Related papers: A discrete time evolution model for fracture netwo…
We suggest a model for data losses in a single node of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. The model shows critical behavior with an abrupt…
We perform a model-independent reconstruction of the cosmic distances using the Multi-Task Gaussian Process (MTGP) framework as well as knot-based spline techniques with DESI-DR2 BAO and DES-SN5YR datasets. We calibrate the comoving sound…
The statistics of randomly branching double-folded ring polymers are relevant to the secondary structure of RNA, the large-scale branching of plectonemic DNA (and thus bacterial chromosomes), the conformations of single-ring polymers…
Flexible road pavements deteriorate primarily due to traffic and adverse environmental conditions. Cracking is the most common deterioration mechanism; the surveying thereof is typically conducted manually using internationally defined…
In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness, i.e. a propagating fractal crack reaches a terminal…
We present a continuum model for the propagation of cracks and fractures in brittle materials. The components of the strain tensor $\epsilon$ are the fundamental variables. The evolution equations are based on a free energy that reduces to…
We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite…
The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…
We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
The aim of this paper is to develop a method for proving almost sure convergence in Gromov-Hausodorff-Prokhorov topology for a class of models of growing random graphs that generalises R\'emy's algorithm for binary trees. We describe the…
As a consequence of shearing, wing cracks can emerge from pre-existing fractures. The process involves the interaction of sliding of the existing fracture surfaces and the tensile material failure that creates wing cracks. This work devises…
We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of…
We consider a new model for complex networks whose underlying mechanism is extending dense subgraphs. In the frustum model, we iteratively extend cliques over discrete-time steps. For many choices of the underlying parameters, graphs…
We study kinetic theories for isotropic, two-dimensional grain boundary networks which evolve by curvature flow. The number densities $f_s(x,t)$ for $s$-sided grains, $s =1,2,\ldots$, of area $x$ at time $t$, are modeled by kinetic…
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
We study the evolution of the cross-correlation between voids and the mass density field - i.e. of void profiles. We show that approaches based on the spherical model alone miss an important contribution to the evolution on large scales of…
We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…
We study growth properties of the number of paths of lenght k for a variant of Cameo graphs introduced in an earlier paper. Sharp results are obtained for threshold for the k-path connectivity and the essential diameter.