相关论文: Dimensionality and Fractals

As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the…

To remove the confusion of concepts about different sorts of geographical space and dimension, a new framework of space theory is proposed in this paper. Based on three sets of fractal dimensions, the geographical space is divided into…

The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a…

We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…

Observations of weak gravitational lensing combined with statistical tomographic techniques have revealed that galaxies have formed along filaments, essentially one-dimensional lines or strings, which form sheets and voids. These have, in…

The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…

Generic cosmological models derived from higher dimensional theories with warped extra dimensions have a nonzero cosmological constant-like term induced on the 3+1 space-time, or a physical 3-brane. In the scenario where this 3+1 space-time…

We argue that de Sitter universes with a small cosmological constant are entropically favored to have three spatial dimensions. The conclusion relies on the causal-patch description of de Sitter space, where fiducial observers experience…

An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency,…

We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…

One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a…

The density perturbation of the universe has been considered in the framework of a Finslerian cosmological model in which the background spacetime of the universe is taken as the spatially flat FLRW spacetime with a Finslerian perturbation.…

The emphasis in the developmet of theories with more than three spatial dimensions has recently shifted towards ``brane world'' picture, which assumes that ordinary matter (with possible exceptions of gravitons and other, hypothetic,…

Under the assumption that General Relativity (GR) correctly describes the phenomenology of our Universe, astronomical observations provide compelling evidence that (1) the dynamics of cosmic structure is dominated by dark matter (DM), an…

We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the…

Stellar and galactic systems are objects in dynamical equilibrium that are composed of ordinary baryonic matter hypothetically embedded in extended dominant dark matter halos. Our aim is to investigate the scaling relations and…

We revise the statistical properties of the primordial cosmological density anisotropies that, at the time of matter radiation equality, seeded the gravitational development of large scale structures in the, otherwise, homogeneous and…

We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with…

This paper discusses the origin of the small parameters with the aim of explaining the Hierarchy problem. The flexible extra dimensions are an essential tool in the process by which physical parameters are formed. The evolution of a…

We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…