Related papers: Minimal fragmentation problem
A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes. Here, we show that this model can be…
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching random walks, which suggests the use of…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
We consider a model of fragmentation of sheet by cracks that move with a velocity in preferred direction, but undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting, and the split cracks…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
We report the binomial multiplicative model for low impact energy fragmentation. Impact fragmentation experiments were performed for low impact energy region, and it was found that the weighted mean mass is scaled by the pseudo control…
We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence…
Given a sequence of $N$ positive real numbers $\{a_1,a_2,..., a_N \}$, the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
Impact fragmentation is the underlying principle of comminution milling of dry, bulk solids. Unfortunately the outcome of the fragmentation process is more or less determined by the dimensionality of the impactor and its impact velocity.…
An overview is given of the methods for treating complicated problems without small parameters, when the standard perturbation theory based on the existence of small parameters becomes useless. Such complicated problems are typical of…
We investigate fragmentation processes with a steady input of fragments. We find that the size distribution approaches a stationary form which exhibits a power law divergence in the small size limit, P(x) ~ x^{-3}. This algebraic behavior…
We study an inverse design problem for the linear multiple fragmentation equation arising in particle dynamics. Our objective is to reconstruct an unknown initial size distribution that evolves, under a prescribed fragmentation law, into a…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
It was recently observed that chiral two-body interactions can be efficiently represented using matrix factorization techniques such as the singular value decomposition. However, the exploitation of these low-rank structures in a few- or…
Nuclear resonances provide a rich and versatile testbed for exploring fundamental aspects of physics, particularly within the domain of strongly correlated many-body systems. The overarching goal of the theory is to develop a consistent and…
Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…