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A Vibrotactile Feedback Device for Seated Balance Assessment and Training

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Weak-chaos ratchet accelerator.

Itzhack Dana¹, Vladislav B Roitberg

¹Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 30, 2011

Summary

This study introduces a Hamiltonian ratchet accelerator that generates directed momentum current even with weak chaos. The maximal current is observed in the limit of arbitrarily weak chaos, unlike previous models requiring strong chaos.

Area of Science:

Nonlinear dynamics
Statistical mechanics
Chaos theory

Background:

Classical Hamiltonian systems with asymmetric, mixed phase spaces can exhibit chaotic ratchet effects, notably directed momentum currents.
Existing models typically require sufficiently strong chaos for these effects to manifest.

Purpose of the Study:

Introduce a novel Hamiltonian ratchet accelerator.
Demonstrate momentum current generation for arbitrarily weak chaos.
Analyze a generalized kicked rotor system for its chaotic ratchet properties.

Main Methods:

Investigate a generalized kicked rotor model, which is partially exactly solvable.
Derive analytical expressions for the momentum current.
Examine the system's behavior across a range of chaos strengths.

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Main Results:

The proposed Hamiltonian ratchet accelerator generates a momentum current even for arbitrarily weak chaos.
Analytical expressions for the momentum current were obtained.
The maximal momentum current was found to occur in the limit of arbitrarily weak chaos in at least one case.

Conclusions:

The developed Hamiltonian ratchet accelerator overcomes the limitation of requiring strong chaos.
The system provides a tractable model for studying chaotic ratchet effects.
The findings highlight the potential for directed motion in systems with weak chaos.