Diffusion in an ultrametric space : a simple case

Diffusion in an ultrametric space : a simple case

Percolation in an ultrametric space

We study percolation in the hierarchical lattice of order N where the probability of connection between two points separated by distance k is of the form ck/N , δ > −1. Since the distance is an ultrametric, there are significant differences with percolation in the Euclidean lattice. We consider three regimes: δ < 1, where percolation occurs, δ > 1, where it does not occur, and δ = 1 which is th...

Non Degenerate Ultrametric Diffusion

General non-degenerate p-adic operators of ultrametric diffusion are introduced. Bases of eigenvectors for the introduced operators are constructed and the corresponding eigenvalues are computed. Properties of the corresponding dynamics (i.e. of the ultrametric diffusion) are investigated.

, interbasin kinetics and ultrametric diffusion

We discuss the interbasin kinetics approximation for random walk on a complex landscape. We show that for a generic landscape the corresponding model of interbasin kinetics is equivalent to an ultrametric diffusion, generated by an ultrametric pseudodifferential operator on the ultrametric space related to the tree of basins. The simplest example of ultrametric diffusion of this kind is describ...

Lipoma of Paraglottic Space in a Child: A Case Report

Introduction: Lipomas of the larynx are very rare benign lesions; macroscopically, they resemble retention cysts, so their diagnosis is usually made after surgery.   Case Report: A rare case of pediatric paraglottic space Lipoma in an 11-year-old boy is explained. The mass was mobile, soft, without fluctuation or pulsation. CT scan revealed a 5.7 cm cervical fat density with regional lymphadeno...