Uniaxial versus biaxial character of nematic equilibria in three dimensions

We study global minimizers of the Landau–de Gennes (LdG) energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary conditions. Our results are specific to an asymptotic limit coined in terms of a dimensionless temperature and material-dependent parameter, t and some constraints on the material parameters, and we work in the t→∞ limit that captures features of the widely used Lyuksyutov constraint (Kralj and Virga in J Phys A 34:829–838, 2001). We prove (i) that (re-scaled) global LdG minimizers converge uniformly to a (minimizing) limiting harmonic map, away from the singular set of the limiting map; (ii) we have points of maximal biaxiality and uniaxiality near each singular point of the limiting map; (iii) estimates for the size of “strongly biaxial” regions in terms of the parameter t. We further show that global LdG minimizers in the restricted class of uniaxial Q-tensors cannot be stable critical points of the LdG energy in this limit

Symmetry of local minimizers for the Ginzburg-Landau functional in 3D.

We classify nonconstant entire local minimizers of the standard Ginzburg–Landau functional for maps in H1 loc.(R3;R3) satisfying a natural energy bound. Up to translations and rotations, such solutions of the Ginzburg–Landau system are given by an explicit solution equivariant under the action of the orthogonal group

Effects of N fertilizers and rates on yield, safety and nutrients in processing spinach genotypes

Two field experiments were carried out at the Experimental Field, Department of Food Science (TE, Italy) in 2004 and 2005 to evaluate the effects of genotypes, different N forms and N rates on yield, safety and nutritional features of processing spinach. Experiment 1, as treatments, included spinach genotypes and N forms (CO(NH2)2; Agricote; NH4NO3); experiment 2 included three N forms (Ca(NO3)2; (NH4)2SO4; NH4NO3) applied at rates of 0, 75, 150, 200 kg N ha1. This research work confirmed differences among spinach genotypes in terms of efficiency in N use and oxalate and nitrate accumulation. Spinach accumulated much more nitrate in petioles and much more oxalate in blades indicating that nitrate and oxalate might play a counterrole to each other. Fertilizers containing N under forms not readily available to the crop, i.e. Agricote, CO(NH2)2 and (NH4)2SO4, increased nitrate and oxalate accumulations less than fast N-release fertilizers, but their effect on yield was limited. Highest yield with contents of nitrate and oxalate lower than the limits imposed to avoid health problems, were achieved with Ca(NO3)2, at rates of 130 and 150 kg N ha1 NH4NO3. A good accumulation in some important macronutrients for the human diet such as Ca, K and P were allowed by application of Ca(NO3)2, at rates of 130 and 150 kg N ha1 NH4NO3. The glucose, fructose, sucrose as well as Mg accumulation were not alterable in spinach with nitrogen fertilization or with genotype choice

CO2 sequestration from Italian cultivated land: opportunities, challemnges and risks

Management of agricultural soils may determine soil carbon emission to the atmosphere (source) or soil carbon sequestration (sink). Conventional agriculture is tillage-based (TA) in industrialised as well as developing countries and relies, as a key procedure for seedbed preparation, on mechanical soil tillage with no organic mulch cover. Generally, it seems to speed up the loss of Soil Organic Matter (SOM), by increasing its mineralization and through soil loss by erosion. In addition, soil tillage is a high energy-consuming operation that uses large amounts of fossil fuel per hectare in mechanised systems. In contrast to tillage-based systems, Conservation Agriculture (CA) is considered to be an agro-ecological approach to resource-conserving agricultural production that requires compliance with three linked practical principles, namely: i) minimum mechanical soil disturbance (with no-till and direct seeding); ii) maintenance of permanent organic soil cover (with crops, cover crops and/or crop residues); and iii) species diversification through crop rotations and associations (involving annual and/or perennial crops including tree and pasture crops) Corsi et al. (2012). CA facilitates good agronomy, such as timely operations, and improves overall land husbandry for rained and irrigated production and is complemented by other good practices, such as the use of quality seeds and integrated pest management (Pisante et al., 2012).There is evidence that, in the medium term, the most effective way for adaptation to climate change is represented by a rational management of the biosphere and in particular of the agricultural sector: by the adoption of specific agricultural practices. Agriculture is potentially able to reduce its emission with minor costs with respect to other activities, to increase carbon sequestration and reduce greenhouse gas emissions. In fact, agricultural activities play a fundamental role in soil carbon sequestration and reduction of emissions, mainly because of the high stock capacity of this element associated with long retention time in the soil. The cultivated land (arable and tree crops) occupy 28% of the Italian territory, for a total of 10.9 million ha which can stock massive reserves of carbon by putting in place agronomic measures and/or agro-ecological infrastructure useful to reduce the amount of CO2 in the atmosphere. The net balance of the two processes on an annual basis can result in positive net flows (emissions) or negative (sequestration). However, the aggregated balance sheet of carbon for agricultural soils is subject to significant uncertainties with estimates that can vary greatly depending on the method and data sources. The average European values, for example, range from losses of -0.17 ± 0.33 Mg C ha-1 y-1 (emissions), when calculated from data in the inventory of agricultural soils (available for 33% of the European cultivated land) to values of accumulation of 0.15 ± 0.15, or loss of -0.08 Mg C ha-1 y-1 when calculated with simulation models. It is estimated that in Italy over the past 70 years, the intensification of agricultural activities has caused a net loss of soil organic carbon by 39% compared to the initial content. The extent of actual SOC sequestration achieved on Italian cultivated land will crucially depend on future policies which could contemplate the inclusion of agriculture in an emissions trading scheme, either as a covered sector, or as an offset provider. It is important to face some research questions mainly aimed at removing this barrier to inclusion of soil carbon in emissions trading. Complementary measures, such as research, development and technology transfer to improve the extension to improve adoption of existing techniques or direct financing to accelerate the adoption of conservation farming systems, should be carried out

Torus-like Solutions for the Landau-de Gennes Model. Part I: The Lyuksyutov Regime

We study global minimizers of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional domains, under a Dirichlet boundary condition. In a relevant range of parameters (which we call the Lyuksyutov regime), the main result establishes the nontrivial topology of the biaxiality sets of minimizers for a large class of boundary conditions including the homeotropic boundary data. To achieve this result, we first study minimizers subject to a physically relevant norm constraint (the Lyuksyutov constraint), and show their regularity up to the boundary. From this regularity, we rigorously derive the norm constraint from the asymptotic Lyuksyutov regime. As a consequence, isotropic melting is avoided by unconstrained minimizers in this regime, which then allows us to analyse their biaxiality sets. In the case of a nematic droplet, this also implies that the radial hedgehog is an unstable equilibrium in the same regime of parameters. Technical results of this paper will be largely employed in Dipasquale et al. (Torus-like solutions for the Landau- de Gennes model. Part II: topology of S1-equivariant minimizers. https://arxiv.org/pdf/2008.13676.pdf; Torus-like solutions for the Landau- de Gennes model. Part III: torus solutions vs split solutions (In preparation)), where we prove that biaxiality level sets are generically finite unions of tori for smooth configurations minimizing the energy in restricted classes of axially symmetric maps satisfying a topologically nontrivial boundary condition

A quantitative second order minimality criterion for cavities in elastic bodies

We consider a functional which models an elastic body with a cavity. We show that if a critical point has positive second variation, then it is a strict local minimizer. We also provide a quantitative estimate