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We show that the class of Krasner hyperfields is not elementary. To show this, we determine the rational rank of quotients of multiplicative groups in field extensions. Our argument uses Chebotarev's density theorem. We also discuss some related questions.

Energy materials with disorder in site occupation are challenging for computational studies due to an exponential scaling of the configuration space. We herein present a grand-canonical optimization method that enables the use of quantum annealing (QA) for sampling the ionic ground state. The method relies on a Legendre transformation of the Coulomb energy cost function that strongly reduces the effective coupling strengths of the fully connected problem, which is essential for effectiveness of QA. The approach is expected to be applicable to a variety of materials optimization problems.

We show that if G is a simply connected semi-simple algebraic group and K is a model complete field, then the theory of the group G(K) is model complete as well.

This expository paper is written in celebration of Boris Zilber's 75th birthday. We discuss Ax-Schanuel type statements focusing on the case of positive characteristic.

This work combines spectroscopic and photometric data of the polluted white dwarf WD0141-675 which has a now retracted astrometric super-Jupiter candidate and investigates the most promising ways to confirm Gaia astrometric planetary candidates and obtain follow-up data. Obtaining precise radial velocity measurement for white dwarfs is challenging due to their intrinsic faint magnitudes, lack of spectral absorption lines, and broad spectral features. However, dedicated radial velocity campaigns are capable of confirming close in giant exoplanets (a few M$_{\textrm{Jup}}$) around polluted white dwarfs, where additional metal lines aid radial velocity measurements. Infrared emission from these giant exoplanets is shown to be detectable with JWST MIRI and will provide constraints on the formation of the planet. Using the initial Gaia astrometric solution for WD0141-675 as a case study, if there were a planet with a 33.65 d period or less with a nearly edge on orbit, 1) ground-based radial velocity monitoring limits the mass to $<$ 15.4 M$_{\textrm{Jup}}$, and 2) space-based infrared photometry shows a lack of infrared excess and in a cloud-free planetary cooling scenario, a sub-stellar companion would have to be $<$ 16 M$_{\textrm{Jup}}$ and be older than 3.7 Gyr. These results demonstrate how radial velocities and infrared photometry can probe the mass of the objects producing some of the astrometric signals, and rule out parts of the brown dwarf and planet mass parameter space. Therefore, combining astrometric data with spectroscopic and photometric data is crucial to both confirm, and characterise astrometric planet candidates around white dwarfs., Comment: Accepted in MNRAS

In the last decade, the use of Machine and Deep Learning (MDL) methods in Condensed Matter physics has seen a steep increase in the number of problems tackled and methods employed. A number of distinct MDL approaches have been employed in many different topics; from prediction of materials properties to computation of Density Functional Theory potentials and inter-atomic force fields. In many cases the result is a surrogate model which returns promising predictions but is opaque on the inner mechanisms of its success. On the other hand, the typical practitioner looks for answers that are explainable and provide a clear insight on the mechanisms governing a physical phenomena. In this work, we describe a proposal to use a sophisticated combination of traditional Machine Learning methods to obtain an explainable model that outputs an explicit functional formulation for the material property of interest. We demonstrate the effectiveness of our methodology in deriving a new highly accurate expression for the enthalpy of formation of solid solutions of lanthanides orthophosphates., Comment: 24 pages, 5 figures

We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered the PAC property is first order.

We show that if $G$ is a finitely generated group such that its profinite completion $\widehat{G}$ is ``far from being projective'' (that is the kernel of the universal Frattini cover of $\widehat{G}$ is not a small profinite group), then the class of existentially closed $G$-actions on fields is not elementary. Since any infinite, finitely generated, virtually free, and not free group is ``far from being projective'', the main result of this paper corrects an error in our paper ``Model theory of fields with virtually free group actions'', Proc. London Math. Soc., (2) 118 (2019), 221--256 by showing the negation of Theorem 3.26 in that paper., Comment: Few typos corrected, added the part about free products

Valence band electronic structure of mixed uranium oxides (UO2, U4O9, U3O7, U3O8, UO3) has been studied by the resonant inelastic X-ray scattering (RIXS) technique at the U M5 edge and by computational methods. We show here that the RIXS technique and recorded U 5f-O 2p charge transfer excitations can be used to proof the validity of theoretical approximations, Comment: Chem Commun (2018)

Computational modeling is an important aspect of the research on nuclear waste materials. In particular, atomistic simulations, when used complementary to experimental efforts, contribute to the scientific basis of safety case for nuclear waste repositories. Here we discuss the state-of-the-art and perspectives of atomistic modeling for nuclear waste management on a few cases of successful synergy of atomistic simulations and experiments. In particular, we discuss here: (1) the potential of atomistic simulations to investigate the uranium oxidation state in mixed valence uranium oxides and (2) the ability of cementitious barrier materials to retain radionuclides such as 226Ra and 90Sr, and of studtite/metastudtite secondary peroxide phases to incorporate actinides such as Np and Am. The new contribution we make here is the computation of the incorporation of Sr by C-S-H (calcium silicate hydrate) phases., Comment: MRS Advances (2020)

We introduce the notion of a coordinate $\mathbf{k}$-algebra scheme and the corresponding notion of a $\mathcal{B}$-operator. This class of operators includes endomorphisms and derivations of the Frobenius map, and it also generalizes the operators related to $\mathcal{D}$-rings from [15]. We classify the (coordinate) $\mathbf{k}$-algebra schemes for a perfect field $\mathbf{k}$ and we also discuss the model-theoretic properties of fields with $\mathcal{B}$-operators.

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse-Schmidt derivations and about Galois actions. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree.

We show that the theory of Galois actions of a torsion Abelian group $A$ is companionable if and only if for each prime $p$, the $p$-primary part of $A$ is either finite or it coincides with the Pr\"{u}fer $p$-group. We also provide a model-theoretic description of the model companions we obtain.

We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializations, we get difference Galois cohomology, difference Picard group and a good theory of difference torsors.

We give algebraic conditions about a finite algebra $B$ over a perfect field of positive characteristic, which are equivalent to the companionability of the theory of fields with "$B$-operators" (i.e. the operators coming from homomorphisms into tensor products with $B$). We show that, in the most interesting case of a local $B$, these model companions admit quantifier elimination in the "smallest possible" language and they are strictly stable. We also describe the forking relation there.