相关论文: Transfer across Random versus Deterministic Fracta…
We investigate the energetics of droplets sourced by the thermal fluctuations in a system undergoing a first-order transition. In particular, we confine our studies to two dimensions with explicit calulations in the plane and on the sphere.…
The evolution of fractal surface structures with flattening of asperities was investigated using isotropically roughened aluminium surfaces loaded in compression. It was found that asperity amplitude, mean roughness and fractal dimension…
We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular feature is that the solution space depends on the actual fractal…
We describe a fluctuating surface-current formulation of radiative heat transfer, applicable to arbitrary geometries, that directly exploits standard, efficient, and sophisticated techniques from the boundary-element method. We validate as…
We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in…
The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Nevertheless, it has been little studied for complex networks such as scale-free and small world networks. Here we study the…
We study the diffusion of tangential tensor-valued data on curved surfaces. For this purpose, several finite-element-based numerical methods are collected and used to solve a tangential surface n-tensor heat flow problem. These methods…
The possible paralelism existing between phase transitions and fracture in disordered materials, is discussed using the well-known Fiber Bundle Models and a probabilistic approach suited to smooth fluctuations near the critical point. Two…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
We study the mean-field version of a model proposed by Leschhorn to describe the depinning transition of interfaces in random media. We show that evolution equations for the distribution of forces felt by the interface sites can be written…
In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension. This dimension stands out from the…
The fractal dimension $\delta_g^{(1)}$ of turbulent passive scalar signals is calculated from the fluid dynamical equation. $\delta_g^{(1)}$ depends on the scale. For small Prandtl (or Schmidt) number $Pr<10^{-2}$ one gets two ranges,…
We discuss properties of random fractals by means of a set of numbers that characterize their universal properties. This set is the generalized singularity specturm that consists of the usual spectrum of mulitfractal dimensions and the…
The definitions and applications of Radial Distribution Function (RDF) and Structure Factor (SF) to study properties of aggregate are found in many papers and books. The approach adopted to calculate the RDF and the SF to determine the…
This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
Fracture networks are ubiquitous in nature, spanning scales from millimeter-sized cracks in botanical peels to hundred-kilometer-long lineae on planetary satellites. The propagation of a crack is a complex, nonlinear phenomenon governed by…
One-dimensional topological edge modes are usually studied considering the interface between two different semi infinite periodic crystals (PCs) with inverted band structure around the Dirac point. Here we consider the case where the two…
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
We consider the morphology of two dimensional cracks observed in experimental results obtained from paper samples and compare these results with the numerical simulations of the random fuse model (RFM). We demonstrate that the data obey…