Related papers: Tropical coefficient dynamics for higher-dimension…
Context: Star clusters form within giant molecular clouds that are strongly altered by the feedback action of the massive stars, but the cluster still remains embedded in a dense, highly turbulent medium and interactions with ambient…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
We describe the tropical curves in toric varieties and define the tropical Gromov-Witten invariants. We introduce amplitudes for the higher topological quantum mechanics (HTQM) on special trees and show that the amplitudes are equal to the…
Dynamical models of star clusters are maturing in the sense that effects other than simple point particle dynamics are taken into account. We summarize the relevance of and prospects for this new generation of N-body models.
We consider a threshold factor model for high-dimensional time series in which the dynamics of the time series is assumed to switch between different regimes according to the value of a threshold variable. This is an extension of threshold…
We shall show that the stable categories of graded Cohen-Macaulay modules over quotient singularities have tilting objects. In particular, these categories are triangle equivalent to derived categories of finite dimensional algebras. Our…
Direct numerical simulation of homogeneous isotropic turbulence shows pronounced clustering of inertial particles in the inertial subrange at high Reynolds number, in addition to the clustering typically observed in the near dissipation…
We put cluster tilting in ageneral framework by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal one-orthogonal subcategory) carries an abelian structure. These abelian quotients turn out…
In this text, we show that locally tropically convex tropical varieties in $\mathbb{R}^n$ have locally a canonical polyhedral structure that satisfies higher balancing conditions at all cells of positive codimension.
Tropical convective clouds evolve over a wide range of temporal and spatial scales, and this makes them difficult to simulate numerically. Here, we propose that their statistical properties can be derived within a simplified…
Let D be a triangulated category with a cluster tilting subcategory U. The quotient category D/U is abelian; suppose that it has finite global dimension. We show that projection from D to D/U sends cluster tilting subcategories of D to…
We show that the ratio of different structure functions have a maximum which depends on energy. We argue, using Golec-Biernat and Wusthoff model, that these maxima are the certain functions of the saturation scale. The analysis of leading…
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…
The mass fraction of hot gas in clusters is a basic quantity whose level and dependence on the cluster mass and redshift are intimately linked to all cluster X-ray and SZ measures. Modeling the evolution of the gas fraction is clearly a…
We present a numerical simulation of a granular material using hydrodynamic equations. We show that, in the absence of external forces, such a system phase-separates into high density and low density regions. We show that this separation is…
We show that the quotient of the continuous cluster category $\mathcal C_\pi$ modulo the additive subcategory generated by any cluster is an abelian category and we show that it is isomorphic to the category of infinite length modules over…
We introduce and study mutation of torsion pairs, as a generalization of mutation of cluster tilting objects, rigid objects and maximal rigid objects. It is proved that any mutation of a torsion pair is again a torsion pair. A geometric…
We give an explicit upper bound for the degree of a tropical basis of a homogeneous polynomial ideal. As an application f-vectors of tropical varieties are discussed. Various examples illustrate differences between Gr\"obner and tropical…
In the framework of the trap-size scaling theory, we study the scaling properties of the Bose-Hubbard model in two dimensions in the presence of a trapping potential at finite temperature. In particular, we provide results for the particle…
This study presents an enhanced method for analyzing cluster dynamics, with a particular focus on tracking clusters' continuity over time using time-series data from molecular dynamics (MD) simulation. The proposed method was applied to…