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A new iterative method models time-dependent nonlocal transport in complex 2D systems. It extends previous work using continuous-time random walk concepts and memory effects for accurate wave propagation analysis.

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Area of Science:

  • Physics
  • Applied Mathematics
  • Complex Systems

Background:

  • Nonlocal transport phenomena are crucial in various scientific fields.
  • Existing methods often struggle with time-dependent behavior in complex geometries.
  • Steady-state transport problems have been addressed by iterative methods.

Purpose of the Study:

  • To develop a novel methodology for describing time-dependent nonlocal transport.
  • To extend the iterative method to handle dynamic phenomena.
  • To incorporate memory effects into transport models.

Main Methods:

  • Extension of the iterative method for steady-state problems.
  • Application of continuous-time random walk (CTRW) concepts.
  • Explicit evaluation of the time integral in the CTRW master equation.
  • Utilization of a modified Mittag-Leffler function for memory effects.

Main Results:

  • A robust methodology for time-dependent nonlocal transport is established.
  • The technique successfully models 'anomalous transport waves'.
  • The impact of memory effects on wave propagation is analyzed.

Conclusions:

  • The developed method provides a powerful tool for analyzing complex transport phenomena.
  • It offers insights into systems with and without memory effects.
  • This approach enhances the understanding of dynamic processes in intricate geometries.