Generalized phase diversity for wave-front sensing

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.     

Does the Schulman's titration of microemulsions really provide meaningful parameters?

In 1955, Bowcott and Schulman coined the term microemulsions and, in passing, proposed a cosurfactant titration of interfaces tailored for water-in-oil systems (Bowcott, J. E.; Schulman, J. H. Z. Elektrochem. 1955, 59, 283). This procedure, elegant and inexpensive, is accomplished by dilution with both oil and cosurfactant up to the onset of microemulsion formation. The rationale they proposed for this method should furnish, with high accuracy, the composition of reverse micelles and continuous bulk in the presence of cosurfactant partition. The present paper demonstrates, by means of pulsed gradient spin-echo NMR, that the Schulman's titration quantitatively describes the cosurfactant partition and that the titration path really corresponds to a dilution path for reverse micelles (at constant composition) dispersed in a continuous bulk (at constant composition).     

Supermassive Black Holes May Be Limited by the Holographic Bound

Supermassive Black Holes are the most entropic objects found in the universe. The Holographic Bound (HB) to the entropy is used to constrain their formation time with initial masses 10^6–8 M , as inferred from observations. We find that the entropy considerations are more limiting than causality for this direct formation. Later we analyze the possibility of SMBHs growing from seed black holes. The growth of the initial mass is studied in the case of accretion of pure radiation and quintessence fields, and we find that there is a class of models that may allow this metamorphosis. Our analysis generalizes recent work for some models of quintessence capable of producing a substantial growth in a short time, while simultaneously obeying the causal and Holographic Bound limits.     

Power-law time distribution of large earthquakes

We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.     

Intersection Local Times of Independent Brownian Motions as Generalized White Noise Functionals

A 'chaos expansion' of the intersection local time functional of two independent Brownian motions in R ^d is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their L ^p -properties are discussed. An important tool for deriving the chaos expansion is a computation of the 'S-transform' of the corresponding regularized intersection local times and a control about their singular limit.     

Synthesis of carbon nanotubes by CVD: Effect of acetylene pressure on nanotubes characteristics

The effect of acetylene partial pressure on the structural and morphological properties of multi-walled carbon nanotubes (MWCNTs) synthesized by CVD on iron nanoparticles dispersed in a SiO₂ matrix as catalyst was investigated. The general growing conditions were: 110 cm³/min flow rate, 690 °C synthesis temperature, 180 Torr over pressure and two gas compositions: 2.5% and 10% C₂H₂/N₂. The catalyst and nanotubes were characterized by HR-TEM, SEM and DRX. TGA and DTA were also carried out to study degradation stages of synthesized CNTs. MWCNTs synthesized with low acetylene concentration are more regular and with a lower amount of amorphous carbon than those synthesized with a high concentration. During the synthesis of CNTs, amorphous carbon nanoparticles nucleate on the external wall of the nanotubes. At high acetylene concentration carbon nanoparticles grow, covering all CNTs’ surface, forming a compact coating. The combination of CNTs with this coating of amorphous carbon nanoparticles lead to a material with high decomposition temperature.     

Density functional theory analysis of reactivity of PtxPdy alloy clusters

We investigate the reactivity of various Pt_xPd_y combinations (with x + y = 10 and various x:y ratios) towards the adsorption of specific intermediates of the oxygen reduction, using the B3PW91 hybrid density functional theory. The reactivity is shown to be not only sensitive to the composition of the cluster, but also to the atomic distribution. The calculations indicate that two different ensembles: one ordered and one randomly mixed, with overall composition Pt₃Pd₇ are thermodynamically more favorable than pure Pt₁₀ for the oxygen reduction reaction. The reasons for this behavior are clearly explained in terms of the atomic and electronic distribution, which makes the Pd atoms to act as electron donors both to Pt atoms and to the adsorbates, thus the reactivity of the Pd atoms in such environment becomes intermediate between Pt and Pd. Moreover, it is found that in a mixed Pt₃Pd₇ state the electronic distribution makes the average atom more similar to Pt than to Pd, whereas in an ordered Pt₃Pd₇ cluster, the average atom is more similar to Pd than to Pt.     

The <Emphasis Type="Italic">k</Emphasis>-Fibonacci matrix and the Pascal matrix

We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.