28,817 research outputs found
Orthogonal linear group-subgroup pairs with the same invariants
The main theorem of Galois theory states that there are no finite
group-subgroup pairs with the same invariants. On the other hand, if we
consider complex linear reductive groups instead of finite groups, the
analogous statement is no longer true: There exist counterexample
group-subgroup pairs with the same invariants. However, it's possible to
classify all these counterexamples for certain types of groups. In [16], we
provided the classification for connected complex irreducible groups, and, in
this paper, for connected complex orthogonal groups, i.e., groups that preserve
some non-degenerate quadratic form.Comment: 27 pages, a part of PhD thesi
Spontaneous Scaling Emergence in Generic Stochastic Systems
We extend a generic class of systems which have previously been shown to
spontaneously develop scaling (power law) distributions of their elementary
degrees of freedom.
While the previous systems were linear and exploded exponentially for certain
parameter ranges, the new systems fulfill nonlinear time evolution equations
similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics
and evolve spontaneously towards "fixed trajectories" indexed by the average
value of their degrees of freedom (which corresponds to the SSB order
parameter). The "fixed trajectories" dynamics evolves on the edge between
explosion and collapse/extinction.
The systems present power laws with exponents which in a wide range () are universally determined by the ratio between the minimal and the
average values of the degrees of freedom. The time fluctuations are governed by
Levy distributions of corresponding power. For exponents there is
no "thermodynamic limit" and the fluctuations are dominated by a few, largest
degrees of freedom which leads to macroscopic fluctuations, chaos and
bursts/intermitency.Comment: latex, 11 page
Power Laws are Logarithmic Boltzmann Laws
Multiplicative random processes in (not necessaryly equilibrium or steady
state) stochastic systems with many degrees of freedom lead to Boltzmann
distributions when the dynamics is expressed in terms of the logarithm of the
normalized elementary variables. In terms of the original variables this gives
a power-law distribution. This mechanism implies certain relations between the
constraints of the system, the power of the distribution and the dispersion law
of the fluctuations. These predictions are validated by Monte Carlo simulations
and experimental data. We speculate that stochastic multiplicative dynamics
might be the natural origin for the emergence of criticality and scale
hierarchies without fine-tuning.Comment: latex, 9 pages with 3 figure
Variations in the total electron content of the ionosphere at mid-latitudes during quiet sun conditions
Faraday rotation effect on satellite signals used to determine ionospheric electron content at midlatitudes during quiet sun condition
Some aspects of core formation in Mercury
An evaluation of existing theories on the existence of the planet's metallic core is presented. Topics considered are: (1) magnetic fields; (2) surface geology; (3) cosmochemical models
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