Finite Size Effects in Addition and Chipping Processes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911789420118016 |
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| author | Dyachenko, Roman R. Matveev, Sergey A. Krapivsky, P. L. |
| author_facet | Dyachenko, Roman R. Matveev, Sergey A. Krapivsky, P. L. |
| contents | We investigate analytically and numerically a system of clusters evolving via collisions with clusters of minimal mass (monomers). Each collision either leads to the addition of the monomer to the cluster or the chipping of a monomer from the cluster, and emerging behaviors depend on which of the two processes is more probable. If addition prevails, monomers disappear in a time that scales as $\ln N$ with the total mass $N\gg 1$, and the system reaches a jammed state. When chipping prevails, the system remains in a quasi-stationary state for a time that scales exponentially with $N$, but eventually, a giant fluctuation leads to the disappearance of monomers. In the marginal case, monomers disappear in a time that scales linearly with $N$, and the final supercluster state is a peculiar jammed state, viz., it is not extensive. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_13111 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite Size Effects in Addition and Chipping Processes Dyachenko, Roman R. Matveev, Sergey A. Krapivsky, P. L. Statistical Mechanics Numerical Analysis Classical Analysis and ODEs Statistics Theory Adaptation and Self-Organizing Systems 82M31, 65L07, 65L99, 60G99 I.6.1; G.1.7; G.1.1 We investigate analytically and numerically a system of clusters evolving via collisions with clusters of minimal mass (monomers). Each collision either leads to the addition of the monomer to the cluster or the chipping of a monomer from the cluster, and emerging behaviors depend on which of the two processes is more probable. If addition prevails, monomers disappear in a time that scales as $\ln N$ with the total mass $N\gg 1$, and the system reaches a jammed state. When chipping prevails, the system remains in a quasi-stationary state for a time that scales exponentially with $N$, but eventually, a giant fluctuation leads to the disappearance of monomers. In the marginal case, monomers disappear in a time that scales linearly with $N$, and the final supercluster state is a peculiar jammed state, viz., it is not extensive. |
| title | Finite Size Effects in Addition and Chipping Processes |
| topic | Statistical Mechanics Numerical Analysis Classical Analysis and ODEs Statistics Theory Adaptation and Self-Organizing Systems 82M31, 65L07, 65L99, 60G99 I.6.1; G.1.7; G.1.1 |
| url | https://arxiv.org/abs/2307.13111 |