Related papers: Distal and non-Distal Behavior in Pairs
We review a range of stastistical methods for analyzing the structures of star clusters, and derive a new measure ${\cal Q}$ which both quantifies, and distinguishes between, a (relatively smooth) large-scale radial density gradient and…
Directional data consists of unit vectors in q-dimensions that can be described in polar or Cartesian coordinates. Axial data can be viewed as a pair of directions pointed in opposite directions or as a projection matrix of rank 1.…
We introduce a minimal model for a collection of self-propelled apolar active particles, also called as `active nematic', on a two-dimensional substrate and study the order-disorder transition with the variation of density. The particles…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
We study a nonlinear semigroup associated to a nonexpansive mapping on a Hadamard space and establish its weak convergence to a fixed point. A discrete-time counterpart of such a semigroup, the proximal point algorithm, turns out to have…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
Pronounced core-halo patterns of dark matter and gas density profiles, observed in relaxed galaxies and clusters, were hitherto fitted by empirical power-laws. On the other hand, similar features are well known from astrophysical plasma…
We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically…
Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…
This paper develops a geometrical model of dislocations and disclinations in single crystals at the mesoscopic scale. In the continuation of previous work the distribution theory is used to represent concentrated effects in the defect lines…
Within a simple SO(8) algebraic model, the coexistence between isoscalar and isovector pairing modes can be successfully described using a mean-field method plus restoration of broken symmetries. In order to port this methodology to real…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
Behavioural distances provide a quantitative approach to comparing the states of transition systems, moving beyond traditional Boolean notions of equivalence. In this paper, we develop a sound and complete axiomatisation of behavioural…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
We study the spatio-temporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. We consider systems initially in an uncorrelated state, and find that correlations…
In equilibrium, the collective behaviour of particles interacting via steep, short-ranged potentials is well captured by the virial expansion of the free energy at low density. Here, we extend this approach beyond equilibrium to the case of…
For a dimer with a non-degenerate orbital built from atomic wave functions of Gaussian shape we evaluate all the electron-phonon couplings derived from the one-body and two-body electronic interactions, considering both the adiabatic and…
There are many papers studying properties of point sets in the Euclidean space $\mathbb{E}^m$ or on integer grids $\mathbb{Z}^m$, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the…
We examine the effects that dynamical instability has on shaping the orbital properties of exoplanetary systems. Using N-body simulations of non-EMS (Equal Mutual Separation), multi-planet systems we find that the lower limit of the…