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At lower energies, the resonances in scattering experiments are often isolated. The crucial parameter is the ratio of average resonance width and average mean level spacing. Towards larger energies, this parameter grows, because the…
Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its…
We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given…
We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically…
We analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large $t$, well defined scaling properties. We suggest a general…
We study the properties of the dilaton in a soft-wall background using two solutions of the Einstein equations. These solutions contain an asymptotically AdS metric with a nontrivial scalar profile that causes both the spontaneous breaking…
Three-dimensional, as well as one- and two-dimensional, studies of multiplicity fluctuation are performed using AMPT model to generate central Au-Au collision events at ${\sqrt s_{NN}}= 200$ GeV. Two- and three-dimensional normalized…
The stochastic Eigen model proposed by Feng et al. (Journal of theoretical biology, 246 (2007) 28) showed that error threshold is no longer a phase transition point but a crossover region whose width depends on the strength of the random…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. Aldous's Brownian continuum random tree, the…
By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix…
We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to…
It is generally believed that the spatial distribution of galaxies does not trace that of the total mass. The understanding of the bias effect is therefore necessary to determine the cosmological parameters and the primordial density…
Quasi-one-dimensional quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the…
Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolation threshold, has been carried out using box-counting functions. It is found that at relevant…
The one-dimensional electron gas exhibits spin-charge separation and power-law spectral responses to many experimentally relevant probes. Ordering in a quasi one-dimensional system is necessarily associated with a dimensional crossover, at…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
In the standard model for structure formation, bound objects originate from the gravitational collapse of small perturbations arising from quantum fluctuations with random phases. In other scenarios, based on defects, structures are seeded…