89,178 research outputs found
Q-ball formation in the gravity-mediated SUSY breaking scenario
We study the formation of Q-balls which are made of flat directions that
appear in the supersymmetric extension of the standard model in the context of
gravity-mediated supersymmetry breaking. The full non-linear calculations for
the dynamics of the complex scalar field are made. Since the scalar potential
in this model is flatter than \phi^2, we have found that fluctuations develop
and go non-linear to form non-topological solitons, Q-balls. The size of a
Q-ball is determined by the most amplified mode, which is completely determined
by the model parameters. On the other hand, the charge of Q-balls depends
linearly on the initial charge density of the Affleck-Dine (AD) field. Almost
all the charges are absorbed into Q-balls, and only a tiny fraction of the
charges is carried by a relic AD field. It may lead to some constraints on the
baryogenesis and/or parameters in the particle theory. The peculiarity of
gravity-mediation is the moving Q-balls. This results in collisions between
Q-balls. It may increase the charge of Q-balls, and change its fate.Comment: 9 pages, RevTex, 11 postscript figures included, to appear in Phys.
Rev.
Q-ball Formation through Affleck-Dine Mechanism
We present the full nonlinear calculation of the formation of a Q-ball
through the Affleck-Dine (AD) mechanism by numerical simulations. It is shown
that large Q-balls are actually produced by the fragmentation of the condensate
of a scalar field whose potential is very flat. We find that the typical size
of a Q-ball is determined by the most developed mode of linearized
fluctuations, and almost all the initial charges which the AD condensate
carries are absorbed into the formed Q-balls, whose sizes and the charges
depend only on the initial charge densities.Comment: 4 pages, RevTex, 3 postscript figures included, the published versio
On contact numbers of totally separable unit sphere packings
Contact numbers are natural extensions of kissing numbers. In this paper we
give estimates for the number of contacts in a totally separable packing of n
unit balls in Euclidean d-space for all n>1 and d>1.Comment: 11 page
Estimation of instrinsic dimension via clustering
The problem of estimating the intrinsic dimension of a set of points in high dimensional space is a critical issue for a wide range of disciplines, including genomics, finance, and networking. Current estimation techniques are dependent on either the ambient or intrinsic dimension in terms of computational complexity, which may cause these methods to become intractable for large data sets. In this paper, we present a clustering-based methodology that exploits the inherent self-similarity of data to efficiently estimate the intrinsic dimension of a set of points. When the data satisfies a specified general clustering condition, we prove that the estimated dimension approaches the true Hausdorff dimension. Experiments show that the clustering-based approach allows for more efficient and accurate intrinsic dimension estimation compared with all prior techniques, even when the data does not conform to obvious self-similarity structure. Finally, we present empirical results which show the clustering-based estimation allows for a natural partitioning of the data points that lie on separate manifolds of varying intrinsic dimension
Simulations of Q-Ball Formation
The fragmentation of the Affleck-Dine condensate is studied by utilizing 3+1
dimensional numerical simulations. The 3+1 dimensional simulations confirm that
the fragmentation process is very similar to the results obtained by 2+1
dimensional simulations. We find, however, that the average size of Q-balls in
3+1 dimensions is somewhat larger that in 2+1 dimensions. A filament type
structure in the charge density is observed during the fragmentation process.
The resulting final Q-ball distribution is strongly dependent on the initial
conditions of the condensate and approaches a thermal one as the energy-charge
ratio of the Affleck-Dine condensate increases.Comment: 9 pages, 8 figures; corrected typos (v2,v3
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