A General Fractional Porous Medium Equation

We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion: \input amssym $$\left\{ {\matrix{ {{{\partial u} \over {\partial t}} + \left( { ‐ \Delta } \right)^{\sigma /2} \left( {\left| u \right|^{m ‐ 1} u} \right) = 0,} \hfill & {x \in {\Bbb R} ^N ,\,\,t > 0,} \hfill \cr {u\left( {x,0} \right) = f\left( x \right),} \hfill & {x \in {\Bbb R} ^N .} \hfill \cr } } \right.$$ We consider data \input amssym $f\in L^1(\Bbb{R}^N)$ and all exponents $0<\sigma<2\;and\;m>0$ . Existence and uniqueness of a strong solution is established for $ m > {m_\ast}={(N-\sigma)_+}/N$ , giving rise to an L¹‐contraction semigroup. In addition, we obtain the main qualitative properties of these solutions. In the lower range ${0 < m} \le {m_\ast}$ existence and uniqueness happen under some restrictions, and the properties of the solutions are different from the ones for the case above m_*. We also study the dependence of solutions on f, m, and σ. Moreover, we consider the above questions for the problem posed in a bounded domain. © 2012 Wiley Periodicals, Inc.     

Highly confined spin-polarized two-dimensional electron gas in SrTiO3/SrRuO3 superlattices

We report first-principles characterization of the structural and electronic properties of (SrTiO3)5/(SrRuO3)1 superlattices. We show that the system exhibits a spin-polarized two-dimensional electron gas, extremely confined to the 4d orbitals of Ru in the SrRuO3 layer. Every interface in the superlattice behaves as a minority-spin half-metal ferromagnet, with a magnetic moment of μ=2.0μ(B)/SrRuO3 unit. The shape of the electronic density of states, half-metallicity, and magnetism are explained in terms of a simplified tight-binding model, considering only the t(2g) orbitals plus (i) the bidimensionality of the system and (ii) strong electron correlations.     

Spin relaxation near the metal-insulator transition: dominance of the Dresselhaus spin-orbit coupling

We identify the Dresselhaus spin-orbit coupling as the source of the dominant spin-relaxation mechanism in the impurity band of a wide class of n-doped zinc blende semiconductors. The Dresselhaus hopping terms are derived and incorporated into a tight-binding model of impurity sites, and they are shown to unexpectedly dominate the spin relaxation, leading to spin-relaxation times in good agreement with experimental values. This conclusion is drawn from two complementary approaches: an analytical diffusive-evolution calculation and a numerical finite-size scaling study of the spin-relaxation time.     

Physical interpretation of the paraxial estimator

The paraxial estimator (PE) is a parameter quantifying the paraxiality of a light beam. Even if some of its features were previously tackled, key details on its behavior were not fully presented. This paper robustly presents the physical meaning of the PE in a global way, enlarging its interpretation out of the paraxial region what permits to get a first view of the beam propagation dynamics from the value of this parameter. The physical interpretation is given in the spatial domain and in the spectral domain as well. In the first one, the value of PE is related to the competition between the fast oscillations and the remaining oscillations of a propagating field. Looking at spectral domain, the PE deals with the spectral dispersion (or width) of the plane waves forming the field. In this context, a negative value of PE concerns the effective contribution of the evanescent waves what only happens in a strong nonparaxial regime. The PE also accounts the geometric and physical features on the concept of the paraxial approximation in a natural way. An analysis performed for beams propagating through a spherical thin lens reveals that the loss of paraxiality is due to the geometric effect of ray bending by the lens and by another physical effect, concerning the nonideal collimation of the beam.     

Bifurcations of the normal modes of the Ne?Br2 complex

We study the classical dynamics of the rare gas-dihalogen Ne?Br₂ complex in its ground electronic state. By considering the dihalogen bond frozen at its equilibrium distance, the system has two degrees of freedom and its potential energy surface presents linear and T-shape isomers. We find the nonlinear normal modes of both isomers that determine the phase space structure of the system. By means of surfaces of section and applying the numerical continuation of families of periodic orbits, we detect and identify the different bifurcations suffered by the normal modes as a function of the system energy. Finally, using the Orthogonal Fast Lyapunov Indicator (OFLI), we study the evolution of the fraction of the phase space volume occupied by regular motions.     

Nitrile Synthesis with Aldoxime Dehydratases: A Biocatalytic Platform with Applications in Asymmetric Synthesis,Bulk Chemicals,and Biorefineries

Nitriles comprise a broad group of chemicals that are currently being industrially produced and used in fine chemicals and pharmaceuticals, as well as in bulk applications, polymer chemistry, solvents, etc. Aldoxime dehydratases catalyze the cyanide-free synthesis of nitriles starting from aldoximes under mild conditions, holding potential to become sustainable alternatives for industrial processes. Different aldoxime dehydratases accept a broad range of aldoximes with impressive high substrate loadings of up to >1 Kg L⁻¹ and can efficiently catalyze the reaction in aqueous media as well as in non-aqueous systems, such as organic solvents and solvent-free (neat substrates). This paper provides an overview of the recent developments in this field with emphasis on strategies that may be of relevance for industry and sustainability. When possible, potential links to biorefineries and to the use of biogenic raw materials are discussed.     

Speciation analysis of thallium using electrothermal AAS following on-line pre-concentration in a microcolumn filled with multiwalled carbon nanotubes

The enrichment ability of carbon nanotubes (CNTs) was investigated and a new method established for the determination of trace thallium species in environmental samples using electrothermal atomization-atomic absorption spectrometry (ETAAS). The CNTs were employed as sorbent substrate in a continuous flow system coupled to ETAAS. Parameters influencing the recoveries of thallium were optimized. Under optimal conditions, the detection limit and precision of the method were 0.009 µg L^?1 and 3.9%, respectively. The method was applied to the determination of thallium in real environmental samples and the recoveries were in the range from 96 to 100%. This system was able to separate thallium (I) from the matrix, which allowed its selective determination. The total thallium content was then determined by reducing Tl(III) with hydroxylamine. All these experimental results indicated that this new procedure can be applied to the determination of trace thallium in drinking water samples.