Related papers: Level spacing statistics and spectral correlations…
The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi-Hubbard model with dimerized hopping amplitude and find…
Synchronous collisions between a large number of solitons are considered in the context of a statistical description. It is shown that during the interaction of solitons of the same signs the wave field is effectively smoothed out. When the…
The performance of spectral clustering relies on the fluctuations of the entries of the eigenvectors of a similarity matrix, which has been left uncharacterized until now. In this letter, it is shown that the signal $+$ noise structure of a…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
We investigate properties of the correlation function of clusters of galaxies using geometrical models. On small scales the correlation function depends on the shape and the size of superclusters. On large scales it describes the geometry…
We provide numerical constructions of one-dimensional hyperuniform many-particle distributions that exhibit unusual clustering and asymptotic local number density fluctuations growing more slowly than the volume of an observation window but…
The distribution of higher order level spacings, i.e. the distribution of $\{s_{i}^{(n)}=E_{i+n}-E_{i}\}$ with $n\geq 1$ is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson…
It is shown that the new Poisson brackets proposed in Part I of this work (J. Math. Phys. 34, 5747(hep-th/9305133)) arise naturally in an extension of the formal variational calculus incorporating divergences. The linear spaces of local…
Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We analyse chimera states in networks of Van der Pol oscillators with hierarchical coupling topology. We investigate…
According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
The power spectrum P(k)\propto k^n with n=-2 is close to the shape of the measured galaxy spectrum on small scales. Unfortunately this spectrum has proven rather difficult to simulate. Further, 2-dimensional simulations have suggested a…
Recently, several studies reported a significant discrepancy between the clustering and lensing of the Baryon Oscillation Spectroscopic Survey (BOSS) galaxies in the $\textit{Planck}$ cosmology. We construct a simple yet powerful model…
SZ scaling relations have been used to test the self-similar prediction for massive galaxy clusters, but little attention has been given to individual galaxy groups. We investigate the scaling relations of galaxy groups and clusters near…
We present the mass-X-ray observable scaling relationships for clusters of galaxies using the XMM-Newton cluster catalog of Snowden et al. Our results are roughly consistent with previous observational and theoretical work, with one major…
We investigate whether the dynamical status of clusters is related to the large-scale structure of the Universe. We find that cluster substructure is strongly correlated with the tendency of clusters to be aligned with their nearest…
This study presents a comprehensive experimental investigation of scalar dispersion from the free end of wall-mounted cylindrical obstacles immersed in a large-Reynolds-number turbulent boundary layer. A key focus is the characterization of…
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…
We study structure, eigenvalue spectra and diffusion dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their…
Gravitational lensing allows to quantify the angular distribution of the convergence field around clusters of galaxies to constrain their connectivity to the cosmic web. We describe in this paper the corresponding theory in Lagrangian space…