The Herglotz variational problem on spheres and its optimal control approach

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.

Geometric Hamiltonian formulation of a variational problem depending on the covariant acceleration

We consider a second-order variational problem depending on the covariant acceleration, which is related to the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of Pontryagin’s maximum principle, allows us to study the dynamics of the control problem.

Alkaline-earth aluminosilicate-based glass and glass-ceramic sealants for functional applications

The planar design of solid oxide fuel cell (SOFC) is the most promising one due to its easier fabrication, improved performance and relatively high power density. In planar SOFCs and other solid-electrolyte devices, gas-tight seals must be formed along the edges of each cell and between the stack and gas manifolds. Glass and glass-ceramic (GC), in particular alkaline-earth alumino silicate based glasses and GCs, are becoming the most promising materials for gas-tight sealing applications in SOFCs. Besides the development of new glass-based materials, new additional concepts are required to overcome the challenges being faced by the currently existing sealant technology. The present work deals with the development of glasses- and GCs-based materials to be used as a sealants for SOFCs and other electrochemical functional applications. In this pursuit, various glasses and GCs in the field of diopside crystalline materials have been synthesized and characterized by a wide array of techniques. All the glasses were prepared by melt-quenching technique while GCs were produced by sintering of glass powder compacts at the temperature ranges from 800−900 ºC for 1−1000 h. Furthermore, the influence of various ionic substitutions, especially SrO for CaO, and Ln2O3 (Ln=La, Nd, Gd, and Yb), for MgO + SiO2 in Al-containing diopside on the structure, sintering and crystallization behaviour of glasses and properties of resultant GCs has been investigated, in relevance with final application as sealants in SOFC. From the results obtained in the study of diopside-based glasses, a bilayered concept of GC sealant is proposed to overcome the challenges being faced by (SOFCs). The systems designated as Gd−0.3 (in mol%: 20.62MgO−18.05CaO−7.74SrO−46.40SiO2−1.29Al2O3 − 2.04 B2O3−3.87Gd2O3) and Sr−0.3 (in mol%: 24.54 MgO−14.73 CaO−7.36 SrO−0.55 BaO−47.73 SiO2−1.23 Al2O3−1.23 La2O3−1.79 B2O3−0.84 NiO) have been utilized to realize the bi-layer concept. Both GCs exhibit similar thermal properties, while differing in their amorphous fractions, revealed excellent thermal stability along a period of 1,000 h. They also bonded well to the metallic interconnect (Crofer22APU) and 8 mol% yttrium stabilized zirconium (8YSZ) ceramic electrolyte without forming undesirable interfacial layers at the joints of SOFC components and GC. Two separated layers composed of glasses (Gd−0.3 and Sr−0.3) were prepared and deposited onto interconnect materials using a tape casting approach. The bi-layered GC showed good wetting and bonding ability to Crofer22APU plate, suitable thermal expansion coefficient (9.7–11.1 × 10–6 K−1), mechanical reliability, high electrical resistivity, and strong adhesion to the SOFC componets. All these features confirm the good suitability of the investigated bi-layered sealant system for SOFC applications.