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Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived from an atomistic representation of crystalline structures that also include features typical of the microscopic scale. Analytic expressions for strain components are obtained from the complex amplitudes of the Fourier modes representing periodic lattice positions, which can be generally provided by atomistic modeling or experiments. The magnitude and phase of these amplitudes, together with the continuous description of strains, are able to characterize crystal rotations, lattice deformations, and dislocations. Moreover, combined with the so-called amplitude expansion of the phase-field crystal model, they provide a suitable tool for bridging microscopic to macroscopic scales. This study enables the in-depth analysis of elasticity effects for macro- and mesoscale systems taking microscopic details into account.
The interaction of C atoms with a screw and an edge dislocation is modelled at an atomic scale using an empirical Fe-C interatomic potential based on the Embedded Atom Method (EAM) and molecular statics simulations. Results of atomic simulations are
A few years ago, the first CNN surpassed human performance on ImageNet. However, it soon became clear that machines lack robustness on more challenging test cases, a major obstacle towards deploying machines in the wild and towards obtaining better c
We describe the proximity effect in a short disordered metallic junction between three superconducting leads. Andreev bound states in the multi-terminal junction may cross the Fermi level. We reveal that for a quasi-continuous metallic density of sta
Since neural networks are data-hungry, incorporating data augmentation in training is a widely adopted technique that enlarges datasets and improves generalization. On the other hand, aggregating predictions of multiple augmented samples (i.e., test-
AI researchers employ not only the scientific method, but also methodology from mathematics and engineering. However, the use of the scientific method - specifically hypothesis testing - in AI is typically conducted in service of engineering objectiv