4,136 research outputs found
Spectral Action Models of Gravity on Packed Swiss Cheese Cosmology
We present a model of (modified) gravity on spacetimes with fractal structure
based on packing of spheres, which are (Euclidean) variants of the Packed Swiss
Cheese Cosmology models. As the action functional for gravity we consider the
spectral action of noncommutative geometry, and we compute its expansion on a
space obtained as an Apollonian packing of 3-dimensional spheres inside a
4-dimensional ball. Using information from the zeta function of the Dirac
operator of the spectral triple, we compute the leading terms in the asymptotic
expansion of the spectral action. They consist of a zeta regularization of a
divergent sum which involves the leading terms of the spectral actions of the
individual spheres in the packing. This accounts for the contribution of the
points 1 and 3 in the dimension spectrum (as in the case of a 3-sphere). There
is an additional term coming from the residue at the additional point in the
real dimension spectrum that corresponds to the packing constant, as well as a
series of fluctuations coming from log-periodic oscillations, created by the
points of the dimension spectrum that are off the real line. These terms detect
the fractality of the residue set of the sphere packing. We show that the
presence of fractality influences the shape of the slow-roll potential for
inflation, obtained from the spectral action. We also discuss the effect of
truncating the fractal structure at a certain scale related to the energy scale
in the spectral action.Comment: 38 pages LaTe
Laplace Operators on Fractals and Related Functional Equations
We give an overview over the application of functional equations, namely the
classical Poincar\'e and renewal equations, to the study of the spectrum of
Laplace operators on self-similar fractals. We compare the techniques used to
those used in the euclidean situation. Furthermore, we use the obtained
information on the spectral zeta function to define the Casimir energy of
fractals. We give numerical values for this energy for the Sierpi\'nski gasket
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Artificial Immune Systems - Models, algorithms and applications
Copyright © 2010 Academic Research Publishing Agency.This article has been made available through the Brunel Open Access Publishing Fund.Artificial Immune Systems (AIS) are computational paradigms that belong to the computational intelligence family and are inspired by the biological immune system. During the past decade, they have attracted a lot of interest from researchers aiming to develop immune-based models and techniques to solve complex computational or engineering problems. This work presents a survey of existing AIS models and algorithms with a focus on the last five years.This article is available through the Brunel Open Access Publishing Fun
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