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Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…
A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
We provide a novel existence result for energy-variational solutions to a general class of evolutionary partial differential equations. Compared to previous works on this solution concept, the generalization is mainly twofold: a relaxation…
This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss non-interacting suspensions and colloids which may exhibit behavior similar to the one-dimensional motion of compressible gas. The…
Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…
Tight and compact binary systems, such as double neutron star binaries, are believed to undergo a common envelope evolution phase, resulting in strongly bound orbits. During this phase, the outer layers of the primary star are expelled,…
Blocking is a mechanism to improve the efficiency of Entity Resolution (ER) which aims to quickly prune out all non-matching record pairs. However, depending on the distributions of entity cluster sizes, existing techniques can be either…
We model the formation and evolution of galaxy clusters in the framework of an extended dark matter halo merger-tree algorithm that includes baryons and incorporates basic physical considerations. Our modified treatment is employed to…
Common envelope evolution (CEE) occurs in some binary systems involving asymptotic giant branch (AGB) or red giant branch (RGB) stars, and understanding this process is crucial for understanding the origins of various transient phenomena.…
Primordial black hole (PBH) binaries experience strong gravitational perturbations in the case of their initial clustering, which significantly affects the dynamics of their mergers. In this work, we develop a new formalism to account for…
We present a new approach to studying the evolution of massive black hole binaries in a stellar environment. By imposing conservation of total energy and angular momentum in scattering experiments, we find the dissipation forces that are…
We examine a discrete model of sticky particles initially subjected to acceleration. We propose a novel generalized variational principle for characterizing clusters (i.e., particle agglomerations) under decreasing acceleration function.…
A dynamical formulation of coupled cluster theory is derived using a variational principle. By allowing time-dependent single-particle functions, a high degree of adaptivity is introduced, allowing complex systems to be simulated with high…
We calculate the structure of a standard accretion disk with corona surrounding a massive Kerr black hole in general relativistic frame, in which the corona is assumed to be heated by the reconnection of the strongly buoyant magnetic fields…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution…
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…
We study the fragment size distributions after crushing of single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…