Evolution of Integrated Energy Densities
These four sets of plots show the integrated energy densities --
potential, gradient, kinetic, and total -- during the evolution of
collapsing textures in the different models. The top two graphs
are those models which do not support either strings or monopoles,
while the bottom two graphs have either one or both. The graphs on
the left are simulations which began with spherically symmetric
energy densities, while the graphs on the right are those which
started in an oblate configuration (obtained from the symmetric
configuration by compression along one axis).
Each form of energy density is integrated over the volume
of the simulation region; the total energy is the sum of the integrated
potential, kinetic and gradient energies. The horizontal axis is
measured in timesteps of the simulations.
These plots serve to show that the models without strings or monopoles
collapse in one general way, while those with either strings or
monopoles collapse in a different fashion. This is clear from the
timescale for collapse as well as the qualitative features of the graphs.
Note that the model without a true texture, SO(5)/SO(4), is only
distinguishable from SO(4)/SO(3) by the slight difference in potential
energy.
Corresponding quadrupole moments.
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