1,074,858 research outputs found
Long-Range Correlations in Self-Gravitating N-Body Systems
Observed self-gravitating systems reveal often fragmented non-equilibrium
structures that feature characteristic long-range correlations. However, models
accounting for non-linear structure growth are not always consistent with
observations and a better understanding of self-gravitating -body systems
appears necessary. Because unstable gravitating systems are sensitive to
non-gravitational perturbations we study the effect of different dissipative
factors as well as different small and large scale boundary conditions on
idealized -body systems. We find, in the interval of negative specific heat,
equilibrium properties differing from theoretical predictions made for
gravo-thermal systems, substantiating the importance of microscopic physics and
the lack of consistent theoretical tools to describe self-gravitating gas.
Also, in the interval of negative specific heat, yet outside of equilibrium,
unforced systems fragment and establish transient long-range correlations. The
strength of these correlations depends on the degree of granularity, suggesting
to make the resolution of mass and force coherent. Finally, persistent
correlations appear in model systems subject to an energy flow.Comment: 20 pages, 21 figures. Accepted for publication in A&
Extending polynomials in maximal and minimal ideals
Given an homogeneous polynomial on a Banach space belonging to some
maximal or minimal polynomial ideal, we consider its iterated extension to an
ultrapower of and prove that this extension remains in the ideal and has
the same ideal norm. As a consequence, we show that the Aron-Berner extension
is a well defined isometry for any maximal or minimal ideal of homogeneous
polynomials. This allow us to obtain symmetric versions of some basic results
of the metric theory of tensor products.Comment: 13 page
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
We study tensor norms that destroy unconditionality in the following sense:
for every Banach space with unconditional basis, the -fold tensor
product of (with the corresponding tensor norm) does not have unconditional
basis. We establish an easy criterion to check weather a tensor norm destroys
unconditionality or not. Using this test we get that all injective and
projective tensor norms different from and destroy
unconditionality, both in full and symmetric tensor products. We present
applications to polynomial ideals: we show that many usual polynomial ideals
never enjoy the Gordon-Lewis property. We also consider the unconditionality of
the monomial basic sequence. Analogous problems for multilinear and operator
ideals are addressed.Comment: 23 page
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