In the perspective of manipulating and controlling heat fluxes, grapheneudrepresents a promising material revealing an unusually high thermaludconductivity �. However, both experimental and theoretical previousudworks lack of a strict thermal conductivity value, estimating resultsudin the range 89-5000 W m-1 K-1. In this scenario, I address grapheneudthermal transport properties by means of molecular dynamics simulationsudusing the novel "approach to equilibrium molecular dynamics"ud(AEMD) technique.udThe first issue is to offer some insight on the active debate aboutudgraphene thermal conductivity extrapolation for infinite sample. Toudthis aim, I perform unbiased (i.e. with no a priori guess) direct atomisticudsimulations aimed at estimating thermal conductivity in samplesudwith increasing size up to the unprecedented value of 0.1 mm. Theudresults provide evidence that thermal conductivity in graphene is definitelyudupper limited, in samples long enough to allow a diffusiveudtransport regime for both single and collective phonon excitations.udAnother important issue is to characterize at atomistic level the experimentaludtechniques used to estimate graphene thermal conductivity.udSome of these use laser source to provide heat. For these reasons,udI deal with the characterization of the transient response to audpulsed laser focused on a circular graphene sample. In order to reproduceudthe laser effect on the sample, the K - A01udand
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