Related papers: Commutative Algebra Modeling in Materials Science …
Vertex algebras (and their modules) can be described as vector spaces together with a linear operator-valued series in one parameter $z$. With the interpretation of $z$ as a coordinate at a point on a curve, one can construct algebraic…
Metal-organic frameworks (MOFs) are crystalline materials consisting of metal centers and organic linkers forming open and porous structures. They have been extensively studied due to various possible applications exploiting their large…
We investigate models of algebraic theories in the category of cocommutative coalgebras over a field. We establish some of their categorical properties, similar to those of algebraic varieties. We introduce a class of categories of…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
Mott physics - the interplay between itinerancy and localization of electrons - is undergoing a paradigm shift from the binary "bandwidth - filling" tuning framework to an intertwining of geometric, topological, and fractionalized degrees…
Two-dimensional (2D) binary transition-metal chalcogenides (TMCs) like molybdenum disulfide exhibits excellent properties as materials for light adsorption devices. Alloying binary TMCs can form 2D compositionally complex TMC alloys…
Condensed Matter Physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many…
Machine learning has become a crucial tool for predicting the properties of crystalline materials. However, existing methods primarily represent material information by constructing multi-edge graphs of crystal structures, often overlooking…
This article explains basic constructions and results on group algebras and their cohomology, starting from the point of view of commutative algebra. It provides the background necessary for a novice in this subject to begin reading Dave…
A metric algebra is a metric variant of the notion of $\Sigma$-algebra, first introduced in universal algebra to deal with algebras equipped with metric structures such as normed vector spaces. In this paper, we showed metric versions of…
Structural prediction for the discovery of novel materials is a long sought after goal of computational physics and materials sciences. The success is rather limited for methods such as the simulated annealing method (SA) that require…
We use homological perturbation machinery specific for the algebra category [P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications vol. 2, n. 5 (2000) 51-88] to give an algorithm for computing the…
Modeling the unsaturated behavior of porous materials with multimodal pore size distributions presents significant challenges, as standard hydraulic models often fail to capture their complex, multi-scale characteristics. A common…
We introduce a composition-weighted symbolic regression framework for interpretable prediction of materials properties directly from chemical composition. The method jointly learns analytical functional forms and task-dependent elemental…
From biological organs to soft robotics, highly deformable materials are essential components of natural and engineered systems. These highly deformable materials can have heterogeneous material properties, and can experience heterogeneous…
Finding new two-dimensional (2D) materials with novel quantum properties is highly desirable for technological innovations. In this work, we studied a series of metal-organic frameworks (MOFs) with different metal cores and discovered…
A partial combinatory algebra (PCA) is a set equipped with a partial binary operation that models a notion of computability. This paper studies a generalization of PCAs, introduced by W. Stekelenburg, where a PCA is not a set but an object…
Predicting the glass-forming ability (GFA) of chemical compositions remains a fundamental challenge in materials science, especially for oxide glasses with broad compositional diversity. Traditional empirical and thermodynamic approaches…
Realistic physical systems are characterised by emergent interactions across multiple length and time scales, posing a significant challenge for predictive machine learning (ML) models. Most scientific ML models focus on a narrow range of…
Much of our understanding of complex structures is based on simplification: for example, metal-organic frameworks are often discussed in the context of "nodes" and "linkers", allowing for a qualitative comparison with simpler inorganic…