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We consider the problem of minimising the $n^{th}-$eigenvalue of the Robin Laplacian in $\mathbb{R}^{N}$. Although for $n=1,2$ and a positive boundary parameter $\alpha$ it is known that the minimiser...
Abstract: The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power networks to d...
Abstract: Factorization of the incompressible Stokes operator linking pressure and velocity is revisited. The main purpose is to use the inverse of the Stokes operator with a large time step as a prec...
Coulomb gas ensemles and Laplacian growth     Coulomb gas ensemles  Laplacian growth       font style='font-size:12px;'> 2011/7/28
Abstract: We consider the normal matrix ensemble under a general confining potential. We find that the eigenvalues condensate on a compact set in the plane, which we call the spectral droplet. We also...
Laplacian growth in the half plane     Laplacian growth  half plane       font style='font-size:12px;'> 2010/4/7
We investigate a version of the Laplacian growth problem with zero surface tension in the half plane and find families of self-similar exact solutions.
A RELATION BETWEEN THE MATCHING NUMBER AND LAPLACIAN SPECTRUM OF A TREE      Tree  Laplacian spectrum  matching numbe          font style='font-size:12px;'> 2007/8/7
Let $T$ be a tree with matching number $\mu(T)$. In this paper we obtain thefollowing result: If $T$ has no perfect matchings, then $\mu(T)$ is a lower bound forthe number of nonzero Laplacian eigenva...

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