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Ideal symmetry is known to break down under almost any noise. One measure of asymmetry in a periodic crystal is the relative multiplicity Z' of geometrically non-equivalent units. However, Z' discontinuously changes under almost any…
To accelerate the development of novel ion-conducting materials, we present a general graph-theoretic analysis framework for ion migration in any crystalline structure. The nodes of the graph represent metastable sites of the migrating ion…
The bicategory of parameterized spectra has a remarkably rich structure. In particular, it is possible to take traces in this bicategory, which give classical invariants that count fixed points. We can also take equivariant traces, which…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
Predicting properties of crystals from their structures is a fundamental yet challenging task in materials science. Unlike molecules, crystal structures exhibit infinite periodic arrangements of atoms, requiring methods capable of capturing…
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…
This paper investigates the use of the most fundamental elements; cables for tension and bars for compression, in the search for the most efficient bridges. Stable arrangements of these elements are called tensegrity structures. We show…
We have developed an efficient and reliable methodology for crystal structure prediction, merging ab initio total-energy calculations and a specifically devised evolutionary algorithm. This method allows one to predict the most stable…
The Wheatstone bridge experiment is fundamental for precise measurement of electrical resistance, holding significant value in both undergraduate physics education and real-life scientific research. This study reimagines the experiment by…
Crystal structure prediction has been a subject of topical interest, but remains a substantial challenge, especially for complex structures as it deals with the global minimization of the extremely rugged high-dimensional potential energy…
We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling…
We define and compare several natural ways to compute the bridge number of a knot diagram. We study bridge numbers of crossing number minimizing diagrams, as well as the behavior of diagrammatic bridge numbers under the connected sum…
A key phase in the bridge design process is the selection of the structural system. Due to budget and time constraints, engineers typically rely on engineering judgment and prior experience when selecting a structural system, often…
We consider the problem of constructing an adaptive bridge regression modeling, which is a penalized procedure by imposing different weights to different coefficients in the bridge penalty term. A crucial issue in the modeling process is…
Crystal structure optimization is fundamental to materials modeling but remains computationally expensive when performed with density-functional theory (DFT). Machine-learning (ML) approaches offer substantial acceleration, yet existing…
The finite element computation of structures such as waveguides can lead to heavy computations when the length of the structure is large compared to the wavelength. Such waveguides can in fact be seen as one-dimensional periodic structures.…
Milestoning is a computational procedure that reduces the dynamics of complex systems to memoryless jumps between intermediates, or milestones, and only retains some information about the probability of these jumps and the time lags between…
Crystal structure prediction is a long-standing challenge in materials science, with most data-driven methods developed for inorganic systems. This leaves an important gap for organic crystals, which are central to pharmaceuticals,…
Crystal-structure match (CSM), the atom-to-atom correspondence between two crystalline phases, is used extensively to describe solid-solid phase transition (SSPT) mechanisms. However, existing computational methods cannot account for all…
As a common appearance defect of concrete bridges, cracks are important indices for bridge structure health assessment. Although there has been much research on crack identification, research on the evolution mechanism of bridge cracks is…