We investigate the electrical response of Milli-Q deionized water by using a fractional diffusion equation of distributed order with the interfaces (i.e., the boundary conditions at the electrodes limiting the sample) governed by integrodifferential equations. We also consider that the positive and negative ions have the same mobility and that the electric potential profile across the sample satisfies Poisson’s equation. In addition, the good agreement between the experimental data and this approach evidences the presence of anomalous diffusion due to the surface effects in this system.

In this work, we analyze the defect and antidefect distribution in the nematic calamitic phase of a lyotropic liquid crystal [the ternary mixture formed by potassium laurate (KL), decanol (DeOH), and water]. We obtain defects with wedge disclinations of strength $\pm 1∕2$, and the scaling exponent determined by the defect-antidefect correlation was $0.29\pm 0.07$. This value is in good agreement with the theoretical value of $1∕4$ obtained by the Kibble mechanism. The constant of the scaling relation of the defect and antidefect distribution is also discussed. We compare our results with the values obtained by Digal et al. [Phys. Rev. Lett. 83, 5030 (1999)] who used a thermotropic liquid crystal.