9 research outputs found
Ultrametricity and Memory in a Solvable Model of Self-Organized Criticality
Slowly driven dissipative systems may evolve to a critical state where long
periods of apparent equilibrium are punctuated by intermittent avalanches of
activity. We present a self-organized critical model of punctuated equilibrium
behavior in the context of biological evolution, and solve it in the limit that
the number of independent traits for each species diverges. We derive an exact
equation of motion for the avalanche dynamics from the microscopic rules. In
the continuum limit, avalanches propagate via a diffusion equation with a
nonlocal, history-dependent potential representing memory. This nonlocal
potential gives rise to a non-Gaussian (fat) tail for the subdiffusive
spreading of activity. The probability for the activity to spread beyond a
distance in time decays as for . The potential
represents a hierarchy of time scales that is dynamically generated by the
ultrametric structure of avalanches, which can be quantified in terms of
``backward'' avalanches. In addition, a number of other correlation functions
characterizing the punctuated equilibrium dynamics are determined exactly.Comment: 44 pages, Revtex, (12 ps-figures included
The Dynamical Instability of Static, Spherically Symmetric Solutions in Nonsymmetric Gravitational Theories
We consider the dynamical stability of a class of static,
spherically-symmetric solutions of the nonsymmetric gravitational theory. We
numerically reproduce the Wyman solution and generate new solutions for the
case where the theory has a nontrivial fundamental length scale \mu^{-1}. By
considering spherically symmetric perturbations of these solutions we show that
the Wyman solutions are generically unstable.Comment: 13 pages, uses amslatex, graphicx and subfigure package
Scalar-field Pressure in Induced Gravity with Higgs Potential and Dark Matter
A model of induced gravity with a Higgs potential is investigated in detail
in view of the pressure components related to the scalar-field excitations. The
physical consequences emerging as an artifact due to the presence of these
pressure terms are analysed in terms of the constraints parting from energy
density, solar-relativistic effects and galactic dynamics along with the dark
matter halos.Comment: 26 pages, 3 figures, Minor revision, Published in JHE