Some Boas-Bellman Type Inequalities in 2-Inner Product Spaces

Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided

Multilayer Thermionic Refrigerator and Generator

A new method of refrigeration is proposed. Cooling is obtained by thermionic emission of electrons over periodic barriers in a multilayer geometry. These could be either Schottky barriers between metals and semiconductors or else barriers in a semiconductor superlattice. The same device is an efficient power generator. A complete theory is provided.Comment: 17 pages with 5 postscript figures, submitted to J. Appl. Phy

Novel substrates for Helium adsorption: Graphane and Graphene-Fluoride

The discovery of fullerenes has stimulated extensive exploration of the resulting behavior of adsorbed films. Our study addresses the planar substrates graphene-fluoride (GF) and graphane (GH) in comparison to graphene. We present initial results concerning the potential energy, energy bands and low density behavior of 4He and 3He films on such different surfaces. For example, while graphene presents an adsorption potential that is qualitatively similar to that on graphite, GF and GH yield potentials with different symmetry, a number of adsorption sites double that on graphene/graphite and a larger corrugation for the adatom. In the case of GF, the lowest energy band width is similar to that on graphite but the He atom has a significantly larger effective mass and the adsorption energy is about three time that on graphite. Implications concerning the monolayer phase diagram of 4He are explored with the exact path integral ground state method. A commensurate ordered state similar to the sqrt{3} x sqrt{3} R30^o state on graphite is found the be unstable both on GF and on GH. The ground states of submonolayer 4He on both GF and GH are superfluids with a Bose Einstein condensate fraction of about 10%.Comment: 6 pages, 3 figures, LT26 proceedings, accepted for publication in Journal of Physics: Conference Serie

Soil quality and fertility in sustainable agriculture, with a contribution to the biological classification of agricultural soils

Soils and crops are particularly vulnerable to climate change and environmental stresses. In many agrosystems, soil biodiversity and ecosystem services provided by soils are under threat from a range of natural and human drivers. Agricultural soils are often subject to agronomic practices that disrupt soil trophic networks and make soils less productive in the long term. In this scenario, sustainable soil use aimed at improving plant/root status, growth and development plays a crucial role for enhancing the biological capacity of agricultural soils. This commentary paper is divided into the following four main sections: (i) the contentious nature of soil organic matter; (ii) soil biological quality/fertility; (iii) soil classification; and, (iv) which agricultural practices can be defined as sustainable? The published literature was analyzed within a holistic framework, with agrosystems considered as living systems where soil, vegetation, fauna and microorganisms co-evolve and are reciprocally influenced. Ultimately, this article will suggest a better stewardship of agricultural soils as a natural capital

Magnetic Structure of Hydrogen Induced Defects on Graphene

Using density functional theory (DFT), Hartree-Fock, exact diagonalization, and numerical renormalization group methods we study the electronic structure of diluted hydrogen atoms chemisorbed on graphene. A comparison between DFT and Hartree-Fock calculations allows us to identify the main characteristics of the magnetic structure of the defect. We use this information to formulate an Anderson-Hubbard model that captures the main physical ingredients of the system, while still allowing a rigorous treatment of the electronic correlations. We find that the large hydrogen-carbon hybridization puts the structure of the defect half-way between the one corresponding to an adatom weakly coupled to pristine graphene and a carbon vacancy. The impurity's magnetic moment leaks into the graphene layer where the electronic correlations on the C atoms play an important role in stabilizing the magnetic solution. Finally, we discuss the implications for the Kondo effect.Comment: 10 pages, 10 fig

Low energy phases of bilayer Bi predicted by structure search in two dimensions

We employ an ab-initio structure search algorithm to explore the configurational space of Bi in quasi two dimensions. A confinement potential restricts the movement of atoms within a pre-defined thickness during structure search calculations within the minima hopping method to find the stable and metastable forms of bilayer Bi. In addition to recovering the two known low-energy structures (puckered monoclinic and buckled hexagonal), our calculations predict three new structures of bilayer Bi. We call these structures the $\alpha$, $\beta$, and $\gamma$ phases of bilayer Bi, which are, respectively, 63, 72, and 83 meV/atom higher in energy than that of the monoclinic ground state, and thus potentially synthesizable using appropriate substrates. We also compare the structural, electronic, and vibrational properties of the different phases. The puckered monoclinic, buckled hexagonal, and $\beta$ phases exhibit a semiconducting energy gap, whereas $\alpha$ and $\gamma$ phases are metallic. We notice an unusual Mexican-hat type band dispersion leading to a van Hove singularity in the buckled hexagonal bilayer Bi. Notably, we find symmetry-protected topological Dirac points in the electronic spectrum of the $\gamma$ phase. The new structures suggest that bilayer Bi provides a novel playground to study distortion-mediated metal-insulator phase transitions