Related papers: The Local load sharing fiber bundle model in highe…
We report a novel critical behavior in the breakdown of an equal load sharing fiber bundle model at a dispersion $\delta_c$ of the breaking threshold of the fibers. For $\delta < \delta_c$, there is a finite probability $P_b$, that…
In this work, phase-field modeling of hydraulic fractures in porous media is extended towards a global-local approach. Therein, the failure behavior is solely analyzed in a (small) local domain. In the surrounding medium, a simplified and…
Liquid droplets on fiber are often observed both in nature and in different engineering applications, like a fog harvesting mesh. Knowledge about drop-on-fiber morphology and its shedding under the influence of gravity can allow for the…
Stochastic models for the development of cracks in 1 and 2 dimensional objects are presented. In one dimension, we focus on particular scenarios for interacting and non-interacting fragments during the breakup process. For two dimensional…
We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition…
Every realistic instance of a percolation problem is faced with some degree of polydispersity, e.g., the pore-size distribution of an inhomogeneous medium, the size distribution of filler particles in composite materials, or the vertex…
In the context of 5G, infrastructure sharing has been identified as a potential solution to reduce the investment costs of cellular networks. In particular, it can help low-income regions build 5G networks more affordably and further bridge…
Around 1920, Kaluza and Klein had the idea to add a fifth dimension to the classical 4-dimensional spacetime of general relativity to create a geometric theory of gravitation and electromagnetism. Today, theoretical evidences, like string…
We introduce an individual-based model for fiber elements having the ability to cross-link or unlink each other and to align with each other at the cross links. We first formally derive a kinetic model for the fiber and cross-links…
This work uses fiber bundles as a framework to describe some effects of number scaling on gauge theory and some geometric quantities. A description of number scaling and fiber bundles over a flat space time manifold, M, is followed by a…
Exploiting two interfering fields which are initially in the same temporal mode but with the spectra altered by propagating through different fibers, we characterize how the spectra of temporal modes changes with the fiber induced…
We investigate the fracture process of a bundle of fibers with random Young modulus and a constant breaking strength. For two component systems we show that the strength of the mixture is always lower than the strength of the individual…
A series of experimental results on the in-plane fracture of a fiber reinforced laminated composite panel is analyzed using the variational multi-scale cohesive method (VMCM). The VMCM results demonstrate the influence of specimen geometry…
We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose $r$-neighbors share any exclusive pair. The $r$-neighbor of a…
The Linear Threshold Model is a widely used model that describes how information diffuses through a social network. According to this model, an individual adopts an idea or product after the proportion of their neighbors who have adopted it…
This paper presents a unified view of manifolds and fiber bundles, which, while superficially different, have strong parallels. It introduces the notions of an m-atlas and of a local coordinate space, and shows that special cases are…
While it is not generally reflected in the `nice' datasets used for benchmarking machine learning algorithms, the real-world is full of processes that would be best described as many-to-many. That is, a single input can potentially yield…
We investigate the failure mechanisms of load sharing complex systems. The system is composed of multiple nodes or components whose failures are determined based on the interaction of their respective strengths and loads (or capacity and…
Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…
Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers from the curse of dimensionality. It is therefore important…