Related papers: Topological Percolation on Hyperbolic Simplicial C…
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2d directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale…
This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build…
Numerical investigation of critical exponents on a hypercubic with L^d random sites with L up to $33 and d up to 7 show that above the critical dimension the phase transitions in Ising model and percolation are not alike.
We study the percolation of strongly connected clusters (SCCs), in which sites are mutually reachable through directed paths, in systems with randomly oriented bonds by extensive simulations on hypercubic lattices from dimension $d=2$ to…
A theoretical and numerically study of dynamical properties in the sol-gel transition is presented. In particular, the complex phenomenology observed experimentally and numerically in gelling systems is reproduced in the framework of…
We propose a new avenue in which percolation, which has been much associated with critical phase transitions, can also dictate the asymptotic dynamics of non-Hermitian systems by breaking PT symmetry. Central to it is our newly-designed…
In discussing the phase transition of the three-dimensional complex |psi|^4 theory, we study the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
We study a dependent site percolation model on the $n$-dimensional Euclidean lattice where, instead of single sites, entire hyperplanes are removed independently at random. We extend the results about Bernoulli line percolation showing that…
We study bootstrap percolation processes on random simplicial complexes of some fixed dimension $d \geq 3$. Starting from a single simplex of dimension $d$, we build our complex dynamically in the following fashion. We introduce new…
Percolation clusters are probably the simplest example for scale--invariant structures which either are governed by isotropic scaling--laws (``self--similarity'') or --- as in the case of directed percolation --- may display anisotropic…
We compare phase transition and critical phenomena of bond percolation on Euclidean lattices, nonamenable graphs, and complex networks. On a Euclidean lattice, percolation shows a phase transition between the nonpercolating phase and…
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem.…
Considering a "random walk in a random environment" in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization"…
We consider the Constrained-degree percolation model on the hypercubic lattice, $\mathbb L^d=(\mathbb Z^d,\mathbb E^d)$ for $d\geq 3$. It is a continuous time percolation model defined by a sequence, $(U_e)_{e\in\mathbb E^d}$, of i.i.d.…
Topological defects (TDs) are crucial for understanding important physical properties of crystalline materials including mechanical failure, ion transport, and two-dimensional melting. This concept has not translated to disordered materials…
The class of traveling wave solutions of the sine-Gordon equation is known to be in 1-1 correspondence with the class of (necessarily singular) pseudospherical surfaces in Euclidean space with screw-motion symmetry: the pseudospherical…
Topological properties of photonic structures described by Hamiltonian matrices have been extensively studied in recent years. Photonic systems are often open systems, and their coupling with the environment is characterized by scattering…
In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological…
Let M be a hyperbolic n-manifold whose cusps have torus cross-sections. In arXiv:0901.0056, the authors constructed a variety of nonpositively and negatively curved spaces as "2\pi-fillings" of M by replacing the cusps of M with compact…