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We analyzed stochastic motion with a nonlinear Coulomb-tanh friction force, bridging linear and solid friction behaviors. Our findings reveal how this friction model impacts velocity distributions and diffusion coefficients.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Stochastic motion is fundamental in physics.
  • Understanding friction is crucial for modeling real-world systems.
  • Existing models often simplify friction to linear or solid (Coulomb) types.

Purpose of the Study:

  • To investigate stochastic motion under a nonlinear Coulomb-tanh friction force.
  • To analytically and numerically characterize the system's behavior.
  • To bridge the gap between linear friction and solid friction models.

Main Methods:

  • Formal analogy between Fokker-Planck and Schrödinger equations for a quantum oscillator.
  • Analytical treatment of stationary velocity statistics.
  • Agent-based simulations and numerical solutions of the Fokker-Planck equation.

Main Results:

  • The Coulomb-tanh friction interpolates between linear and solid friction behaviors.
  • Analytical solutions for diffusion coefficients were derived and confirmed by simulations.
  • Spatial distribution functions develop exponential tails at intermediate timescales.
  • Velocity distributions and diffusion coefficients approach those of linear or solid friction depending on driving magnitude.

Conclusions:

  • The Coulomb-tanh friction model provides a versatile framework for stochastic motion.
  • This model is applicable to phenomena like shear-thinning environments.
  • The study offers insights into systems where friction is velocity-dependent.