A Vlasov approach to bunching and selfordering of particles in optical resonators

We develop a Vlasov type continuum density description for the coupled nonlinear dynamics of polarizable particles moving in the light field of a high Q optical resonator. The intracavity light field, which exerts optical forces on the particles, depends itself on the dynamics of the particle density, which constitutes a time dependent refractive index. This induces mode frequency shifts, losses and coupling. For typical geometries we find solid analytic criteria for the stability of an initial homogeneous particle density for a wide class of initial velocity distributions including thermal distributions. These agree with previously found bunching and self-ordering instabilities but are extended to a wider range of parameters and initial conditions. Using a linear perturbation expansion we calculate the growth exponents of small density perturbations in the parameter region beyond this instability threshold. Numerical solutions of the full equations as well as simulations of the underlying many particle trajectories confirm these results. In addition the equations allow to extract analytical scaling laws to extrapolate cavity cooling and selfordering dynamics to higher particle numbers

Cortico-reticulo-spinal circuit reorganization enables functional recovery after severe spinal cord contusion.

Severe spinal cord contusions interrupt nearly all brain projections to lumbar circuits producing leg movement. Failure of these projections to reorganize leads to permanent paralysis. Here we modeled these injuries in rodents. A severe contusion abolished all motor cortex projections below injury. However, the motor cortex immediately regained adaptive control over the paralyzed legs during electrochemical neuromodulation of lumbar circuits. Glutamatergic reticulospinal neurons with residual projections below the injury relayed the cortical command downstream. Gravity-assisted rehabilitation enabled by the neuromodulation therapy reinforced these reticulospinal projections, rerouting cortical information through this pathway. This circuit reorganization mediated a motor cortex-dependent recovery of natural walking and swimming without requiring neuromodulation. Cortico-reticulo-spinal circuit reorganization may also improve recovery in humans