Related papers: O(N^2) fragmentation algorithm
In most current debris disc models, the dynamical and the collisional evolutions are studied separately, with N-body and statistical codes, respectively, because of stringent computational constraints. We present here LIDT-DD, the first…
An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters, and pairwise…
Modelling the formation of super-km-sized planetesimals by gravitational collapse of regions overdense in small particles requires numerical algorithms capable of handling simultaneously hydrodynamics, particle dynamics and particle…
We derive the initial condition for the perturbative fragmentation function of a heavy quark through order O(alpha_s^2) in the MS-bar scheme. This initial condition is useful for computing heavy quark (or lepton, in case of QED) energy…
Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
Fractals are defined as geometric shapes that exhibit symmetry of scale. This simply implies that fractal is a shape that it would still look the same even if somebody could zoom in on one of its parts an infinite number of times. This…
We present a method to perform fully selfconsistent density-functional calculations, which scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis…
Understanding the collisional fragmentation and subsequent reaccumulation of fragments is crucial for studies of the formation and evolution of the small-body populations. Using an SPH / N-body approach, we investigate the size-frequency…
The dynamics of the fragmentation equation with size diffusion is investigated when the size ranges in (0, $\infty$). The associated linear operator involves three terms and can be seen as a nonlocal perturbation of a Schr{\"o}dinger…
We study the efficiency of forming large bodies, starting from a sea of equal-sized planetesimals. This is likely one of the earlier steps of planet formation and relevant for the formation of the asteroid belt, the Kuiper belt and…
A spin system is a framework in which the vertices of a graph are assigned spins from a finite set. The interactions between neighbouring spins give rise to weights, so a spin assignment can also be viewed as a weighted graph homomorphism.…
Compact object clusters are likely to exist in the centre of some galaxies because of mass segregation. The high densities and velocities reached in them deserves a better understanding. The formation of binaries and their subsequent…
Properly estimating correlations between objects at different spatial scales necessitates $\mathcal{O}(n^2)$ distance calculations. For this reason, most widely adopted packages for estimating correlations use clustering algorithms to…
In this paper we introduce a new classification algorithm called Optimization of Distributions Differences (ODD). The algorithm aims to find a transformation from the feature space to a new space where the instances in the same class are as…
We investigate the effect of fragmentation on the homogeneous free cooling of inelastic hard spheres, using Boltzmann kinetic theory and Direct Monte Carlo simulations. We analyze in detail a model where dissipative collisions may…
The exponential increase in orbital debris and active satellites will lead to congested orbits, necessitating more frequent collision avoidance maneuvers by satellites. To minimize fuel consumption while ensuring the safety of satellites,…
In this paper, we present a new hybrid algorithm for the time integration of collisional N-body systems. In this algorithm, gravitational force between two particles is divided into short-range and long-range terms, using a…
Stratified sampling is a fast and simple method to generate point sets with uniform distribution in hypercubes. However, for the most common paraxial stratfication it has the prominent drawback that the number of sampled points in n…
In this study, a species-clustered ordinary differential equations (ODE) solver for chemical kinetics with large detailed mechanisms based on operator-splitting is presented. The ODE system is split into clusters of species by using graph…