Study of porous silicon nanostructures as hydrogen reservoirs

The amount of hydrogen present in porous silicon (PS) nanostructures is analyzed in detail. Concentration of atomic hydrogen chemically bound to the specific surface of PS is quantitatively evaluated by means of attenuated total reflection infrared (ATR-IR) spectroscopy and temperature-programmed desorption (TPD) spectroscopy. The concentration values are correlated to the PS nanoscale morphology. In particular, the influence of porosity, silicon nanocrystallite dimension, and shape on hydrogen concentration values is described. Hydrogen concentrations in fresh, aged, as well as in chemically and thermally treated PS layers are measured. Maximal hydrogen concentration of 66 mmol/g is detected in nanoporous layers with high (>95%) porosity consisting of nanocrystallites with dimensions of about 2 nm. Mass energy density that can be potentially obtained from this amount of hydrogen through a low-temperature fuel cell is estimated to be about 2176 W-h/kg and is found to be comparable with other substances containing hydrogen, such as hydride materials and methanol, which are usually used as hydrogen reservoirs.     

Well-posedness for a mean field model of Ginzburg–Landau vortices with opposite degrees

In this paper we analyze the hydrodynamic equations for Ginzburg–Landau vortices as derived by E (Phys. Rev. B. 50(3):1126–1135, 1994). In particular, we are interested in the mean field model describing the evolution of two patches of vortices with equal and opposite degrees. Many results are already available for the case of a single density of vortices with uniform degree. This model does not take into account the vortex annihilation, hence it can also be seen as a particular instance of the signed measures system obtained in Ambrosio et al. (Ann. Inst. H. Poincaré Anal. Non Linéaire 28(2):217–246, 2011) and related to the Chapman et al. (Eur. J. Appl. Math. 7(2):97–111, 1996) formulation. We establish global existence of L ^p solutions, exploiting some optimal transport techniques introduced in this context in Ambrosio and Serfaty (Commun. Pure Appl. Math. LXI(11):1495–1539, 2008). We prove uniqueness for L ^∞ solutions, as expected by analogy with the incompressible Euler equations in fluidodynamics. We also consider the corresponding Dirichlet problem in a bounded domain. Moreover, we show some simple examples of 1-dimensional dynamic.     

Embeddings of general curves in projective spaces: the range of the quadrics

Let C ì mathbbP^r C subset {mathbb{P}^r} be a general embedding of prescribed degree of a general smooth curve with prescribed genus. Here we prove that either h⁰( mathbbP^r,I_C(2) ) = 0 {h^0}left( {{mathbb{P}^r},{mathcal{I}_C}(2)} right) = 0 or h¹( mathbbP^r,I_C(2) ) = 0 {h^1}left( {{mathbb{P}^r},{mathcal{I}_C}(2)} right) = 0 (a problem called the maximal rank conjecture in the range of quadrics).     

Simultaneous kinetic determination of uric acid ascorbic acid mixtures

A kinetic stopped-flow method is described for the simultaneous determination of uric acid and ascorbic acid with tris (2,2'-bipyridine)iron(III). For the least favourable ratios of uric to ascorbic acid, in a total concentration of 10^-5 M, the error in the determination of uric acid is estimated at ±10%.     

Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters

Most modeling efforts involve multiple physical or biological processes. All physical or biological processes take time to complete. Therefore, multiple time delays occur naturally and shall be considered in more advanced modeling efforts. Carefully formulated models of such natural processes often involve multiple delays and delay dependent parameters. However, a general and practical theory for the stability analysis of models with more than one discrete delay and delay dependent parameters is nonexistent. The main purpose of this paper is to present a practical geometric method to study the stability switching properties of a general transcendental equation which may result from a stability analysis of a model with two discrete time delays and delay dependent parameters that dependent only on one of the time delay. In addition to simple and illustrative examples, we present a detailed application of our method to the study of a two discrete delay SIR model.     

Conservative perturbations of conservative operators

The paper is devoted to investigating a class of unbounded perturbations of conservative linear operators. In the particular case of operators defined on compact differentiable manifolds, the Lie sum of two conservative operators is considered, extending a classical perturbation formula of the theory of Lie groups.