Related papers: Eigenvalue Clustering, Control Energy, and Logarit…
The local and global properties of the Goetz thick plane domain wall space-time are studied. It is found that when the surface energy of the wall is greater than a critical value $\sigma_{c}$, the space-time will be closed by intermediate…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
Simulation results of Ising systems for several update rules, observables, and dimensions are analyzed. The lattice-size dependence is discussed for the autocorrelation times and for the weights of eigenvalues, giving fit results in the…
In the current work, we study the eigenvalue distribution results of a class of non-normal matrix-sequences which may be viewed as a low rank perturbation, depending on a parameter $\beta>1$, of the basic Toeplitz matrix-sequence…
In order to improve the efficiency and sustainability of electricity systems, most countries worldwide are deploying advanced metering infrastructures, and in particular household smart meters, in the residential sector. This technology is…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
We apply the Charge Simulation Method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many "small" components. This application allows to use just a single charge point for each component. The…
This article attempts answering the following problematic: How to model and classify energy consumption profiles over a large distributed territory to optimize the management of buildings' consumption? Doing case-by-case in depth auditing…
We observe that the distribution of the eigenvalues of an $N$-by-$N$ GUE random matrix is log-concave on $\mathbb{R}^N$, and that the same is true for the law of a single gap between two consecutive eigenvalues. We use this observation to…
We investigate monopoles in four-dimensional compact U(1) with Wilson action. We focus our attention on monopole clusters as they can be identified unambiguously contrary to monopole loops. We locate the clusters and determine their…
We generalize the small scale dynamics of the universe by taking into account models with an equation of state which evolves with time, and provide a complete formulation of the cluster virialization attempting to address the nonlinear…
The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analysed as a multivariate…
In order to understand controlling a complex system, an estimation of the required effort needed to achieve control is vital. Previous works have addressed this issue by studying the scaling laws of energy cost in a general way with…
Whether embedding spaces use all their dimensions equally, i.e., whether they are isotropic, has been a recent subject of discussion. Evidence has been accrued both for and against enforcing isotropy in embedding spaces. In the present…
It is known that a matrix polynomial with unitary matrix coefficients has its eigenvalues in the annular region $\frac{1}{2} < |\lambda| < 2$. We prove in this short note that under certain assumptions, matrix polynomials with either doubly…
We estimate galaxy clustering under a modified gravitational potential. In particular, the modifications in gravitational potential energy occur due to a power-law and cosmological constant terms. We derive a canonical partition function…
We study the limiting eigenvalue distribution of $n\times n$ banded Toeplitz matrices as $n\to \infty$. From classical results of Schmidt-Spitzer and Hirschman it is known that the eigenvalues accumulate on a special curve in the complex…
A novel methodology is proposed for clustering multivariate time series data using energy distance defined in Sz\'ekely and Rizzo (2013). Specifically, a dissimilarity matrix is formed using the energy distance statistic to measure…
We derive bounds on the eigenvalues of a generic form of double saddle-point matrices. The bounds are expressed in terms of extremal eigenvalues and singular values of the associated block matrices. Inertia and algebraic multiplicity of…
We show that the locations where finite- and infinite-time clustering occurs for the 1D Euler-alignment system can be determined using only the initial data. Our present work provides the first results on the structure of the finite-time…