2020/10/19 by C. Alard, Alard, C.
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2010.09400
openalex publication_date 2020/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Numerical simulations demonstrate a link between dynamically cold initial solutions and an evolution towards self-similarity. However the nature of this link is not fully understood. In this work the link between cold initial conditions and self-similarity near equilibrium is established. The evolution towards self-similarity is analyzed using an analytical solution in a power-law potential. The analytical solution indicates a convergence towards self-similarity after a number of dynamical times even if the inital conditions are far from self-similarity. The power-law model is extended by using perturbative analysis. The perturbative analysis shows that once the power-law potential is initiated it tends to become stronger and propagate. This behavior demonstrates the mechanism behind the convergence towards auto-similarity. The cold solutions are compatible with a broad range of self-similar solutions. As a consequence some seed of a specific self similarity class must appear to induce a convergence mechanism. In practice some local induction of a power-law potential is necessary and some examples of such inductive mechanisms are given.