Related papers: Crystal Frameworks, Matrix-valued Functions and Ri…
Using a motif-network search scheme, we studied the tetrahedral structures of the dilithium/disodium transition metal orthosilicates A2MSiO4 with A = Li or Na and M = Mn, Fe or Co. In addition to finding all previously reported structures,…
By treating idealized zeolite frameworks as periodic mechanical trusses, we show that the number of flexible folding mechanisms in zeolite frameworks is strongly peaked at the minimum density end of their flexibility window. 25 of the 197…
The supersymmetric hybrid formalism for Type II strings is used to study partial supersymmetry breaking in four and three dimensions. We use worldsheet techniques to derive effects of internal Ramond-Ramond fluxes such as torsions,…
The structural degrees of freedom of a material are the various distortions most straightforwardly activated by external stimuli. A highly successful design strategy in materials chemistry involves controlling these individual distortions…
In the framework of density functional theory (DFT) simulations of molecules and materials, anharmonic terms of the potential energy surface are commonly computed numerically, with an associated cost that rapidly increases with the size of…
We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously…
The random first-order transition (RFOT) theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it…
In mathematical crystallography and computational materials science, it is important to infer flexibility properties of framework materials from their geometric representation. We study combinatorial, geometric and kinematic properties for…
We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a…
Contact and related phenomena, such as friction, wear or elastohydrodynamic lubrication, remain as one of the most challenging problem classes in nonlinear solid and structural mechanics. In the context of their computational treatment with…
We performed a first principles investigation on the structural, electronic, and optical properties of crystals made of chemically functionalized adamantane molecules. Several molecular building blocks, formed by boron and nitrogen…
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic…
We describe two crystal structures on set-valued decomposition tableaux. These provide the first examples of interesting "$K$-theoretic" crystals on shifted tableaux. Our first crystal is modeled on a similar construction of Monical,…
The geometric crystal operators and geometric $R$-matrices (or geometric Weyl group actions) give commuting actions on the field of rational functions in $mn$ variables. We study the invariants of various combinations of these actions,…
We describe a coupled cluster framework for coupled systems of electrons and phonons. Neutral and charged excitations are accessed via the equation-of-motion version of the theory. Benchmarks on the Hubbard-Holstein model allow us to assess…
Spin crossover frameworks and molecular crystals display fascinating collective behaviours. This includes multi-step transitions with hysteresis and a wide variety of long-range ordered patterns of high-spin and low-spin metal centres. From…
We investigate a system composed of an ensemble of room temperature rare-earth ions embedded in a bulk crystal, intrinsically coupled to internal strain via their sensitivity to the surrounding crystal field. We evidence the generation of a…
We establish several fundamental properties of the Rigid Unit Mode (RUM) spectrum for symmetric frameworks with a discrete abelian symmetry group and arbitrary linear constraints. In particular, we identify a nonempty subset of the RUM…
We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…
Metal halide perovskites have shown extraordinary performance in solar energy conversion technologies. They have been classified as "soft semiconductors" due to their flexible corner-sharing octahedral networks and polymorphous nature.…