相关论文: Spiderweb central configurations

In this paper, for the spatial Newtonian $2n$-body problem with equal masses, by proving the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial…

In this paper we investigate, using high resolution N-body simulations, the density profiles and the morphologies of galaxy clusters in seven models of structure formation. We show that these properties of clusters are closely related to…

Nuclear stellar cluster (NSCs) are known to exist around massive black holes (MBHs) in galactic nuclei. They are thought to have formed through in-situ star formation following gas inflow to the nucleus of the galaxy and/or through the…

According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive and negative edges are respectively located inside and between the…

Throughout this paper, a persistence diagram ${\cal P}$ is composed of a set $P$ of planar points (each corresponding to a topological feature) above the line $Y=X$, as well as the line $Y=X$ itself, i.e., ${\cal P}=P\cup\{(x,y)|y=x\}$.…

Many processes within galaxy clusters, such as those believed to govern the onset of thermally unstable cooling and AGN feedback, are dependent upon local dynamical timescales. However, accurately mapping the mass distribution within…

We derive the renormalization group equations for the neutrino masses and mixing angles in explicit form and discuss the possible classes of their solutions. We identify fixed points in the equations for mixing angles, which can be reached…

Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on…

The symmetry and topology of the coincidence structure, i.e. the locus of points in configuration space corresponding to particles in the same position, plays a critical role in extracting universal properties for few-body models with…

Core collapse is a prominent evolutionary stage of self-gravitating systems. In an idealised collisionless approximation, the region around the cluster core evolves in a self-similar way prior to the core collapse. Thus, its radial density…

We introduce a shell-model theory that combines traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformations, and test the validity of…

Based on two involutions and a bijection, we completely determine the difference between the number of $\ell$-regular partitions of $n$ into an even number of parts and into an odd number of parts for all positive integers $n$ and $\ell>1$,…

Nuclear star clusters (NSCs) are dense, compact stellar systems only a few parsecs across, located at galaxy centers. Their small sizes make them difficult to resolve spatially. NSCs often coexist with massive black holes, and both trace…

For the planar $N$-body problem, we first introduce a class of moving frame suitable for orbits near central configurations, especially for total collision orbits, which is the main new ingredient of this paper. The moving frame allows us…

Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…

Core-periphery (CP) structure is an important meso-scale network property where nodes group into a small, densely interconnected {core} and a sparse {periphery} whose members primarily connect to the core rather than to each other. While…

We report on a series of tests of agreement between three types of N-body simulations: PM, P$^3$M, and Tree codes. We find good agreement in both the individual and the statistical properties only on scales larger than the mean…

Preliminary results are presented about a fully self-consistent N-body simulation of a sample of four massive globular clusters in close interaction within the central region of a galaxy. The N-body representation (with N=1.5x10^6 particles…

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each…

Many-body-localization (MBL) transitions are studied in a family of single-spin-flip spin-$\frac12$ models, including the one-dimensional (1D) chain with nearest-neighbor interactions, the quantum dot (QD) model with all-to-all pair…