May the dU/dx be with you

  • Geometry Rescaling

    September 22, 2019 by

    One of the major issues with the stability of the timemachine is whether or not your Hessians are PSD. A non-PSD Hessian induces a transition matrix with a spectral radius , causing a divergent trajectory. Recall Brownian dynamics: Assuming a zero mixed partial, we can differentiate with respect to G and H are the Gradients… Read more

  • Derivatives and Internal Coordinates

    September 19, 2019 by

    Brownian Dynamics has the following equations of motion, where we assume that the geometries is dependent on the forcefield parameters We can differentiate the above w.r.t. For the purposes of stability analysis and without loss of generality we can assume: So we can proceed to simplify into: It can be shown that this converges if… Read more

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