Related papers: Scaled Oscillation and Level Sets
We study vibrational modes and spectrum of a model system of atoms and springs on a scale-free network in order to understand the nature of excitations with many degrees of freedom on the scale-free network. We assume that the atoms and…
For the minimal graph with strict convex level sets, we find an auxiliary function to study the Gaussian curvature of the level sets. We prove that this curvature function is a concave function with respect to the height of the minimal…
The growing need for affordable and accessible higher education is a major global challenge for the 21st century. Consequently, there is a need to develop a deeper understanding of the functionality and taxonomy of universities and colleges…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
We develop a formalism to study the use of Level Set Method (LSM) in the investigation of evolution of observables in terms of parameters of the Hamiltonian, both of the system itself and the control part. A simple example with an analytic…
We consider {\it small solutions} of a vibrating system with smooth non-linearities for which we provide an approximate solution by using a double scale analysis; a rigorous proof of convergence of a double scale expansion is included; for…
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere $S^{n-1}$. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded…
We study the regularity properties of Gaussian fields defined over spheres cross time. In particular, we consider two alternative spectral decompositions for a Gaussian field on $\mathbb{S}^d \times \mathbb{R}$. For each decomposition, we…
The whole class of minimally coupled and massive scalar fields which may be responsible for flattening of galactic rotation curves is found. An interesting relation with a class of scalar-tensor theories able to isotropise anisotropic…
The mobility of two interacting particles in a random potential is studied, using the sensitivity of their levels to a change of boundary conditions. The delocalization in Hilbert space induced by the interaction of the two particle Fock…
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…
The goal of this note is to extend the result bounding from bellow the minimal possible growth of frequently oscillating subharmonic functions to a larger class of functions that carry similar properties. We refine and find further…
Oscillons are localised long-lived pulsating states in the three-dimensional $\phi^4$ theory. We gain insight into the spatio-temporal structure and bifurcation of the oscillons by studying time-periodic solutions in a ball of a finite…
We study numerically the phase-ordering kinetics of the two-dimensional site-diluted Ising model. The data can be interpreted in a framework motivated by renormalization-group concepts. Apart from the usual fixed point of the non-diluted…
The use of machine learning models in system identification has increased due to their ability to approximate complex nonlinear dynamics with high accuracy. However, often it is not clear how the performance of trained models scales with…
Long-range dependent random fields with spectral densities which are unbounded at some frequencies are investigated. We demonstrate new examples of covariance functions which do not exhibit regular varying asymptotic behaviour at infinity.…
We address the question whether the sequence of areas between coalescing random walkers displays multiscaling and in the process calculate the second moment as well as the two point correlation function exactly. The scaling of higher order…
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a…
A combination of methods originating from non-stationary timeseries analysis is applied to two datasets of near surface turbulence in order to gain insights on the non-stationary enhancement mechanism of intermittent turbulence in the…
Model sets (also called cut and project sets) are generalizations of lattices, and multi-component model sets are generalizations of lattices with colourings. In this paper, we study self-similarities of multi-component model sets. The main…