Related papers: The Efficacy of Event Isotropy as an Event Shape O…
We propose a novel method for testing isotropy of a three-dimensional distribution using Shannon entropy. We test the method on some Monte Carlo simulations of isotropic and anisotropic distributions and find that the method can effectively…
This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element $h_I=\bigtriangleup x_i\bigtriangleup p_i$. Varying $h_I$ leads to variations in the amount of measured information of a…
This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately…
In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We examine isotropic as well as anisotropic media. Part of the…
Transverse spherocity, an event shape observable, has a very unique capability to separate the events based on their geometrical shape, i.e. jetty and isotropic. In this work, we use transverse spherocity for the first time in heavy-ion…
The verification of whether small-scale turbulence is isotropic remains a grand challenge. The difficulty arises because the presence of small-scale anisotropy is tied to the dissipation tensor, whose components require the full…
The decay of large-scale anisotropies in small-scale turbulent flow is investigated. By introducing two different kinds of estimators we discuss the relation between the presence of a hierarchy for the isotropic and the anisotropic scaling…
Isotropization occurs on time scales much shorter than the thermal equilibration time. This is a crucial ingredient for the understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in complex many body…
Azimuthal angle dependence of the pion source radii has been measured applying the event shape engineering technique at the PHENIX experiment. When events with higher magnitude of second-order flow vector are selected, the oscillation of…
One of the event shape observables, the transverse spherocity ($S_0$), has been studied successfully in small collision systems such as proton-proton collisions at the LHC as a tool to separate jetty and isotropic events. It has a unique…
The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…
A measure of asymmetry is a quantification method that allows for the comparison of categorical evaluations before and after treatment effects or among different target populations, irrespective of sample size. We focus on square…
We present a numerical study of two-particle dispersion from point-sources in 3D incompressible Homogeneous and Isotropic turbulence, at Reynolds number Re \simeq 300. Tracer particles are emitted in bunches from localized sources smaller…
Certain anomalies at large angular scales in the cosmic microwave background measured by WMAP have been suggested as possible evidence of breakdown of statistical isotropy(SI). Most CMB photons free-stream to the present from the surface of…
We define the projected entropy S(T) at a given temperature T in the context of an Ising model transition matrix calculation as the entropy associated with the distribution of Markov chain realizations in energy-magnetization, E-H, space.…
Tipping points (TP) are often described as low-dimensional bifurcations, and are associated with early-warning signals (EWS) due to critical slowing down (CSD). CSD is an increase in amplitude and correlation of noise-induced fluctuations…
Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses…
Input-to-State Stability (ISS) is fundamental in mathematically quantifying how stability degrades in the presence of bounded disturbances. If a system is ISS, its trajectories will remain bounded, and will converge to a neighborhood of an…
In high energy particle collisions the shape of the event, i.e. the relative distribution of particles in momentum space, is often used to try to select events with certain topologies. It is claimed that an event shape observable like…
A primary goal of integral field spectroscopic (IFS) surveys is to provide a statistical census of galaxies classified by their internal kinematics. As a result, the observational spin parameter, $\lambda_R$, has become one of the most…