Related papers: Two particles on a star graph II
Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac…
Using a simple deterministic model for the Internet graph we show that the eigenvalue power law distribution for its adjacency matrix is a direct consequence of the degree distribution and that the graph must contain many star subgraphs.
In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of…
A biclique of a graph $G$ is an induced complete bipartite subgraph of $G$ such that neither part is empty. A star is a biclique of $G$ such that one part has exactly one vertex. The star graph of $G$ is the intersection graph of the…
We define an evolution of multiple particles on a discrete manifold $G$. Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move deterministically and reversibly on the frame bundle $P$ of…
Non-equilibrium self-organized patterns formed by particles interacting through competing range interaction are driven over a substrate by an external force. We show that, with increasing driving force, the pre-existed static patterns…
We consider the Penrose process with the charged particles in the Reissner-Nordstr\"{o}m (RN) background. Let parent particle 0 decay to particles 1 and 2. With the assumption that all three particles move in the equatorial plane, the exact…
Aims: I report results in numerical simulations of star-disk magnetospheric interaction. A thin accretion disk with corona above a rotating stellar surface is simulated in a parameter study, to find trends in the angular momentum flux. The…
We show that for an infinitely many natural numbers $k$ there are $k$-uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\mathcal{A}(k,I, n)$ denote the class of $k$-graphs on $n$ vertices in…
In this paper we investigate a system describing electrically charged particles in the whole space R^2. Our main goal is to describe large time behavior of solutions which start their evolution from initial data of small size. This is…
We first provide a classification of the pure rotational motion of 2 particles on a sphere interacting via a repelling potential. This is achieved by providing a simple geometric equivalence between repelling particles and attracting…
We consider the symmetric group $\mathrm{Sym}_n,\,n\geqslant 2$, generated by the set $S$ of transpositions $(1~i),\,2 \leqslant i \leqslant n$, and the Cayley graph $S_n=Cay(\mathrm{Sym}_n,S)$ called the Star graph. For any positive…
We study the problem of calculating two-loop three-point diagrams with irreducible numerators (i.e. numerators which cannot be expressed in terms of the denominators). For the case of massless internal particles and arbitrary (off-shell)…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
Several recent imaging experiments access the equilibrium density profiles of interacting particles confined to a two-dimensional substrate. When these particles are in a fluid phase, we show that such data yields precise information…
We explore single and multi-loop conformal integrals, such as the ones appearing in dual conformal theories in flat space. Using Mellin amplitudes, a large class of higher loop integrals can be written as simple integro-differential…
Two-dimensional plasma crystals are characterized by a strong up-and-down asymmetry not only due to gravity but also due to the presence of plasma flow at the location of particles. We study for the first time the interaction of a…
A prescription invented a long time ago by Case and Danilov is used to get the wave function of point interactions in two and three dimensions.
Associated to a graph $G$ is a set $\mathcal{S}(G)$ of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent, and the diagonal entries are free to be…
A self-action problem for a pointlike charged particle arbitrarily moving in flat spacetime of three dimensions is considered. Outgoing waves carry energy-momentum and angular momentum; the radiation removes energy and angular momentum from…