High-order harmonic generation with a strong laser field and an attosecond-pulse train: The Dirac-Delta comb and monochromatic limits

In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time delayed attosecond-pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is the most adequate way to approximate the attosecond-pulse train in a semianalytic framework. Employing the strong-field approximation and saddle-point methods, we make a detailed assessment of the spectra obtained by modeling the attosecond-pulse train by either a monochromatic wave or a Dirac-Delta comb. These are the two extreme limits of a real train, which is composed by a finite set of harmonics. Specifically, in the monochromatic limit, we find the downhill and uphill sets of orbits reported in the literature, and analyze their influence on the high-harmonic spectra. We show that, in principle, the downhill trajectories lead to stronger harmonics, and pronounced enhancements in the low plateau region. These features are analyzed in terms of quantum interference effects between pairs of quantum orbits, and compared to those obtained in the Dirac-Delta limit.     

On the domain of attraction of an operator between supremum and sum

Summary Between the operations which produce partial maxima and partial sums of a sequenceY ₁,Y ₂, ..., lies the inductive operation:X _n =X _n-1(X _n-1+Y _n ),n1, for 0<<1. If theY _n are independent random variables with common distributionF, we show that the limiting behavior of normed sequences formed from {X _n ,n1}, is, for 0<<1, parallel to the extreme value case =0. ForFD() we give a full proof of the convergence, whereas forFD()D(), we only succeeded in proving tightness of the involved sequence. The processX _n is interesting for some applied probability models.     

Evolution of Physicochemical Parameters during the Thermal-Based Production of Água-mel,a Traditional Portuguese Honey-Related Food Product

The purpose of this work was to investigate the physicochemical changes occurring during the thermal-based production of água-mel, a traditional Portuguese honey-related food product. The refractive index, color parameters (hue angle, H°; chroma, C*), and the content of total reducing sugars, glucose, fructose, total brown pigments, and 5-hydroxymethylfurfural were monitored along the entire production process, and their evolution was kinetically modelled. Thermal processing caused a gradual decrease in sugars, which was accompanied by the formation of brown pigments and 5-hydroxymethylfurfural, increased concentration of soluble solids as evaluated through refractive index measurements, as well as the appearance of darker colors. In particular, a zero-order kinetic model could explain the changes in H° and reducing sugars, while the evolution of refractive index, brown pigments, 5-hydroxymethylfurfural, C*, fructose, and glucose were best fitted using a first-order kinetics model.     

Unprecedented Double aza‐Michael Addition within a Sapphyrin Core

A novel sapphyrin derivative was obtained from the reaction between a free‐base sapphyrin and dimethyl acetylenedicarboxylate (DMAD). The formation of the new compound involved a double aza‐Michael addition of two pyrrolic NH groups to a DMAD molecule, with the formation of a disubstituted ethano bridge. The NMR spectral data reveal a product with an unsymmetrical structure; DFT calculations provided support for a structure in which the ethano bridge links two adjacent pyrrole units. The present study provides a seemingly unprecedented example of an N,N′‐dinucleophile reacting with DMAD to form a heterocyclic compound in which the two N‐atoms are linked to the two sp³ carbon atoms derived from a substituted acetylene.     

Synthesis of series of 1- and 3-differently substituted xanthines from imidazoles

A new and general method is described for the synthesis, in three steps and in good overall yields, of tetrasubstituted xanthines from an easily prepared imidazole precursor. The method is especially useful for the preparation in standardized conditions of series of xanthines combining a broad variety of primary or secondary alkyl, benzyl or aryl groups at N1 and of alkyl or arylmethyl groups at N3, that are not readily available by other methods.     

A supramolecular cup-and-ball C60-porphyrin conjugate system

In addition to the ammonium-crown ether recognition, pi-stacking interactions between the C60 sphere and the porphyrin moiety have been evidenced in a supramolecular complex obtained from a porphyrin-crown ether conjugate and a fullerene derivative bearing an ammonium unit.     

Finite-time blowup for a complex Ginzburg–Landau equation with linear driving

In this paper, we consider the complex Ginzburg–Landau equation ${u_t = e^{i\theta} [\Delta u + |u|^\alpha u] + \gamma u}$ on ${\mathbb{R}^N}$ , where ${\alpha > 0,\,\gamma \in \mathbb{R}}$ and ${-\pi /2 < \theta < \pi /2}$ . By convexity arguments, we prove that, under certain conditions on ${\alpha,\theta,\gamma}$ , a class of solutions with negative initial energy blows up in finite time.     

Fluctuation theorems and 1/f noise from a simple matrix

Here we present a model for a small system combined with an explicit entropy bath that iscomparably small. The dynamics of the model is defined by a simple matrix, M. Each row ofM corresponds to a macrostate of the system, e.g. net alignment, while the elements in therow represent microstates. The constant number of elements in each row ensures constantentropy, which allows reversible fluctuations, similar to information theory where aconstant number of bits allows reversible computations. Many elements in M come from themicrostates of the system, but many others come from the bath. Bypassing the bath statesyields fluctuations that exhibit standard white noise; whereas with bath states the powerspectral density varies as S(f) ∝ 1 /f overa wide range of frequencies, f. Thus, the explicit entropy bath is the mechanismof 1/f noisein this model. Both forms of the model match Crooks’ fluctuation theorem exactly,indicating that the theorem applies not only to infinite reservoirs, but also tofinite-sized baths. The model is used to analyze measurements of 1/f-like noise from asub-micron tunnel junction.