

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 semipolished 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 scienceattic!
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
 FluctuationDissipationTheorem for Brownian motion [pdf]
 The Henderson Theorem (uniqueness of pairpotential for given g(r)) [pdf]
 Microcanonical and canonical twodimensional Ising model: an example [pdf]
 Onedimensional 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]
 Linear and logarithmic interpolation [pdf]
 Some random notes on data fitting [pdf]
Electrostatics
 Electric field of a periodically chargemodulated plane [pdf]
 Electric field of a plane with a charge modulation of "sharp" stripes [pdf]
Quantum Mechanics
 RayleighRitz and GibbsBogoliubov [pdf]
 Uncertainty relation for selfadjoint operators [pdf]
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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