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Oscillations in Aggregation-Shattering Processes.

S A Matveev1,2,3, P L Krapivsky4, A P Smirnov2,3

  • 1Skolkovo Institute of Science and Technology, 143026 Moscow, Russia.

Physical Review Letters
|January 13, 2018
PubMed
Summary
This summary is machine-generated.

Never-ending oscillations occur in aggregation-shattering systems. These persistent oscillations emerge in specific parameter ranges, challenging previous assumptions about system dynamics without particle loss.

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Area of Science:

  • Physics
  • Chemistry
  • Materials Science

Background:

  • Collision-controlled aggregation and shattering are fundamental processes in various scientific domains.
  • Understanding the long-term dynamics of such systems is crucial for predicting material properties and evolution.

Purpose of the Study:

  • To investigate the emergence and persistence of oscillations in aggregation-shattering systems.
  • To determine the conditions under which these oscillations become never-ending.

Main Methods:

  • Analytical solutions for stationary cluster size distribution.
  • Numerical solutions of rate equations for aggregation-shattering processes.
  • Investigation of aggregation kernels K_{i,j}=(i/j)^{a}+(j/i)^{a} and shattering kernels F_{i,j}=λK_{i,j}.

Main Results:

  • Monotonic approach to a steady state for 0≤a<1/2 across all shattering strengths (λ).
  • Emergence of oscillations in the 1/2
  • Persistence of oscillations for shattering strengths below a critical value λ_{c}(a), indicating never-ending oscillations.

Conclusions:

  • Never-ending oscillations are possible in closed aggregation-shattering systems.
  • The interplay between aggregation and shattering kernels dictates the system's dynamic behavior.
  • Parameter 'a' in the aggregation kernel plays a critical role in the onset of oscillatory behavior.