I am a professor in pure mathematics, with interest in applied problems. I work in the field of partial differential equations and free boundary problems. 


Address: Department of Mathematics, KTH,

Lindstedtsvägen 25,  100 44 Stockholm


Phone: 46-8-7906754
Fax: 46-8-723 17 88
E-mail:
henriksh@kth.se                                       

Henrik Shahgholian

 

The left image is a Boundary Sandpile with initial distribution concentrated at points (34, 0), (-34,0), (0,34), (0,-34) on Z^2, all having mass 40 000, and the boundary capacity is set to 400. The clusters barely survive intersection by one lattice site. On the right, is a Boundary Sandpile having capacity 400, where mass 40 000 is concentrated on each of the sites (33, 0), (-33,0), (0,33), (0,-33).


The pictures indicate instability/jump of Boundary Sandpile process, with regards to the initial mass. Similar situations happen for Bernoulli type free boundary problems.


Paper available at:         Discrete_Balayage_and_Boundary_Sandpile