相关论文: Fractal Plate Tectonics
The break-up of a two-dimensional circular disc by normal and oblique impact on a hard frictionless plate is investigated by molecular dynamics simulations. The disc is composed of numerous unbreakable randomly shaped convex polygons…
We study ballistic aggregation on a two dimensional square lattice, where particles move ballistically in between momentum and mass conserving coalescing collisions. Three models are studied based on the shapes of the aggregates: in the…
Functionally graded porous plates have been validated as remarkable lightweight structures with excellent mechanical characteristics and numerous applications. With inspiration from the high strength-to-volume ratio of triply periodic…
Atmospheric flows exhibit fractal fluctuations and inverse power law form for power spectra indicating an eddy continuum structure for the selfsimilar fluctuations. A general systems theory for fractal fluctuations developed by the author…
We consider dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation and pair distribution function of the disk…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
We present a review of the history and the present state of the fractal approach to the large-scale distribution of galaxies. Angular correlation function was used as a general instrument for the structure analysis. It was realized later…
In this report we present a study on the strength of rocks which are partially fractured from before. We have considered a two dimensional case of a rock in the form of a lattice structure. The fiber bundle model is used for modelling the…
The aim of this work is to study the asymptotic behavior of a structure made of plates of thickness $2\delta$ when $\delta\to 0$. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on…
We present experiments on the dynamic buckling and fragmentation of slender rods axially impacted by a projectile. By combining the results of Saint-Venant and elastic beam theory, we derive a preferred wavelength lambda for the buckling…
Spatial networks of land cover are well-described by power law rank-size distributions. Continuous field proxies for human settlements, agriculture and forest cover have similar spatial scaling properties spanning 4 to 5 orders of…
Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale $\ell$, where the fragments are subsequently allowed to settle under…
In this paper we develop a generalization of foliated manifolds in the context of metric spaces. In particular we study dendritations of surfaces that are defined as maximal atlases of compatible upper semicontinuous local decompositions…
A vibrating plate is set into a chaotic state of wave turbulence by either a periodic or a random local forcing. Correlations between the forcing and the local velocity response of the plate at the forcing point are studied. Statistical…
We present a new route to ergodicity breaking via Hilbert space fragmentation that displays an unprecedented level of robustness. Our construction relies on a single emergent (prethermal) conservation law. In the limit when the conservation…
Studies of fragmentation and parton density functions are a core component of researchin high energy particle and nuclear physics. These quantities are inherently interestingas a probe of the quantum nature of the strong force and are also…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
One of the most important scaling laws of time dependent fracture is Basquin's law of fatigue, namely, that the lifetime of the system increases as a power law with decreasing external load amplitude, $t_f\sim \sigma_0^{-\alpha}$, where the…
Analysis on fractals is a growing field, with hints of potential for widespread applicability across all of STEM. One of the most heavily researched type of fractals are the nested fractals, fractal shapes defined by virtue of being made of…