We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a co
ncrete and efficient computational method, providing a unified treatment of relativistic and non-relativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wavefunction) propagates in space-time as a classical statistical process (Boltzmann distribution).
Numerical simulations of assemblies of grains under cyclic loading exhibit ``granular ratcheting: a small net deformation occurs with each cycle, leading to a linear accumulation of deformation with cycle number. We show that this is due to a curious
property of the most frequently used models of the particle-particle interaction: namely, that the potential energy stored in contacts is path-dependent. There exist closed paths that change the stored energy, even if the particles remain in contact and do not slide. An alternative method for calculating the tangential force removes granular ratcheting.
