  We examine transport in a holographic model in which the dynamics of the
charged degrees of freedom is described by the nonlinear Dirac-Born-Infeld
(DBI) action. Axionic scalar fields are included to break translational
invariance and generate momentum dissipation in the system. Scaling exponents
are introduced by using geometries which are nonrelativistic and
hyperscaling-violating in the infrared. In the probe DBI limit the theory
reproduces the anomalous temperature dependence of the resistivity and Hall
angle of the cuprate strange metals, $\rho \sim T$ and $\cot\Theta_H \sim T^2$.
These scaling laws would not be present without the nonlinear dynamics encoded
by the DBI interactions. We further show that because of its richness the DBI
theory supports a wide spectrum of temperature scalings. This model provides
explicit examples in which transport is controlled by different relaxation
times. On the other hand, when only one quantity sets the temperature scale of
the system, the Hall angle and conductivity typically exhibit the same
temperature behavior. We illustrate this point using new fully backreacted
analytical dyonic black brane solutions.
