Moduli of equivariant sheaves and Kronecker-McKay modules

We extend Alvarez-Consul and King description of moduli of sheaves over projective schemes to moduli of equivariant sheaves over projective Gamma-schemes, for a finite group Gamma. We introduce the notion of Kronecker-McKay modules and construct the moduli of equivariant sheaves using a natural functor from the category of equivariant sheaves to the category of Kronecker-McKay modules. Following Alvarez-Consul and King, we also study theta functions and homogeneous co-ordinates of moduli of equivariant sheaves.

Hydrogen energy future with formic acid: a renewable chemical hydrogen storage system

Formic acid, the simplest carboxylic acid, is found in nature or can be easily synthesized in the laboratory (major by-product of some second generation biorefinery processes); it is also an important chemical due to its myriad applications in pharmaceuticals and industry. In recent years, formic acid has been used as an important fuel either without reformation (in direct formic acid fuel cells, DFAFCs) or with reformation (as a potential chemical hydrogen storage material). Owing to the better efficiency of DFAFCs compared to several other PEMFCs and reversible hydrogen storage systems, formic acid could serve as one of the better fuels for portable devices, vehicles and other energy-related applications in the future. This perspective is focused on recent developments in the use of formic acid as a reversible source for hydrogen storage. Recent developments in this direction will likely give access to a variety of low-cost and highly efficient rechargeable hydrogen fuel cells within the next few years by the use of suitable homogeneous metal complex/heterogeneous metal nanoparticle-based catalysts under ambient reaction conditions. The production of formic acid from atmospheric CO2 (a greenhouse gas) will decrease the CO2 content and may be helpful in reducing global warming.

Dynamos driven by weak thermal convection and heterogeneous outer boundary heat flux

We use numerical dynamo models with heterogeneous core-mantle boundary (CMB) heat flux to show that lower mantle lateral thermal variability may help support a dynamo under weak thermal convection. In our reference models with homogeneous CMB heat flux, convection is either marginally supercritical or absent, always below the threshold for dynamo onset. We find that lateral CMB heat flux variations organize the flow in the core into patterns that favour the growth of an early magnetic field. Heat flux patterns symmetric about the equator produce non-reversing magnetic fields, whereas anti-symmetric patterns produce polarity reversals. Our results may explain the existence of the geodynamo prior to inner core nucleation under a tight energy budget. Furthermore, in order to sustain a strong geomagnetic field, the lower mantle thermal distribution was likely dominantly symmetric about the equator. (C) 2015 Elsevier B.V. All rights reserved.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Ionothermal Synthesis of High-Voltage Alluaudite Na2+2xFe2-x(SO4)(3) Sodium Insertion Compound: Structural, Electronic, and Magnetic Insights

Exploring future cathode materials for sodium-ion batteries, alluaudite class of Na2Fe2II(SO4)(3) has been recently unveiled as a 3.8 V positive insertion candidate (Barpanda et al. Nat. Commun. 2014, 5, 4358). It forms an Fe-based polyanionic compound delivering the highest Fe-redox potential along with excellent rate kinetics and reversibility. However, like all known SO4-based insertion materials, its synthesis is cumbersome that warrants careful processing avoiding any aqueous exposure. Here, an alternate low temperature ionothermal synthesis has been described to produce the alluaudite Na2+2xFe2-xII(SO4)(3). It marks the first demonstration of solvothermal synthesis of alluaudite Na2+2xM2-xII(SO4)(3) (M = 3d metals) family of cathodes. Unlike classical solid-state route, this solvothermal route favors sustainable synthesis of homogeneous nanostructured alluaudite products at only 300 degrees C, the lowest temperature value until date. The current work reports the synthetic aspects of pristine and modified ionothermal synthesis of Na2+2xFe2-xII(SO4)(3) having tunable size (300 nm similar to 5 mu m) and morphology. It shows antiferromagnetic ordering below 12 K. A reversible capacity in excess of 80 mAh/g was obtained with good rate kinetics and cycling stability over 50 cycles. Using a synergistic approach combining experimental and ab initio DFT analysis, the structural, magnetic, electronic, and electrochemical properties and the structural limitation to extract full capacity have been described.