Transport with multiple-rate exchange in disordered media.

Area of Science:

• Statistical Physics
• Transport Phenomena
• Complex Systems

Background:

• Particle transport is fundamental in various scientific disciplines.
• Understanding the interplay of transition and exchange dynamics is crucial for modeling complex systems.
• Disorder at micro and macro scales significantly impacts transport behavior.

Purpose of the Study:

• To investigate particle transport under exchange mechanisms using the continuous-time random-walk (CTRW) framework.
• To analyze how macroscale and microscale disorder influence particle transition and exchange.
• To determine the conditions under which transition or exchange dominates asymptotic transport.

Main Methods:

• Utilized the continuous-time random-walk (CTRW) framework to model particle transport.
• Employed the multiple-rate exchange model to represent diverse exchange mechanisms.
• Derived the crossing-time density, h(t;L), dependent on microscale (g) and joint (f) disorder functions.

Main Results:

• Identified two distinct regions of asymptotic transport dominance based on power-law exponents (eta, alpha(tau), alpha(mu)).
• Demonstrated that microscale disorder (eta) and macroscale disorder (alpha(tau), alpha(mu)) jointly define transport behavior.
• Showed that for uniform exchange, both transition and exchange influence late-time behavior, with microscale exchange dominating if eta<0 or if eta>0 and transition is asymptotically Gaussian.

Conclusions:

• The CTRW framework effectively models particle transport with exchange influenced by multi-scale disorder.
• The interplay between transition and exchange dynamics, governed by disorder characteristics, dictates transport regimes.
• Specific conditions on disorder exponents determine whether transition or exchange ultimately dominates particle movement.