The determination of the nuclear equation of state (EOS) is one of the key issue concerning Nuclear Physics. The characterisation of its dependence in term of density, temperature and isospin are mandatory to describe accurately as well heavy-ion collisions and properties of neutron stars. The EOS can be seen as the macroscopic consequence of the properties concerning the underlying nucleon-nucleon (NN) interaction in nuclear matter. Studying the EOS is then directly related to the study of NN interaction, namely its density dependence via many-body correlations, and its isovector properties via the symmetry term of EOS. In order to probe these features, we currently use heavy ion induced reactions in the Fermi energy domain and perform exclusive measurements using the 4p array INDRA. This allows to access to the dynamical (transport properties) and the thermodynamical features of hot and compressed nuclear matter. INDRA is a international collaboration grouping 5 institutes : GANIL Caen, IPN Orsay, LPC Caen, Laval University (Québec) and INFN Napoli (Italy). INDRA is in operation since 1993 and 8 large data takings (campaigns) have been performed at GANIL (stable beams + SPIRAL1/CIME beams) in France and GSI in Germany. The collaboration is composed by 18 physicists + 3 PHD + 1 post-doc (2013) and still continue to maintain INDRA in order to be ready for SPIRAL2 and GANIL beams in a near future. The collaboration is also deeply involved since 10 years on the next-generation 4p array ; it is the FAZIA project. Taking advantage from the experience concerning 4p arrays, we are currently developping a new prototype of 4p detector and are in the present time in phase 2 of the FAZIA program. This phase consists in building a fully operational demonstrator, composed of 12 blocks made of 16 identification telescopes Si-Si-CsI with their embedded digital electronics.
Several research topics have been developped in the laboratory concerning the study of the dynamical and thermodynamical properties of nuclei with INDRA as well as instrumental developments for FAZIA. In section 1, we present an analysis concerning the study of transport properties in nuclear matter and the determination of some fundamental in-medium quantities such as the nucleon-nucleon mean free path and cross section. In section 2, we address temperature and excitation energy measurements from an experimental point of view ; indeed, these observables are at the centre of any thermodynamical study and therefore also for the accurate determination of the nuclear EOS. In section 3, we present a recent experimental work concerning the evaluation of the symmetry energy term on the nuclear EOS. In section 4, we show an experimental program aiming at the evaluation of the best Pulse Shape Analysis which can be achieved with highly homogeneous silicon detectors for the FAZIA project. At last, Section 5 is devoted to the modelization of current signals produced in Silicon detectors, in order to optimize the Pulse Shape Analysis for FAZIA.