Related papers: Different Aspects of a Model for Random Fragmentat…
Many biological processes and objects can be described by fractals. The paper uses a new type of objects - blinking fractals - that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that…
Quantum field model of unstable particles with random mass is suggested to describe the finite-width effects in decay rate. Within the framework of this model we derive the convolution formula for a width of the channels with unstable…
Everyday thousands of meteoroids enter the Earth's atmosphere. The vast majority burn up harmlessly during the descent, but the larger objects survive, occasionally experiencing intense fragmentation events, and reach the ground. These…
Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
"Emergence", the phenomenon where a complex system displays properties, behaviours, or dynamics not trivially reducible to its constituent elements, is one of the defining properties of complex systems. Recently, there has been a concerted…
We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…
This chapter deals with error and uncertainty in data. Treats their measuring methods and meaning. It shows that uncertainty is a natural property of many data sets. Uncertainty is fundamental for the survival os living species, Uncertainty…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
We introduce an analytically solvable model for a fragmented object that, despite of a low degree of randomness and of the extreme simplicity of the breaking process, displays non self-averaging effects in its thermodynamic limit.
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
I present a short review of models for transverse-momentum distributions and transversity, with a particular attention on general features common to many models. I compare some model results with experimental extractions. I discuss the…
Many complex generative systems use languages to create structured objects. We consider a model of random languages, defined by weighted context-free grammars. As the distribution of grammar weights broadens, a transition is found from a…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
We introduce a model for the dynamics of mud cracking in the limit of of extremely thin layers. In this model the growth of fracture proceeds by selecting the part of the material with the smallest (quenched) breaking threshold. In…
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
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…