相关论文: Explosive percolation on the Bethe lattice is ordi…

Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory, in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic…

A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes $s = 0,1,2,...$, in units of lattice space, diffuses asymmetrically on the lattice. A related…

Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…

The concept of exceptional point (EP) is demonstrated experimentally in the case of a simple mechanical system consisting of two linearized coupled pendulums. Exceptional points correspond to specific values of the system parameters that…

Motivated by the recent growing interest in the field of $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems we theoretically study the emergency of singularities called Exceptional Points ($\textit{EP}$s) in the eigenspectrum of…

We study how varying the P \'eclet number (Pe) affects the steady state sedimentation of colloidal particles that interact through short-ranged attractions. By employing a hybrid molecular dynamics simulation method we demonstrate that the…

The finite-size scaling (FSS) theory for continuous phase transitions has been useful in determining the critical behavior from the size dependent behaviors of thermodynamic quantities. When the phase transition is discontinuous, however,…

We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting…

We study the distribution of finite clusters in slightly supercritical ($p \downarrow p_c$) Bernoulli bond percolation on transitive nonamenable graphs, proving in particular that if $G$ is a transitive nonamenable graph satisfying the…

The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close…

We derive three critical exponents for Bernoulli site percolation on the on the Uniform Infinite Planar Triangulation (UIPT). First we compute explicitly the probability that the root cluster is infinite. As a consequence, we show that the…

Two ensembles are often used to model random graphs subject to constraints: the microcanonical ensemble (= hard constraint) and the canonical ensemble (= soft constraint). It is said that breaking of ensemble equivalence (BEE) occurs when…

We construct a theory to introduce the concept of topologically robust exceptional points (EP). Starting from an ordered system with $N$ elements, we find the necessary condition to have the highest order exceptional point, namely…

We investigate percolation, a probabilistic model for continuous phase transition (CPT), on square and weighted planar stochastic lattices. In its thermal counterpart, entropy is minimally low where order parameter (OP) is maximally high…

The combined processes of anodization and electrodeposition lead to highly ordered arrays of cylindrical nanowires. This template-based self-assembly fabrication method yields nanowires embedded in alumina. Commonly, chemical etching is…

Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…

Aldous introduced a modification of the bond percolation process on the binary tree where clusters stop growing (freeze) as soon as they become infinite. We investigate the site version of this process on the triangular lattice where…

`With persistence, a drop of water hollows out the stone' goes the ancient Greek proverb. Yet, canonical percolation models do not account for interactions between a moving tracer and its environment. Recently, we have introduced the…

We consider supercritical bond percolation on a family of high-girth $d$-regular expanders. Alon, Benjamini and Stacey (2004) established that its critical probability for the appearance of a linear-sized ("giant'') component is…

We present the results of a percolation-like model that has been restricted compared to standard percolation models in the sense that we do not allow finite sized clusters to break up once they have formed. We calculate the critical…