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<p>We investigate the dynamics of a continuous cluster-eating particle aggregation system as modelled in the literature by the Redner–Ben–Avraham–Kahng (RBK) aggregation equation (Redner et al. in J. Phys. A, 20:1231, 1987). The original model proposed is in the finite-dimensional discrete framework. Therefore, the passage from the original discrete RBK equation to the continuous framework is also established. This model is characterized by unusual cluster-eating or annihilation property which inherently loses particle mass and hence is unable to attain a stationary-state solution. Therefore to overcome this mass loss, terms representing particle addition and extraction are injected into the system and the dynamical behaviour of the new model is analysed. The existence of a stationary-state solution is attained through a dynamical approach. This includes the estimates of the significant quantities and moments in order to stabilize the system. Further emphasizing the theoretical results, numerical simulations are presented to visualize both failure and attainment of a stationary-state solution.</p>

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Stationary-state solutions to the continuous Redner–Ben–Avraham–Kahng cluster system due to injection of source and efflux

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Farel William Viret Kharchandy,
  • Vamsinadh Thota,
  • Jitraj Saha

摘要

We investigate the dynamics of a continuous cluster-eating particle aggregation system as modelled in the literature by the Redner–Ben–Avraham–Kahng (RBK) aggregation equation (Redner et al. in J. Phys. A, 20:1231, 1987). The original model proposed is in the finite-dimensional discrete framework. Therefore, the passage from the original discrete RBK equation to the continuous framework is also established. This model is characterized by unusual cluster-eating or annihilation property which inherently loses particle mass and hence is unable to attain a stationary-state solution. Therefore to overcome this mass loss, terms representing particle addition and extraction are injected into the system and the dynamical behaviour of the new model is analysed. The existence of a stationary-state solution is attained through a dynamical approach. This includes the estimates of the significant quantities and moments in order to stabilize the system. Further emphasizing the theoretical results, numerical simulations are presented to visualize both failure and attainment of a stationary-state solution.