Nonlinear modelling of data in photomineralization kinetics of organic micropollutants by photocatalytic membranes immobilizing titanium dioxide in membrane reactors

Kinetic fitting of substrate disappearance and of total organic carbon (TOC) mineralization of organic micropollutants, in water and air, by photocatalytic membranes immobilizing titanium dioxide, was carried out. A model was used in which mineralization of substrate to CO₂ is supposed to occur, with kinetic constant k₁, through one single intermediate, mediating the behaviour of all the numerous real intermediates formed in the path to CO₂, kinetic constant of formation of the latter being k₂. A competitive Langmuirian‐type adsorption of both substrate and ‘intermediate’ was also supposed to be operative, as expressed by pseudo‐thermodynamic constants K₁ and K₂ respectively, these constants possessing a, partly at least, kinetic significance. Nonlinear models could be fitted to data by using the least‐squares method. The very satisfactory matching is shown for the laboratory‐scale mineralization kinetics of methane, as model molecule of aliphatic contaminants, both in the gas phase and in aqueous solution. Furthermore, in pilot plant experiments, using phenol, as model molecule of aromatics, modelling of quantum yields was carried out, as a function of concentration and of adsorbed radiant power. Kinetics of hydroxyl radicals reacting between themselves, leading to hydrogen peroxide, other than with substrate or intermediates leading to mineralization, was considered, paralleled by a second competition kinetics due to superoxide anion radical and its conjugate acid, equally leading to mineralization. In this model the contribution of hydroxyl radicals to mineralization decreases with irradiance, while the contribution of superoxide anion radical and its conjugate acid increases. If the regression equations of these two contributions are considered together, in a linear combination, the surface model perfectly fits the experimental data. Copyright © 2008 John Wiley & Sons, Ltd.     

Universal Low-energy Behavior in a Quantum Lorentz Gas with Gross-Pitaevskii Potentials

We consider a quantum particle interacting with N obstacles, whose positions are independently chosen according to a given probability density, through a two-body potential of the form N²V (Nx) (Gross-Pitaevskii potential). We show convergence of the N dependent one-particle Hamiltonian to a limiting Hamiltonian where the quantum particle experiences an effective potential depending only on the scattering length of the unscaled potential and the density of the obstacles. In this sense our Lorentz gas model exhibits a universal behavior for N large. Moreover we explicitely characterize the fluctuations around the limit operator. Our model can be considered as a simplified model for scattering of slow neutrons from condensed matter.     

Precise predictions for same-sign W-boson scattering at the LHC

Vector-boson scattering processes are of great importance for the current run-II and future runs of the Large Hadron Collider. The presence of triple and quartic gauge couplings in the process gives access to the gauge sector of the Standard Model (SM) and possible new-physics contributions there. To test any new-physics hypothesis, sound knowledge of the SM contributions is necessary, with a precision which at least matches the experimental uncertainties of existing and forthcoming measurements. In this article we present a detailed study of the vector-boson scattering process with two positively-charged leptons and missing transverse momentum in the final state. In particular, we first carry out a systematic comparison of the various approximations that are usually performed for this kind of process against the complete calculation, at LO and NLO QCD accuracy. Such a study is performed both in the usual fiducial region used by experimental collaborations and in a more inclusive phase space, where the differences among the various approximations lead to more sizeable effects. Afterwards, we turn to predictions matched to parton showers, at LO and NLO: we show that on the one hand, the inclusion of NLO QCD corrections leads to more stable predictions, but on the other hand the details of the matching and of the parton-shower programs cause differences which are considerably larger than those observed at fixed order, even in the experimental fiducial region. We conclude with recommendations for experimental studies of vector-boson scattering processes.     

Effectiveness of measures of performance during speculative bubbles

Statistical analysis of financial data mostly focused on testing the validity of Brownian motion (Bm). Analyses performed on several time series have shown deviation from the Bm hypothesis, that is at the base of the evaluation of many financial derivatives. We analyze the behavior of performance measures based on maximum drawdown movements (MDD(T)), testing their stability when the underlying process deviates from the Bm hypothesis. In particular we consider the fractional Brownian motion (fBm), and fluctuations estimated empirically on raw market data. The case study of the rising part of speculative bubbles is reported.     

Dielectric properties of ice and liquid water from first-principles calculations

We present a first-principles study of the static dielectric properties of ice and liquid water. The eigenmodes of the dielectric matrix E are analyzed in terms of maximally localized dielectric functions similar, in their definition, to maximally localized Wannier orbitals obtained from Bloch eigenstates of the electronic Hamiltonian. We show that the lowest eigenmodes of E (-1) are localized in real space and can be separated into groups related to the screening of lone pairs, intra-, and intermolecular bonds, respectively. The local properties of the dielectric matrix can be conveniently exploited to build approximate dielectric matrices for efficient, yet accurate calculations of quasiparticle energies.     

A model for transits in dynamic response theory

The first goal of vibration-transit (V-T) theory was to construct a tractable approximate Hamiltonian from which the equilibrium thermodynamic properties of monatomic liquids can be calculated. The Hamiltonian for vibrations in an infinitely extended harmonic random valley, together with the universal multiplicity of such valleys, gives an accurate first-principles account of the measured thermodynamic properties of the elemental liquids at melt. In the present paper, V-T theory is extended to nonequilibrium properties, through an application to the dynamic structure factor S(q,omega). It was previously shown that the vibrational contribution alone accurately accounts for the Brillouin peak dispersion curve for liquid sodium, as compared both with molecular-dynamics (MD) calculations and inelastic x-ray scattering data. Here it is argued that the major effects of transits will be to disrupt correlations within the normal-mode vibrational motion and to provide an additional source of inelastic scattering. We construct a parametrized model for these effects and show that it is capable of fitting MD results for S(q,omega) in liquid sodium. A small discrepancy between model and MD at large q is attributed to multimode vibrational scattering. In comparison, mode coupling theory formulates S(q,omega) in terms of processes through which density fluctuations decay. While mode coupling theory is also capable of modeling S(q,omega) very well, V-T theory is the more universal since it expresses all statistical averages, thermodynamic functions, and time correlation functions alike, in terms of the same motional constituents, vibrations and transits.     

The synthesis and conformation of oxygenated trianglimine macrocycles

The synthesis of series of D(2h) and C(2v) symmetric oxygenated aromatic dicarboxaldehydes, using dilithiation methodology, is described along with their reactivity in the [3+3] cyclocondensation reaction with (1R,2R)-diaminocyclohexane to give oxygenated trianglimine macrocycles. Macrocycles derived from C(2v) symmetric dialdehydes give macrocycles with a stereogenic aromatic plane with complete diastereocontrol, as a mixture of rotamers.     

Existence and Lipschitz regularity for minima

We prove the existence, uniqueness and Lipschitz regularity of the minima of the integral functional

on ( ) for a class of integrands that are convex in and for boundary data satisfying some barrier conditions. We do not impose regularity or growth assumptions on .

     

Self-healing of CdSe nanocrystals: first-principles calculations

Ab initio calculations of the structural, electronic, and optical properties of CdSe nanoparticles are presented. The atomic structures of the clusters are relaxed both in vacuum and in the presence of surfactant ligands. In both cases, we predict significant geometrical rearrangements of the nanoparticle surface while the wurtzite core is maintained. These reconstructions lead to the opening of an optical gap without the aid of passivating ligands, thus "self-healing" the surface electronic structure. Our calculations also predict the existence of a midgap state responsible for recently observed subband emission.