Related papers: A Physically-informed Graph-based Order Parameter …
In this Letter, we construct a set of order parameters for non-Abelian gauge theories which probe directly the unbroken group and are free of the deficiencies caused by quantum fluctuations and gauge fixing which have plagued all previous…
Quasi-continuous structural transformation from the crystalline to amorphous state takes place in graphite during ball-milling. The quantitative characteristics of a short- and a medium-range orders in carbon nanomaterials structure are…
Many physical systems are well modeled as collections of interacting particles. Nevertheless, a general approach to quantifying the absolute degree of order immediately surrounding a particle has yet to be described. Motivated thus, we…
A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…
Ordering at arbitrarily high temperature - entropic order - has been argued to take place in a class of generalized Ising models parameterised by a real interaction parameter $p$ when $p\ge 1$. We give a rigorous proof of this conjecture.…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…
Newly designed Li-ion battery cathode materials with high capacity and greater flexibility in chemical composition will be critical for the growing electric vehicles market. Cathode structures with cation disorder were once considered…
We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the $H$-orthogonality of a few near-degenerate lowest states of the Hamiltonian describing a given…
Recent advances in scanning transmission electron and scanning tunneling microscopies allow researchers to measure materials structural and electronic properties, such as atomic displacements and charge density modulations, at an Angstrom…
The structural tunability and compositional diversity of multicomponent perovskite oxides have enabled their various applications, including catalysis and electronics. The cation ordering in these oxides, ranging from disordered (i.e.,…
Modelling and understanding properties of materials from first principles require knowledge of the underlying atomistic structure. This entails knowing the individual identity and position of all involved atoms. Obtaining such information…
Structural global parameter identifiability indicates whether one can determine a parameter's value in an ODE model from given inputs and outputs. If a given model has parameters for which there is exactly one value, such parameters are…
Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust…
A very active area of materials research is to devise methods that use machine learning to automatically extract predictive models from existing materials data. While prior examples have demonstrated successful models for some applications,…
The use of machine learning methods for accelerating the design of crystalline materials usually requires manually constructed feature vectors or complex transformation of atom coordinates to input the crystal structure, which either…
Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph…
Quantum phase transitions reveal deep insights into the behavior of many-body quantum systems, but identifying these transitions without well-defined order parameters remains a significant challenge. In this work, we introduce a novel…
An algorithm is developed for structure identification of amorphous carbonaceous nanomaterials with a joint x-ray and neutron diffraction data analysis, using the data on the chemical composition of the sample from other diagnostics. The…
We establish a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. At the center of this framework lies the concept of a $\leqslant$-parametric graph:…
Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…