Exploring isospectral spring-mass systems with firefly algorithm

This paper investigates in-line spring-mass systems (An), fixed at one end and free at the other, with n-degrees of freedom (d.f.). The objective is to find feasible in-line systems (B(n)) that are isospectral to a given system. The spring-mass systems, A(n) and B(n), are represented by Jacobi matrices. An error function is developed with the help of the Jacobi matrices A(n) and B(n). The problem of finding the isospectral systems is posed as an optimization problem with the aim of minimizing the error function. The approach for creating isospectral systems uses the fact that the trace of two isospectral Jacobi matrices A(n) and B(n) should be identical. A modification is made to the diagonal elements of the given Jacobi matrix (A(n)), to create the isospectral systems. The optimization problem is solved using the firefly algorithm augmented by a local search procedure. Numerical results are obtained and resulting isospectral systems are shown for 4 d.f. and 10 d.f. systems.

Running neutrino mass from six dimensions

In the present talk, we will discuss a six dimensional mass generation for the neutrinos. The SM neutrinos live on a 3-brane and interact via a brane localised mass term with a Weyl singlet neutrino residing in all the six dimensions. We present the physical neutrino mass spectrum and show that the active neutrino mass and the KK masses have a logarithmic cut-off dependence at the tree level. This translates in to a renormalisation group running of n -masses above the KK compactification scale coming from classical effects without any SM particles in the spectrum.This could have effects in neutrinoless double beta decay experiments.