Related papers: Trees within trees II: Nested Fragmentations
The dynamics of dislocations is reported to exhibit glassy properties. We study numerically various versions of 2d edge dislocation systems in the absence of externally applied stress. Two types of glassy behavior are identified: (i)…
We present a coalescent process where three particles merge at each coagulation step. Using a random walk representation, we prove duality with a fragmentation process, whose fragmentation law we specify explicitly. Furthermore, we give a…
This is the first of a series of three articles that treats fracture localization as a critical phenomenon. This first article establishes a statistical mechanics based on ensemble averages when fluctuations through time play no role in…
This note presents a simple criterion for the tightness of stochastic fragmentation processes. Our work is motivated by an application to a fragmentation process derived from deleting edges in a conditioned Galton-Watson tree studied by…
The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular…
Breakage is generally understood in mechanical terms, yet nano-structures can rupture not only under external loads but also via thermal activation. Here we treat in a general framework the statistical mechanics of thermally induced…
This contribution presents a review of our present theoretical as well as experimental knowledge of different fluctuation observables relevant to nuclear multifragmentation. The possible connection between the presence of a fluctuation peak…
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…
We introduce a reversible Markovian coagulation-fragmentation process on the set of partitions of $\{1,\ldots,L\}$ into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be…
A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first…
Mostly for the purpose of applications for the energy and the environment and for the design of sources of neutrons or exotic nuclides, intense research has been dedicated to spallation, induced by protons or light projectiles at incident…
We study creep flow and yielding of particulate depletion gels under constant shear stress, combining data on different length and time scales. We characterise the breakage of meso-scale strands in the gel. Breakage events are distributed…
Fragmentation process in a cylindrical magnetized cloud is studied with the nested grid method. The nested grid scheme use 15 levels of grids with different spatial resolution overlaid subsequently, which enables us to trace the evolution…
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…
A nested occupancy scheme in random environment is a generalization of the classical Karlin infinite balls-in-boxes occupancy scheme in random environment (with random probabilities). Unlike the Karlin scheme in which the collection of…
Consider a weighted branching process generated by the lengths of intervals obtained by stick-breaking of unit length (a.k.a. the residual allocation model) and associate with each weight a `box'. Given the weights `balls' are thrown…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time…
Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov…
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…