- Calculated exact expressions for second-order moments of particle position.
Main Results:
- Identified shear-induced cross-correlations and angular momentum.
- Demonstrated cooperation effects: energetic instability, multiresonance, and anomalous diffusion.
- Discovered two critical memory exponents signaling dynamical transitions (stationary, subdiffusive, superdiffusive).
Conclusions:
- The interplay of shear flow, memory, and multiplicative noise drives complex system dynamics.
- Memory exponents dictate transitions between different diffusion regimes.
- Findings offer insights into particle behavior in complex, fluctuating environments.
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