相关论文: Statistical Topography of Glassy Interfaces

We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…

For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by…

We study the crossover scaling behavior of the height-height correlation function in interface depinning in random media. We analyze experimental data from a fracture experiment and simulate an elastic line model with non-linear couplings…

The spectral properties of disordered fully-connected graphs with a special type of the node-node interactions are investigated. The approximate analytical expression for the ensemble-averaged spectral density for the Hamiltonian defined on…

Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…

Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…

Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…

Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…

Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical…

We apply renormalized entropy as a complexity measure to the logistic and sine-circle maps. In the case of logistic map, renormalized entropy decreases (increases) until the accumulation point (after the accumulation point up to the most…

Although the leading-order scaling of entanglement entropy is non-universal at a quantum critical point (QCP), sub-leading scaling can contain universal behaviour. Such universal quantities are commonly studied in non-interacting field…

We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or…

Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for…

Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…

We study the four dimensional site-diluted Ising model using finite-size scaling techniques. We explore the whole parameter space (density-coupling) in order to determine the Universality Class of the transition line. Our data are…

The singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields. Myriad applications including clustering, classification, and dimensionality reduction involve studying and exploiting the geometric…

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems…

We develop a computational method for simulating the nonlinear dynamics of an elastic tumor-host interface. This work is motivated by the recent linear stability analysis of a two-phase tumor model with an elastic membrane interface in 2D.…

The analysis of contours of scalar fields plays an important role in visualization. For example the contour tree and contour statistics can be used as a means for interaction and filtering or as signatures. In the context of tensor field…