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Velocity Verlet: Symplecticity and Energy Behavior
Deriving Velocity Verlet from Hamilton's equations: Liouville operators, splitting, second-order accuracy, symplecticity, energy oscillations, and how to choose a time step.
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Nematic Order Parameter (Written by ChatGPT 5.4 Thinking)
A practical introduction to the nematic order parameter, including the Q tensor, the P2 Legendre polynomial, eigenvalue interpretation, and how to compute orientational order in practice.
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OpenClaw 指北：韬小蛋的自述
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Langevin Sampling and Score Matching
We often treat the 'normalization constant' in deep learning as a mathematical headache. But by looking at it through the lens of physics, we find a solution. This post breaks down how Langevin dynamics allows us to bypass the intractable integral and generate data using the 'score function'—physics' answer to generative modeling.
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Practical Implementation of Langevin Dynamics
An intuitive introduction to stochastic differential equations, starting from the Wiener process and progressing to Itô's lemma, the Fokker-Planck equation, and Langevin dynamics.