Related papers: Cut-out sets, fractal voids and cosmic structure
We apply the adhesion approximation to study the formation and evolution of voids in the Universe. Our simulations -- carried out using 128$^3$ particles in a cubical box with side 128 Mpc -- indicate that the void spectrum evolves with…
Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent singularities and, as N approaches infinite, fractals -- and thereby,scale-free networks. Any…
The self-similar structure of the attracting subshift of a primitive substitution is carried over to the limit set of the repelling tree in the boundary of Outer Space of the corresponding irreducible outer automorphism of a free group.…
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial…
Break-up fragmentation patterns together with kinetic and configurational energy fluctuations are investigated in the framework of a microcanonical model with fragment degrees of freedom over a broad excitation energy range. As far as…
We derive discontinuity relations, also known as cutting rules, and explore the analytic properties of cosmological correlators, fundamental observables of the primordial universe. Our emphasis is on how these relations arise from unitarity…
On the one hand, the large scale structure of matter is arguably scale invariant, and, on the other hand, halos and voids are recognized as prominent features of that structure. To unify both approaches, we propose to model the dark matter…
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…
We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are…
Reduction from a higher-dimensional to a lower-dimensional field theory can display special features when the zero-level ground state has nontrivial dependence on the reduction coordinates. In particular, a delayed `covert' form of…
The interrelations between (upper and lower) Minkowski contents and (upper and lower) surface area based contents (S-contents) as well as between their associated dimensions have recently been investigated for general sets in R^d (cf. [3]).…
The statistical analysis and the spherical wavelet analysis of the SDSS DR7 quasars distribution and of the WMAP CMB anisotropy are performed. They revealed the qualitative agreement between the angular power spectrum of CMB and the angular…
Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the…
We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0<\varepsilon<\tfrac12$, we obtain dimension bounds for the set of exceptional points where the upper porosity of $E$ is less…
We estimate a Box-counting dimension of fractal surfaces which are generated by iterated function systems with a vertical contraction factor function on an arbitrary data set over rectangular grids and can express well a lot of natural…
The model of the universe is considered in which background of the universe is not defined by the matter but is a priori specified as a homogenous and isotropic flat space. The scale factor of the universe follows the linear law. The scale…
The precise theoretical characterization of a fractionalized phase in spatial dimensions higher than one is through the concept of ``topological order''. We describe a physical effect that is a robust and direct consequence of this hidden…
We consider the influence of the Fermi statistics of nucleons on the binding energy of a new type of nuclear structures such as fractal nuclear clusters (fractal isomers of nuclei). It is shown that the fractal nuclear isomers possess a…
In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension $d$ at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is…
The formation length of particles produced in the relativistic collisions of hadrons and nuclei has relevance to fundamental principles of physics at small interaction distances. The relation is expressed by z scaling observed in the…