215 research outputs found
Local Indicators for Plurisubharmonic Functions
A notion of local indicator for a plurisubharmonic function is introduced.
The indicator is a certain plurisubharmonic function in the unit polydisc,
which controls the behavior of the considered function near a fixed point of
its singularity, as well as the residual Monge-Ampere mass of the function at
this point. A pluricomplex Green function with respect to given indicators is
constructed and applied to the Dirichlet problem for the Monge- Ampere operator
in the class of plurisubharmonic functions with isolated singularities.Comment: 18 pages, LaTeX; to appear in J. Math. Pures App
Long time behaviour of a stochastic nano particle
In this article, we are interested in the behaviour of a single ferromagnetic
mono-domain particle submitted to an external field with a stochastic
perturbation. This model is the first step toward the mathematical
understanding of thermal effects on a ferromagnet. In a first part, we present
the stochastic model and prove that the associated stochastic differential
equation is well defined. The second part is dedicated to the study of the long
time behaviour of the magnetic moment and in the third part we prove that the
stochastic perturbation induces a non reversibility phenomenon. Last, we
illustrate these results through numerical simulations of our stochastic model.
The main results presented in this article are the rate of convergence of the
magnetization toward the unique stable equilibrium of the deterministic model.
The second result is a sharp estimate of the hysteresis phenomenon induced by
the stochastic perturbation (remember that with no perturbation, the magnetic
moment remains constant)
- …