Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

Materials chemistry is being profoundly influenced by the uptake of machine learning methodologies. Machine learning techniques, in combination with established techniques from computational physics, promise to accelerate the discovery of new materials by elucidating complex structure–property relationships from massive material databases. Despite exciting possibilities, further methodological developments call for a greater synergism between materials chemists, physicists, and engineers on one side, with computer science and math majors on the other. In this review, we provide a non-exhaustive account of machine learning in materials chemistry for computer scientists and applied mathematicians, with an emphasis on molecule datasets and materials chemistry problems. The first part of this review provides a tutorial on how to prepare such datasets for subsequent model building, with an emphasis on the construction of feature vectors. We also provide a self-contained introduction to density functional theory, a method from computational physics which is widely used to generate datasets and compute response variables. The second part reviews two machine learning methodologies which represent the status quo in materials chemistry at present – kernelized machine learning and Bayesian machine learning – and discusses their application to real datasets. In the third part of the review, we introduce some emerging machine learning techniques which have not been widely adopted by materials scientists and therefore present potential avenues for computer science and applied math majors. In the final concluding section, we discuss some recent machine learning-based approaches to real materials discovery problems and speculate on some promising future directions.

DOI： 10.1016/j.mlwa.2022.100265

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Authorship：Corresponding author   Publisher：ESAIM - Control, Optimisation and Calculus of Variations  

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DOI： 10.1051/cocv/2022029

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a nearest-neighbor-type energy for the atomic bonds with an additional term to penalize change in volume. We enforce the appearance of disclinations by means of a special boundary condition.
Our main result is the discrete-to-continuum limit of this energy as the lattice size tends to zero. Our proof method is relaxation of the energy. The main mathematical novelty of our proof is a density theorem for the special boundary condition. In addition to our limit theorem, we construct examples of planar disclinations as solutions to numerical minimization of the model and show that classical results for wedge disclinations are recovered by our analysis.

DOI： 10.1051/cocv/2021025

Other Link： https://www.esaim-cocv.org/articles/cocv/abs/2021/02/cocv200124/cocv200124.html

Language：English   Publishing type：Research paper (scientific journal)  

In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results of CONTI et al. (Proc R Soc A 473(2203):20170235, 2017). Passing to the limit $n\to\infty$, this allows us to treat solid crystals and nematic elastomer differential inclusions simultaneously. In particular, we recover and generalise (non-linear) planar tripole star type deformations which were experimentally observed in KITANO and KIFUNE (Ultramicroscopy 39(1–4):279–286, 1991), MANOLIKAS and AMELINCKX (Physica Status Solidi (A) 60(2):607–617, 1980; Physica Status Solidi (A) 61(1):179–188, 1980). Furthermore, we discuss the corresponding geometrically linearised problem.

DOI： https://doi.org/10.1007/s00205-020-01511-9

Other Link： https://link.springer.com/article/10.1007/s00205-020-01511-9#citeas

Language：English   Publishing type：Research paper (scientific journal)  

We present a method for constructing similarity solutions of a fourth-order nonlinear partial differential equation for axisymmetric surface diffusion by extending an inverse method previously used for the second-order one-dimensional nonlinear diffusion equation. After imposing a solution profile, both a feasible surface tension, and a compatible mobility function are deduced simultaneously. Although the profile is not one-to-one, an optimization algorithm is implemented to construct a mobility function that is a function of surface orientation, with no practical difference in mobility between different arms of the many-to-one profile. It is shown that the solution of the linear model well approximates the solution of the nonlinear model, in which the surface tension and mobility are close to constant for a wide range of surface angles, even when nonlinear geometric terms are included.

DOI： 10.1016/j.physd.2019.132288

Other Link： https://www.sciencedirect.com/science/article/pii/S016727891930082X?via%3Dihub

Language：English   Publishing type：Research paper (scientific journal)  

We compute the Gamma-limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic membrane. We work in the regime of infinitesimal displacements and model the orientation of the liquid crystal according to the order tensor theories of both Frank and De Gennes. We describe the asymptotic regime by analysing a family of functionals parametrised by the vanishing thickness of the membranes and the ratio of the elastic constants, establishing that, in the limit, the system is represented by a two-dimensional integral functional interpreted as a linear membrane on top of a nematic active foundation involving an effective De Gennes optic tensor which allows for low order states. The latter can suppress shear energy by formation of microstructure as well as act as a pre-strain transmitted by the foundation to the overlying film.

DOI： 10.1142/S021820251850063X

Other Link： https://www.worldscientific.com/doi/abs/10.1142/S021820251850063X

Language：English   Publishing type：Research paper (scientific journal)  

Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near critical temperature. Solutions are given for the changing phase of cylindrical or spherical inclusion, allowing for a “mushy” zone with a mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions

DOI： 10.3390/sym10030072

Other Link： https://www.mdpi.com/2073-8994/10/3/72

Language：English   Publishing type：Research paper (scientific journal)  

We model and analyze the two-dimensional triangle-to-centred rectangle transformation of elastic crystals. By considering a Ginzburg–Landau type model, we compute the relaxation of the total energy both in the case of compressible and incompressible materials and construct some possible explicit microstructures as the approximate solutions of a non-convex minimization problem.

DOI： 10.1007/978-981-10-0962-4_11

Event date： 2024.10

Language：English   Presentation type：Oral presentation (invited, special)  

Venue：Sewong, South Korea   Country：Korea, Republic of  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Event date： 2024.1

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Event date： 2024.1

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Event date： 2023.11

Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Venue：JSPS-AAA Annual Workshop, Australian Academy of Science, Canberra   Country：Australia  

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Number of participants：1,000