Reconsidering the Origins of Forsbergh Birefringence Patterns

In 1949, P. W. Forsbergh Jr. reported spontaneous spatial ordering in the birefringence patterns seen in flux-grown BaTiO3 crystals [1], under the transmission polarized light microscope [2]. Stunningly regular square-net arrays were often only found within a finite temperature window and could be induced on both heating and cooling, suggesting genuine thermodynamic stability. At the time, Forsbergh rationalized the patterns to have resulted from the impingement of ferroelastic domains, creating a complex tessellation of variously shaped domain packets. However, evidence for the intricate microstructural arrangement proposed by Forsbergh has never been found. Moreover, no robust thermodynamic argument has been presented to explain the region of thermal stability, its occurrence just below the Curie Temperature and the apparent increase in entropy associated with the loss of the Forsbergh pattern on cooling. As a result, despite decades of research on ferroelectrics, this ordering phenomenon and its thermodynamic origin have remained a mystery. In this paper, we re-examine the microstructure of flux-grown BaTiO3 crystals, which show Forsbergh birefringence patterns. Given an absence of any obvious arrays of domain polyhedra, or even regular shapes of domain packets, we suggest an alternative origin for the Forsbergh pattern, in which sheets of orthogonally oriented ferroelastic stripe domains simply overlay one another. We show explicitly that the Forsbergh birefringence pattern occurs if the periodicity of the stripe domains is above a critical value. Moreover, by considering well-established semiempirical models, we show that the significant domain coarsening needed to generate the Forsbergh birefringence is fully expected in a finite window below the Curie Temperature. We hence present a much more straightforward rationalization of the Forsbergh pattern than that originally proposed, in which exotic thermodynamic arguments are unnecessary.

Making personalised nutrition the easy choice: Creating policies to break down the barriers and reap the benefits

Personalised diets based on people’s existing food choices, and/or phenotypic, and/or genetic information hold potential to improve public dietary-related health. The aim of this analysis, therefore, has been to examine the degree to which factors which determine uptake of personalised nutrition vary between EU countries to better target policies to encourage uptake, and optimise the health benefits of personalised nutrition technology. A questionnaire developed from previous qualitative research was used to survey nationally representative samples from 9 EU countries (N = 9381). Perceived barriers to the uptake of personalised nutrition comprised three factors (data protection; the eating context; and, societal acceptance). Trust in sources of information comprised four factors (commerce and media; practitioners; government; family and, friends). Benefits comprised a single factor. Analysis of Variance (ANOVA) was employed to compare differences in responses between the United Kingdom; Ireland; Portugal; Poland; Norway; the Netherlands; Germany; and, Spain. The results indicated that respondents in Greece, Poland, Ireland, Portugal and Spain, rated the benefits of personalised nutrition highest, suggesting a particular readiness in these countries to adopt personalised nutrition interventions. Greek participants were more likely to perceive the social context of eating as a barrier to adoption of personalised nutrition, implying a need for support in negotiating social situations while on a prescribed diet. Those in Spain, Germany, Portugal and Poland scored highest on perceived barriers related to data protection. Government was more trusted than commerce to deliver and provide information on personalised nutrition overall. This was particularly the case in Ireland, Portugal and Greece, indicating an imperative to build trust, particularly in the ability of commercial service providers to deliver personalised dietary regimes effectively in these countries. These findings, obtained from a nationally representative sample of EU citizens, imply that a parallel, integrated, public-private delivery system would capture the needs of most potential consumers.

Eating from the same plate? Revisiting the role of labile carbon inputs in the soil food web

An increasing number of empirical studies are challenging the central fundamentals on which the classical soil food web model is built. This model assumes that bacteria consume labile substrates twice as fast as fungi, and that mycorrhizal fungi do not decompose organic matter. Here, we build on emerging evidence that points to significant consumption of labile C by fungi, and to the ability of ectomycorrhizal fungi to decompose organic matter, to show that labile C constitutes a major and presently underrated source of C for the soil food web. We use a simple model describing the dynamics of a recalcitrant and a labile C pool and their consumption by fungi and bacteria to show that fungal and bacterial populations can coexist in a stable state with large inputs into the labile C pool and a high fungal use of labile C. We propose a new conceptual model for the bottom trophic level of the soil food web, with organic C consisting of a continuous pool rather than two or three distinct pools, and saprotrophic fungi using substantial amounts of labile C. Incorporation of these concepts will increase our understanding of soil food web dynamics and functioning under changing conditions.

The proof of Kontsevich's periodicity conjecture on noncommutative birational transformations

For an arbitrary associative unital ring RR, let J1J1 and J2J2 be the following noncommutative, birational, partly defined involutions on the set M3(R)M3(R) of 3×33×3 matrices over RR: J1(M)=M−1J1(M)=M−1 (the usual matrix inverse) and J2(M)jk=(Mkj)−1J2(M)jk=(Mkj)−1 (the transpose of the Hadamard inverse).

We prove the surprising conjecture by Kontsevich that (J2∘J1)3(J2∘J1)3 is the identity map modulo the DiagL×DiagRDiagL×DiagR action (D1,D2)(M)=D−11MD2(D1,D2)(M)=D1−1MD2 of pairs of invertible diagonal matrices. That is, we show that, for each MM in the domain where (J2∘J1)3(J2∘J1)3 is defined, there are invertible diagonal 3×33×3 matrices D1=D1(M)D1=D1(M) and D2=D2(M)D2=D2(M) such that (J2∘J1)3(M)=D−11MD2(J2∘J1)3(M)=D1−1MD2.