Theoretical and Computational Biological Physics
Part of the Biological Physics Initiative
Carnegie Mellon University, Department of Physics
Random Acts of Knowledge
Over time I have established a somewhat (but not completely) "random" collection of scientific notes on topics which I came across at some point. The idea was to preserve some essential insights in a semi-polished fashion, such as to be able to access it quickly and efficiently later. If you're interested, you're very welcome to rummage in our science-attic!
If you should indeed find something which turns out to be useful to you, I'd of course be most happy to learn about that! If something's wrong — dito!
Statistical Mechanics
- Fluctuation-Dissipation-Theorem for Brownian motion [pdf]
- The Henderson Theorem (uniqueness of pair-potential for given g(r)) [pdf]
- Microcanonical and canonical two-dimensional Ising model: an example [pdf]
- One-dimensional diffusion on a finite region [pdf]
- Thermal softening of Helfrich membranes [pdf]
- Van der Waals equation, Maxwell construction, and Legendre transforms [pdf]
Computational topics
- Equidistributed points on the surface of a sphere [pdf]
- How to calculate g(r) under periodic boundary conditions [pdf]
- How to generate exponentially correlated Gaussian random numbers [pdf]
- Analytical expressions for the blocking error of exponentially correlated Gaussian data [pdf]
- Linear and logarithmic interpolation [pdf]
- Some random notes on data fitting [pdf]
Electrostatics
- Electric field of a periodically charge-modulated plane [pdf]
- Electric field of a plane with a charge modulation of "sharp" stripes [pdf]
Quantum Mechanics
Miscellaneous
- Randomness and intuition [pdf]
- Probability density of the sum of uncorrelated random variables is not their convolution [pdf]
- Rotation matrices and their infinitesimal generators [pdf]
- The shape of a straight fluid meniscus [pdf]
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