arXiv subjects

Bijan Mohammadi

Publications and source records attributed to Bijan Mohammadi.

3 recordsLinked to original sources

arXiv2026

The Elusive Relatively K-Unstable Delzant Octagon: A Numerical Search

Relative K-stability of toric varieties can be tested through explicit Donaldson-Futaki computations, yet finding unstable examples remains challenging. We develop a reproducible symbolic-numeric framework to investigate all fifteen families of Delzant octagons corresponding to smooth toric surfaces of Picard rank six. While numerical optimization identifies several apparently destabilizing configurations, exact rational reconstruction systematically removes the observed instability. We explain why Wang and Zhou's 2014 tentative construction of a relatively K-unstable octagon does not allow to find an explicit example.

math.AG↗

arXiv2018

Numerical upper bounds on growth of automata groups

The growth of a finitely generated group is an important geometric invariant which has been studied for decades. It can be either polynomial, for a well-understood class of groups, or exponential, for most groups studied by geometers, or intermediate, that is between polynomial and exponential. Despite recent spectacular progresses, the class of groups with intermediate growth remains largely mysterious. Many examples of such groups are constructed using Mealy automata. The aim of this paper is to give an algorithmic procedure to study the growth of such automata groups, and more precisely to provide numerical upper bounds on their exponents. Our functions retrieve known optimal bounds on the famous first Grigorchuk group. They also improve known upper bounds on other automata groups and permitted us to discover several new examples of automata groups of intermediate growth. All the algorithms described are implemented in GAP, a language dedicated to computational group theory.

math.GR↗

arXiv2010

An asymptotic preserving approach for nonlinear Schrodinger equation in the semiclassical limit

We study numerically the semiclassical limit for the nonlinear Schroedinger equation thanks to a modification of the Madelung transform due to E.Grenier. This approach is naturally asymptotic preserving, and allows for the presence of vacuum. Even if the mesh size and the time step do not depend on the Planck constant, we recover the position and current densities in the semiclassical limit, with a numerical rate of convergence in accordance with the theoretical results, before shocks appear in the limiting Euler equation. By using simple projections, the mass and the momentum of the solution are well preserved by the numerical scheme, while the variation of the energy is not negligible numerically. Experiments suggest that beyond the critical time for the Euler equation, Grenier's approach yields smooth but highly oscillatory terms.

math.NA↗