Competition between Diffusion and Fragmentation: An Important Evolutionary Process of Nature

2003/10/31 by Jesper Ferkinghoff‐Borg, Jesper Ferkinghoff-Borg, Mogens H. Jensen +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Protein Structure and Dynamics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #q-bio.QM

paper · pdf · doi:10.1103/physrevlett.91.266103

published as Phys. Rev. Lett. 91, 266103 (2003) · 4 pages, 3 figures, (minor changes)

openalex publication_date 2003/12/23 · arxiv created 2003/12/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we solve exactly in terms of Bessel functions. The stationary state is a universal Bessel distribution described by one parameter, which fits perfectly experimental data from two very different systems of nature, namely, the distribution of ice-crystal sizes from the Greenland ice sheet and the length distribution of alpha helices in proteins.

Citations

• Dictionary of protein secondary structure: Pattern recognition of hydrogen‐bonded and geometrical features

Related

• The fragmentation equation with size diffusion: Small and large size behavior of stationary solutions
• Investigation of the kinetic equation of cascade fragmentation theory at not self-similar subdivision
• A spatially-dependent fragmentation process
• Habitat fragmentation: the possibility of a patch disrupting its neighbor
• Statistical properties of fragment isospin in multifragmentation