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Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian
Robin Laplacian Eigenvalues Optimisation
2012/4/18
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...
Structural Analysis of Laplacian Spectral Properties with Application to Electric Transmission Networks
Laplacian Spectral Properties Electric Transmission Networks Optimization and Control
2011/8/18
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...
On direct inverse of Stokes, Helmholtz and Laplacian operators in view of time-stepper-based Newton and Arnoldi solvers in incompressible CFD
Stoke Helmholtz Laplacian operators time-stepper-based Newton Arnoldi solvers incompressible CFD
2011/8/4
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...
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...
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
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...