Related papers: Superstable Geometry in Triadic Percolation
We study corotational wave maps from $(1+3)$-dimensional Minkowski space into the three-sphere. We establish the asymptotic stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev…
The analytical characterization of coverage probability in finite three-dimensional wireless networks has long remained an open problem, hindered by the loss of spatial independence in finite-node settings and the coupling between link…
The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are performed using an efficient star-triangle…
We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of the random environment. The structure of…
A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which…
Motivated by the finding of nearly isotropic superconductivity in $\mathrm{(Ba,K)Fe_2As_2}$, we use renormalized mean field theory to investigated the $t$-$J$ model on three-dimensional simple cubic lattice. A tunable anisotropic parameter…
We study large uniform random maps with one face whose genus grows linearly with the number of edges, which are a model of discrete hyperbolic geometry. In previous works, several hyperbolic geometric features have been investigated. In the…
In this paper, we study the classical two-predators-one-prey model. The classical model described by a system of 3 ordinary differential equations can be reduced to a one-dimensional bimodal map. We prove that this map has at most two…
Triadic interactions are higher-order interactions that occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among…
It is pointed out that if we allow for the possibility of a multilayered universe, it is possible to maintain exact supersymmetry and arrange, in principle, for the vanishing of the cosmological constant. Superpartner(s) of a known particle…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
Using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations.…
Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classes of graphs, significantly increasing the number and variety…
Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property,…
Two-dimensional superconductivity has become a major frontier in condensed matter physics. It holds the key to the mechanism of high-temperature superconductors and offers an exceptional arena to stabilize emergent quantum states enabled by…
We prove that the supercritical phase of Voronoi percolation on $\mathbb{R}^d$, $d\geq 3$, is well behaved in the sense that for every $p>p_c(d)$ local uniqueness of macroscopic clusters happens with high probability. As a consequence,…
We investigate site and bond percolation in triangular and square lattices subjected to linear distortion. In contrast to previously studied distortion schemes that preserve lattice geometry, linear distortion dislocates regular lattice…
The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest neighbor bonds. This constitutes a rigidity percolation…
We analyze the nucleation of supersolid order out of the superfluid ground state of bosons on the triangular lattice. While the stability of supersolidity against phase separation in this system is by now well established for…
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system…