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Fluctuations in a diffusive medium with gain.

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Summary
This summary is machine-generated.

We developed a stochastic model for amplifying, diffusive media, revealing that multiplicative random-advection causes intermittency and power-law energy distributions, especially in smaller samples and lower dimensions.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Amplifying, diffusive media exhibit complex energy field dynamics.
  • Understanding intermittency and power-law distributions is crucial in these systems.

Purpose of the Study:

  • To develop a stochastic model for amplifying, diffusive media.
  • To investigate the origins of intermittency and power-law distributions in energy fields.

Main Methods:

  • Developed a stochastic model based on a random-walk approach.
  • Derived a stochastic partial differential equation for the energy field.
  • Incorporated a multiplicative random-advection term.

Main Results:

  • The model predicts intermittency and power-law distributions for the energy field.
  • Dimensional analysis suggests these features are more pronounced in smaller samples.
  • Lower spatial dimensions enhance the likelihood of observing these phenomena.

Conclusions:

  • The derived stochastic model effectively captures intermittency in amplifying, diffusive media.
  • The presence of multiplicative random-advection is key to generating power-law distributions.
  • Experimental observations of these features are favored under specific conditions (small samples, low dimensions).