Related papers: O(N^2) fragmentation algorithm
One important tool is the optimal clustering of data into useful categories. Dividing similar objects into a smaller number of clusters is of importance in many applications. These include search engines, monitoring of academic performance,…
Recently it has been proposed to use colliding drops for producing advanced particles or well defined capsules, or to perform chemical reactions where the merged drops constitute a micro-reactor. For all these promising applications it is…
In many statistical multifragmentation models the volume available to the $N$ nonoverlapping fragments forming a given partition is a basic ingredient serving to the simplification of the density of states formula. One therefore needs…
The Brownian triangulation is a random compact subset of the unit disk introduced by Aldous. For $\epsilon>0$, let $N(\epsilon)$ be the number of triangles whose sizes (measured in different ways) are greater than $\epsilon$ in the Brownian…
A method is presented that allows exact calculations of fragment multiplicity distributions for a canonical ensemble of non-interacting clusters. Fragmentation properties are shown to depend on only a few parameters. Fragments are shown to…
We present, within Kohn-Sham Density Functional Theory calculations, a quantitative method to identify and assess the partitioning of a large quantum mechanical system into fragments. We then show how within this framework simple…
Analysis on fractals is a growing field, with hints of potential for widespread applicability across all of STEM. One of the most heavily researched type of fractals are the nested fractals, fractal shapes defined by virtue of being made of…
The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any…
By means of quantum-dynamical and classical trajectory calculations of H2+ photodissociation in strong laser fields, it is shown that for certain combinations of pulse durations and intensities the rotational dynamics can lead to…
In this note, we give a quantum algorithm that finds collisions in arbitrary r-to-one functions after only O((N/r)^(1/3)) expected evaluations of the function. Assuming the function is given by a black box, this is more efficient than the…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
Dispersion of mobile robots over the nodes of an anonymous graph is an important problem and turns out to be a crucial subroutine for designing efficient algorithms for many fundamental graph problems via mobile robots. In this problem,…
The large N_f self consistency method is applied to the computation of perturbative information in the operator product expansion used in deep inelastic scattering. The O(1/N_f) critical exponents corresponding to the anomalous dimensions…
We consider the motion of a finite though large number $N$ of hard spheres in the whole space $\mathbb{R}^n$. Particles move freely until they experience elastic collisions. We use our recent theory of Compensated Integrability in order to…
The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can…
Within the framework of many-body perturbation theory based on Green's functions, the $GW$ approximation has emerged as a pivotal method for computing quasiparticle energies and excitation spectra. However, its high computational cost and…
We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the…
An efficient O($N$) divide-conquer (DC) method based on localized natural orbitals (LNOs) is presented for large-scale density functional theories (DFT) calculations of gapped and metallic systems. The LNOs are non-iteratively calculated by…