On the euler equation: Bi-Hamiltonian structure and integrals in involution

We propose a bi-Hamiltonian formulation of the Euler equation for the free n-dimensional rigid body moving about a fixed point. This formulation lives on the physical phase space so(n), and is different from the bi-Hamiltonian formulation on the extended phase space sl(n), considered previously in the literature. Using the bi-Hamiltonian structure on so(n), we construct new recursion schemes for the Mishchenko and Manakov integrals of motion.     

Immobilization of kojic acid in ZnAl-hydrotalcite like compounds

Kojic acid (KOJ) is a melanin synthesis inhibitor widely used as skin lightening agent in topical preparations. Unfortunately it is easily susceptible to photo-oxidation, phenomenon responsible for chemical and organoleptic modifications. The aim of this work was the intercalation of KOJ in hydrotalcite-like compounds (HTlc) in order to stabilize KOJ and to reduce its photolability. Hydrotalcite containing Zn and Al (ZnAl-HTlc) was used as host to obtain the final compound ZnAl-HTlc-KOJ. The intercalation was carried out, after many attempts, by ionic exchange mechanism by means of the strong base EtO^? in anhydrous ethanol/dimethylsulfoxide (DMSO) mixture as solvent in order to generate KOJ^? anions. The final product was characterized by the X-ray powder diffraction (XRPD), FT-IR spectroscopy, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC) and elemental analysis. The intercalated compound was formulated in a siliconic water free self-emulsifying ointment and the in vitro release profile was evaluated. All samples (intercalation compound and its formulation) were submitted also to spectrophotometric assays in order to evaluate the matrix protective effect towards ultraviolet rays.     

Reconfigurable silicon filter with continuous bandwidth tunability

We present the design and the fabrication of compact tunable silicon-on-insulator bandpass filters based on the integration of a Mach-Zehnder interferometer with ring resonators and activated via thermo-optic phase shifters. The proposed architecture provides wide filter bandwidth tunability from 10% to 90% of the free spectral range preserving the filter off-band rejection. Possible applications are channel subset selection in wavelength division multiplexing optical systems, adaptive filtering to signal bandwidth, and reconfigurable filters for gridless networking.     

Are there more than five linearly-independent collision invariants for the Boltzmann equation?

The problem of finding the summational collision invariants for the Boltzmann equation is tackled with the aim of proving that the most general solution of the problem is not different from the standard one even when the equation defining a collision invariant is only satisfied almost everywhere inR ³×R ³×S ². The collision invariant is assumed to be in the Hilbert spaceH of the functions which are square integrable with respect to a Maxwellian weight.     

Dispersion and localization of electronic states at a ferrocene/Cu(111) interface

Low-temperature scanning tunneling microscopy and spectroscopy combined with first-principles simulations reveal a nondissociative physisorption of ferrocene molecules on a Cu(111) surface, giving rise to ordered molecular layers. At the interface, a 2D-like electronic band is found, which shows an identical dispersion as the Cu(111) Shockley surface-state band. Subsequent deposition of Cu atoms forms charged organometallic compounds that localize interface-state electrons.     

Stretching in a model of a turbulent flow

Using a multi-scaled, chaotic flow known as the KS model of turbulence [J.C.H. Fung, J.C.R. Hunt, A. Malik, R.J. Perkins, Kinematic simulation of homogeneous turbulence by unsteady random fourier modes, J. Fluid Mech. 236 (1992) 281-318], we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds number and the maximum Lyapunov exponent, which is similar to that for a turbulent flow with the same energy spectrum. Our results show that the Lyapunov exponents are sensitive to the advection of small eddies by large eddies, which can be explained by considering the Lagrangian correlation time of the smallest scales. We also relate the number of stagnation points within a flow to the maximum Lyapunov exponent, and suggest a linear dependence between the two characteristics.     

On the mechanism of decomposition of the benzyl radical

The C₇H₇ potential energy surface was studied from first principles to determine the benzyl radical decomposition mechanism. The investigated high temperature reaction pathway involves 15 accessible energy wells connected by 25 transition states. The analysis of the potential energy surface, performed determining kinetic constants of each elementary reaction using conventional transition state theory, evidenced that the reaction mechanism has as rate determining step the isomerization of the 1,3-cyclopentadiene, 5-vinyl radical to the 2-cyclopentene,5-ethenylidene radical and that the fastest reaction channel is dissociation to fulvenallene and hydrogen. This is in agreement with the literature evidences reporting that benzyl decomposes to hydrogen and a C₇H₆ species. The benzyl high-pressure decomposition rate constant estimated assuming equilibrium between the rate determining step transition state and benzyl is k₁(T) = 1.44 × 10¹³T^0.453exp(−38400/T) s⁻¹, in good agreement with the literature data. As fulvenallene reactivity is mostly unknown, we investigated its reaction with hydrogen, which has been proposed in the literature as a possible decomposition route. The reaction proceeds fast both backward to form again benzyl and, if hydrogen adds to allene, forward toward the decomposition into the cyclopentadienyl radical and acetylene with high-pressure kinetic constants k₂(T) = 8.82 × 10⁸T^1.20exp(1016/T) and k₃(T) = 1.06 × 10⁸T^1.35exp(1716/T) cm³/mol/s, respectively. The computed rate constants were then inserted in a detailed kinetic mechanism and used to simulate shock tube literature experiments.     

Coupling atomistic and finite element approaches for the simulation of optoelectronic devices

Multiscale methods coupling quantum mechanical/atomistic models such as envelope function and tight binding approaches with continuous media models e.g. for strain or electronic transport are very useful for an accurate simulation of modern and emerging electronic and optoelectronic devices based on nanostructured active regions. We present simulations using TiberCAD whose main focus is on providing an integrated multiscale/multiphysics simulation environment.     

MRI characterization of residual mediastinal masses in Hodgkin's disease: long-term follow-up

Our purpose was to evaluate the role of MRI in distinguishing fibrous from active residual masses in treated Hodgkin's disease. Forty patients with residual mediastinal mass larger than 1.5 cm underwent MRI 1, 3, 6, and 12 months after the end of cycles of prescribed chemotherapy or combined chemoradiotherapy. The MRI examinations were performed on a 0.5 and a 1.5 T systems, using T(1) before and after gadolinium injection and T(2)-weighted sequences. Each time the residual mass was evaluated in size and signal intensity on spin echo (SE) T(2)-weighted images and on SE T(1)-weighted images after contrast medium. Low signal intensity and low contrast enhancement were considered signs of inactive residues; homogeneous high signal intensity and high contrast enhancement were indicative of active residual disease; heterogeneous signal intensity and heterogeneous contrast enhancement were indicative of partial remission or necrotic/inflammatory phenomena. MR showed high diagnostic accuracy in the evaluation of Hodgkin's mediastinal residues after treatment, if performed at least 6 months after the end of therapy, reaching the highest sensitivity and specificity values at 12 month follow-up (considering the three parameters-T(2) signal intensity, contrast-enhancement, and size-all together). If we consider the single parameters individually, we can observe that size variation remains the more valuable parameter to predict or to exclude a relapse. MR diagnostic accuracy at the 6-month follow-up was lower due to the higher incidence of inhomogeneous pattern. The accuracy of MR performed at 1 and at 3 months after the end of therapy was not satisfying. This represents a clinical problem because the most important clinical decisions have to be taken just in this early post-treatment phase.     

An open volume, high isolation, radio frequency surface coil system for pulsed magnetic resonance

We present an open volume, high isolation, RF system suitable for pulsed NMR and EPR spectrometers with reduced dead time. It comprises a set of three RF surface coils disposed with mutually parallel RF fields and a double-channel receiver (RX). Theoretical and experimental results obtained with a prototype operating at about 100 MHz are reported. Each surface RF coil (diameter 5.5 cm) was tuned to f₀ = 100.00 ± 0.01 MHz when isolated. Because of the mutual coupling and the geometry of the RF coils, only two resonances at f₁ = 97.94 MHz and f₂ = 101.85 MHz were observed. We show they are associated with two different RF field spatial distributions. In continuous mode (CW) operation the isolation between the TX coil and one of the RX coils (single-channel) was about −10 dB. By setting the double-channel RF assembly in subtraction mode the isolation values at f₁ or f₂ could be optimised to about −75 dB. Following a TX RF pulse (5 μs duration) an exponential decay with time constant of about 600 ns was observed. The isolation with single-channel RX coil was about −11 dB and it increased to about −47 dB with the double-channel RX in subtraction mode. Similar results were obtained with the RF pulse frequency selected to f₂ and also with shorter (500 ns) RF pulses. The above geometrical parameters and operating frequency of the RF assembly were selected as a model for potential applications in solid state NMR and in free radical EPR spectroscopy and imaging.