相关论文: Exotic trees
The spatial distribution of unvisited/persistent sites in $d=1$ $A+A\to\emptyset$ model is studied numerically. Over length scales smaller than a cut-off $\xi(t)\sim t^{z}$, the set of unvisited sites is found to be a fractal. The fractal…
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…
We consider minimum-cost spanning trees, both in lattice and Euclidean models, in d dimensions. For the cost of the optimum tree in a box of size L, we show that there is a correction of order L^theta, where theta < 0 is a universal…
We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model…
We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different…
We consider flexible branched polymer, with quenched branch structure, and show that its conformational entropy as a function of its gyration radius $R$, at large $R$, obeys, in the scaling sense, $\Delta S \sim R^2/(a^2L)$, with $a$ bond…
We introduce a class of random compact metric spaces L(\alpha) indexed by \alpha \in (1,2) and which we call stable looptrees. They are made of a collection of random loops glued together along a tree structure, and can be informally be…
We prove that the extrinsic Hausdorff dimension is always greater than or equal to the intrinsic Hausdorff dimension in models of triangulated random surfaces with action which is quadratic in the separation of vertices. We furthermore…
Within the framework of string field theory the intrinsic Hausdorff dimension d_H of the ensemble of surfaces in two-dimensional quantum gravity has recently been claimed to be 2m for the class of unitary minimal models (p = m+1,q = m).…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
We study a special case of the vertex splitting model which is a recent model of randomly growing trees. For any finite maximum vertex degree $D$, we find a one parameter model, with parameter $\alpha \in [0,1]$ which has a so--called…
We study numerically the fractal structure of the intrinsic geometry of random surfaces coupled to matter fields with $c=1$. Using baby universe surgery it was possible to simulate randomly triangulated surfaces made of 260.000 triangles.…
Trees are key roughness elements in urban environments, shaping airflow, microclimates, and pollutant dispersion. Yet the aerodynamic drag of complex tree-like structures at high Reynolds numbers remains poorly characterized compared with…
The geometric properties of the critical fluctuations in abelian gauge theories such as the Ginzburg-Landau model are analyzed in zero background field. Using a dual description, we obtain scaling relations between exponents of geometric…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…
We investigate the validity of the "Einstein relations" in the general setting of unimodular random networks. These are equalities relating scaling exponents: $d_w = d_f + \tilde{\zeta}$ and $d_s = 2 d_f/d_w$, where $d_w$ is the walk…
We study universal aspects of polymer conformations and transverse fluctuations for a single swollen chain characterized by a contour length $L$ and a persistence length $\ell_p$ in two dimensions (2D) and in three dimensions (3D) in the…
We define, analyze, and give efficient algorithms for two kinds of distance measures for rooted and unrooted phylogenies. For rooted trees, our measures are based on the topologies the input trees induce on triplets; that is, on…
It has recently been shown that networks possessing scale-free and fractal properties may exhibit a bifractal nature, in which local structures are described by two different fractal dimensions. In this study, we investigate random walks on…
Scale-free networks are prevalently observed in a great variety of complex systems, which triggers various researches relevant to networked models of such type. In this work, we propose a family of growth tree networks $\mathcal{T}_{t}$,…