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Internal and External Forces01:12

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Newton's first law states that a net external force causes a change in motion. External forces act on an object or system, originating outside of the object or system. In contrast, internal forces originate inside the system of interest and do not lead to any acceleration. In simpler words, internal forces are forces that act on one part of an object and are exerted by another part of the same object. External forces are forces that act on an object due to some other object. Therefore, when...
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Related Experiment Video

Updated: Jun 16, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Anomalous diffusion in external-force-affected deterministic systems.

Jin Liu1, Kehui Sun1, Huihai Wang2

  • 1School of Physics, <a href="https://ror.org/00f1zfq44">Central South University</a>, Changsha 410083, China.

Physical Review. E
|August 20, 2024
PubMed
Summary
This summary is machine-generated.

External forces significantly alter particle movement, causing anomalous diffusion and ergodicity breaking. Linear forces mimic urn models, while sinusoidal forces create fractal diffusion patterns.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Brownian motion and normal diffusion are fundamental concepts in statistical physics.
  • Understanding particle dynamics under external forces is crucial for various scientific fields.
  • Piecewise linear maps provide simplified models for complex dynamical systems.

Purpose of the Study:

  • To investigate the influence of position-dependent linear and time-dependent sinusoidal external forces on particle movement.
  • To analyze the resulting diffusion patterns, including ensemble-averaged mean-squared displacement (EAMSD), aging, and ergodicity.
  • To characterize the dynamical behavior and compare it with established models like the Langevin equation and Markov chains.

Main Methods:

  • Numerical simulations of a box piecewise linear map model.
  • Analysis of particle trajectories under two distinct external force types.
  • Calculation and examination of the ensemble-averaged mean-squared displacement (EAMSD).
  • Characterization of diffusion patterns, aging, and ergodicity breaking.

Main Results:

  • Anomalous dynamical behavior observed, including nonlinear EAMSD growth, aging, and ergodicity breaking.
  • Linear forces result in diffusion resembling an Ehrenfest double urn model, aligning with Langevin equation predictions.
  • Sinusoidal forces lead to particle movement akin to an inhomogeneous Markov chain, with fractal diffusion coefficient structures.
  • Insights into the formation of fractal structures via turnstiles dynamics.

Conclusions:

  • External forces introduce significant deviations from normal diffusion, leading to complex dynamics.
  • The type of external force dictates the specific diffusion behavior and its underlying model.
  • The study reveals fractal characteristics in diffusion under periodic forces, offering new perspectives on particle dynamics.