On the Thermodynamics of Granular Media

A thermodynamic formulation for moving granular material is proposed. The fluctuations due to the constant flux and dissipation of energy are controlled in a `granular' ensemble by a pressure $\wp$ (`compression') which is conjugate to a contact volume (`contactopy'). The corresponding response function (`dissipativity') describes how dissipation increases with $\wp$ and should serve to identify the fluidization transition and 1/f noise. In the granular ensemble one can consider the granular medium as a gas of elastically colliding particles and define a ``granular'' temperature and other standard thermodynamic quantities. PACS: 05.70, 46.10Comment: 11 p., no figs., plain Te

On the Shape of the Tail of a Two Dimensional Sand Pile

We study the shape of the tail of a heap of granular material. A simple theoretical argument shows that the tail adds a logarithmic correction to the slope given by the angle of repose. This expression is in good agreement with experiments. We present a cellular automaton that contains gravity, dissipation and surface roughness and its simulation also gives the predicted shape.Comment: LaTeX file 4 pages, 4 PS figures, also available at http://pmmh.espci.fr

A Growth model for DNA evolution

A simple growth model for DNA evolution is introduced which is analytically solvable and reproduces the observed statistical behavior of real sequences.Comment: To be published in Europhysics Letter

Diffusion and spectral dimension on Eden tree

We calculate the eigenspectrum of random walks on the Eden tree in two and three dimensions. From this, we calculate the spectral dimension $d_s$ and the walk dimension $d_w$ and test the scaling relation $d_s = 2d_f/d_w$ ($=2d/d_w$ for an Eden tree). Finite-size induced crossovers are observed, whereby the system crosses over from a short-time regime where this relation is violated (particularly in two dimensions) to a long-time regime where the behavior appears to be complicated and dependent on dimension even qualitatively.Comment: 11 pages, Plain TeX with J-Phys.sty style, HLRZ 93/9