Related papers: Fractality of wave functions on a Cayley tree: Dif…

When one studies geometric properties of graphs, local finiteness is a common implicit assumption, and that of transitivity a frequent explicit one. By compactness arguments, local finiteness guarantees several regularity properties. It is…

We present a new approach to the statistics of the cosmic density field and to the mass distribution of high-contrast structures, based on the formalism of Cayley trees. Our approach includes in one random process both fluctuations and…

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as…

We consider a partially hinged rectangular plate and its normal modes. There are two families of modes, longitudinal and torsional. We study the variation of the corresponding eigenvalues under domain deformations. We investigate the…

Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to a point; and the fact that they have a well-defined notion of…

For a harmonic function on a tree with random walk whose transition probabilities are bounded between two constants in (0,1/2), it is known that the radial and stochastic properties of convergence, boundedness and finiteness of energy are…

We study basic spectral features of graph Laplacians associated with a class of rooted trees which contains all regular trees. Trees in this class can be generated by substitution processes. Their spectra are shown to be purely absolutely…

In order to elucidate the presence of non-localized states in doped graphene, an scaling analysis of the wave function moments known as inverse participation ratios is performed. The model used is a tight- binding hamiltonian considering…

A compacted binary tree is a directed acyclic graph encoding a binary tree in which common subtrees are factored and shared, such that they are represented only once. We show that the number of compacted binary trees of size $n$ grows…

We introduce a model for growing Cayley trees with thermal noise. The evolution of these hierarchical networks reduces to the Eden model and the Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively. We show that the…

We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold…

The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. In this paper, we perform…

This article delves into the intricate dynamics of Rayleigh wave propagation within a nonlocal orthotropic medium, where the presence of void and diffusion adds an intriguing layer to the analysis. Grounded in Eringen nonlocal elasticity…

We consider a segmented structure, possibly connected with a continuous medium, as initially homogeneous, where discontinuities arise as localized strains induced by self-equilibrated localized actions. Under this formulation augmented by…

We study the problem of random search in finite networks with a tree topology, where it is expected that the distribution of the first-passage time F(t) decays exponentially. We show that the slope of the exponential tail is independent of…

The wavefront dislocation is an important and ubiquitous phenomenon in wave fields. It is closely related to the phase singularity in a wave function. Some recent studies have verified that the wavefront dislocations in the local density of…

We show that the Euler walk on a Cayley tree exhibits two regimes (dynamic phases): a condensed phase and a low-density phase. In the condensed phase the self-organized area grows as a compact domain. In the low-density phase the proportion…

We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph, as…

Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay…

Node betweenness has been studied recently by a number of authors, but until now less attention has been paid to edge betweenness. In this paper, we present an exact analytic study of edge betweenness in evolving scale-free and…