The transport properties of nematic aerogels, which consist of oriented mullite nanofibers coated with a graphene shell, were studied. It is shown that the magnetoresistance of this system is well approximated by two contributions - negative one, described by the formula for systems with weak localization , and positive contribution, linear in the field and unsaturated in large magnetic fields. The behavior of phase coherence length on temperature obtained from the analysis of the negative contribution indicates the main role of the electron-electron interaction in the destruction of phase coherence and, presumably, the transition at low temperatures from a two-dimensional weak localization regime to a one-dimensional one. The positive linear contribution to magnetoresistance is apparently due to the inhomogeneous distribution of the local carrier density in the conductive medium. It has also been established that the temperature dependence of the resistance for graphenized aerogels with a low carbon content, when the graphene coating is apparently incomplete, can be represented as the sum of two contributions, one of which is characteristic of weak localization, and the second is described by hopping mechanism corresponding to the Shklovskii-Efros law in the case of a granular conductive medium. For samples with a high carbon content, there is no second contribution.

Here, we present the results of vibrating wire experiments in pure $^3$He (without $^4$He coverage) in nematic aerogel. We investigated the dependence of splitting of the superfluid transition temperature of $^3$He in aerogel on magnetic field. In addition to our previous work, we used a wider range of magnetic fields (up to 31 kOe) and managed to detect both the "upper" and "lower" superfluid transition temperatures. The solid paramagnetic $^3$He layer on the aerogel strands activates the magnetic scattering channel. According to theory, it should result in linear splitting at high ($\ge20$ kOe) fields, while at lower fields the splitting is expected to be nonlinear. We were able to observe this nonlinearity, but we have a discrepancy with theoretical predictions regarding the range of fields where nonlinearity occurs. Possible reasons for this are discussed.

We present results of nuclear magnetic resonance (NMR) experiments in superfluid 3He in two samples of nematic aerogel consisting of nearly parallel mullite strands. The samples were cut from the same piece of the aerogel, but one of them was squeezed by 30% in the direction transverse to the strands. In both samples the superfluid transition of 3He occurred into the polar phase, where no qualitative difference between NMR properties of 3He in these samples was found. The difference, however, has appeared on further cooling, after the transition to the polar-distorted A phase (PdA phase) with the orbital part of the order parameter in the 2D Larkin-Imry-Ma (LIM) state. In the squeezed sample the 2D LIM state is anisotropic that results in changes in the NMR, which can be used as an additional marker of the PdA phase and have allowed us to measure the value of the anisotropy.