Department of Physics @ Carnegie Mellon

Theoretical and Computational Biological Physics

 

Part of the Biological Physics Initiative
Carnegie Mellon University, Department of Physics

www.cmu.edu
 
  budding simulation  

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]
  • 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

  • Rayleigh-Ritz and Gibbs-Bogoliubov [pdf]
  • Uncertainty relation for self-adjoint 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]

 

 

 

Scherk's minimal surface

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twisted torus

Funding:

NIH

NSF

 

Volkswagenstiftung