Related papers: Cluster expansion constructed over Jacobi-Legendre…
Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modelling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message passing frameworks. Such frameworks…
We present a machine-learning workflow for the calculation of the infrared spectrum of molecules, and more generally of other temperature-dependent electronic observables. The main idea is to use the Jacobi-Legendre cluster expansion to…
The combined structural and electronic complexity of iron oxides poses many challenges to atomistic modeling. To leverage limitations in terms of the accessible length and time scales, one requires a physically justified interatomic…
Recent progress towards universal machine-learned interatomic potentials holds considerable promise for materials discovery. Yet the accuracy of these potentials for predicting phase stability may still be limited. In contrast, cluster…
The cluster expansion formalism used in materials science is reconstructed on an axiomatic basis with the aims of clarifying underlying concepts and improving computational procedures, and without using conventional cluster functions.…
We present a new theoretical framework for modelling the cluster growing process. Starting from the initial tetrahedral cluster configuration, adding new atoms to the system and absorbing its energy at each step, we find cluster growing…
A model is constructed in which pair potentials are combined with the cluster expansion method in order to better describe the energetics of structurally relaxed substitutional alloys. The effect of structural relaxations away from the…
Crystalline alloys and related mixed systems make up a large family of materials with high tunability which have been proposed as the solution to a large number of energy related materials design problems. Due to the presence of chemical…
We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just renormalizable theory, and allows the…
Lattice models parameterized using first-principles calculations constitute an effective framework to simulate the thermodynamic behavior of physical systems. The cluster expansion method is a flexible lattice-based method used extensively…
We introduce ACEpotentials.jl, a Julia-language software package that constructs interatomic potentials from quantum mechanical reference data using the Atomic Cluster Expansion (Drautz, 2019). As the latter provides a complete description…
We present a new theoretical framework for modelling the fusion process of Lennard-Jones (LJ) clusters. Starting from the initial tetrahedral cluster configuration, adding new atoms to the system and absorbing its energy at each step, we…
A quantitative first-principles description of complex substitutional materials like alloys is challenging due to the vast number of configurations and the high computational cost of solving the quantum-mechanical problem. Therefore,…
Twisted multilayer graphene, characterized by its moir\'e patterns arising from inter-layer rotational misalignment, serves as a rich platform for exploring quantum phenomena. Machine learning interatomic potentials (MLIPs) are a promising…
We present an atomic cluster expansion (ACE) for carbon that improves over available classical and machine learning potentials. The ACE is parameterized from an exhaustive set of important carbon structures at extended volume and energy…
We consider a binary system of small and large objects in the continuous space interacting via a non-negative potential. By integrating over the small objects, the effective interaction between the large ones becomes multi-body. We prove…
As one myth of polynomial interpolation and quadrature, Trefethen [30] revealed that the Chebyshev interpolation of $|x-a|$ (with $|a|<1 $) at the Clenshaw-Curtis points exhibited a much smaller error than the best polynomial approximation…
For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal…
In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight…
We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect…