Block copolymer nanoparticles of controlled sizes via ring‐opening metathesis polymerization

This article describes the formation and characterization of self‐assembled nanoparticles of controlled sizes based on amphiphilic block copolymers synthesized by ring‐opening metathesis polymerization. We synthesized a novel hydrophobic derivative of norbornene; this monomer could be polymerized using Grubbs' catalyst [Cl₂Ru(CHPh)(PCy₃)₂] forming polymers of controlled molecular weight. We synthesized amphiphilic block copolymers of controlled composition and showed that they assemble into nanoparticles of controlled size. The nanoparticles were characterized using dynamic light scattering and transmission electron microscopy. Tuning the composition of the block copolymer enables the tuning of the diameters of the nanoparticles in the 30‐ to 80‐nm range. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3352–3359, 2004     

On the Long-Time Behavior of the Quantum Fokker-Planck Equation

We analyze the long-time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type diffusion operator, subject to confining potentials of harmonic oscillator type. We establish the existence and uniqueness of a non-equilibrium steady state for the corresponding dynamics. Further, using a (classical) convex Sobolev inequality, we prove an optimal exponential rate of decay towards this state and additionally give precise dispersion estimates in those cases, where no stationary state exists.     

Spatial Vector Solitons in Nonlinear Photonic Crystal Fibers

We study spatial vector solitons in a photonic crystal fiber (PCF) made of a material with the focusing Kerr nonlinearity. We show that such two-component localized nonlinear waves consist of two mutually trapped components confined by the PCF linear and the self-induced nonlinear refractive indices, and they bifurcate from the corresponding scalar solitons. We demonstrate that, in a sharp contrast with an entirely homogeneous nonlinear Kerr medium where both scalar and vector spatial solitons are unstable and may collapse, the periodic structure of PCF can stabilize the otherwise unstable two-dimensional spatial optical solitons. We apply the matrix criterion for stability of these two-parameter solitons, and verify it by direct numerical simulations.     

Mineralogical analysis of auriferous ores from the El Diamante mine, Colombia

X-ray diffraction (XRD), Mössbauer spectrometry (MS), secondary ions mass spectroscopy (SIMS) and laser-ablation microprobe–inductively coupled plasma–mass spectrometry (LAM–ICP–MS) were used to study mineral samples of Colombian auriferous ores collected from the “El Diamante” mine, located in the municipality of Guachavez-Nariño, in Colombia. The samples were prepared as polished thin sections and polished sections. From XRD data, quartz, sphalerite and pyrite were detected and their respective cell parameters were estimated. From MS analyses, pyrite, arsenopyrite and chalcopyrite were identified; their respective hyperfine parameters and respective texture were deduced. Multiple regions of approximately 200 × 200 μm in each sample were analyzed with SIMS; the occurrence of “invisible gold” associated mainly with pyrite and secondarily with arsenopyrite could thus be assigned. It was also found that pyrite is of the arsenious type. Spots from 30 to 40 μm in diameter were analyzed with LAM–ICP–MS for pyrite, arsenopyrite and sphalerite; Au is “homogeneously” distributed inside the structure of the arsenious pyrite and the arsenopyrite (not as inclusions); the chemical composition indicates similarities of this “invisible gold”, forming a solid solution with arsenious pyrite and arsenopyrite. One hundred nineteen and 62 ppm of ‘invisible gold’ was quantified in 21 spots analyzed on pyrite and in 14 spots on arsenopyrite, respectively.     

Finitely additive integration and local integration with respect to upper integrals

Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the q_l-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as q_l-integrable f with q(|f|) < ∞, and of q_l-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most finitely additive integration theories.     

Analysis of Antennas with PBG Substrate

The use of photonic materials has been used in the theory of optical waves. The PBG (Photonic Band Gap) theory and material, was developed recently for optical frequencies and can be easily applied to millimeter waves, microwaves and planar antenna frequencies. The presence of photonic materials as substrate in antennas has some good characteristics such as, supression of light spontaneous emission and suppression of surface waves, allowing the application in planar antenna array. In this work an elaborate analysis using the full wave Transverse Transmission Line - TTL method, that provides efficient and concise results is applied to the planar antennas array with PBG substrate.     

Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equation

We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. While the only small self-similar solution in the strong L^p{\cal L}^{p} space is the null solution, infinitely many self-similar solutions do exist in weak- L^p{\cal L}^{p} spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained.     

Decay Rates in Probability Metrics Towards Homogeneous Cooling States for the Inelastic Maxwell Model

We quantify the long-time behavior of solutions to the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell molecules by means of the contraction property of a suitable metric in the set of probability measures. Existence, uniqueness, and precise estimates of overpopulated high energy tails of the self-similar profile proved in ref. 9 are revisited and derived from this new Liapunov functional. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t → ∞ to the self-similar solution in this distance, which metrizes the weak convergence of measures. Moreover, we can relate this Fourier distance to the Euclidean Wasserstein distance or Tanaka functional proving also its exponential convergence towards the homogeneous cooling states. The findings are relevant in the understanding of the conjecture formulated by Ernst and Brito in refs. 15, 16, and complement and improve recent studies on the same problem of Bobylev and Cercignani⁽⁹⁾ and Bobylev, Cercignani and one of the authors.⁽¹¹⁾     

Structure,Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onions

We describe the topology, structure, and stability of giant fullerenes exhibiting various symmetries (I, I _h , D _2h , T). Our results demonstrate that it is possible to create two new families of nested chiral icosahedral (I) fullerenes namely C₂₆₀@C₅₆₀@C₉₈₀@C₁₅₂₀@, ...,and C₁₄₀@C₃₈₀@C₇₄₀@C₁₂₂₀@ ..., which exhibit interlayer separations of ca. 3.4 Å. These chiral fullerenes are thought to possess metalliclike conduction properties. We discuss in detail the transformation of polyhedral graphitic particles into quasispherical nested giant fullerenes by reorganization of carbon atoms, which result in the formation of additional pentagonal and heptagonal carbon rings. These spherical structures are metastable and we believe they could be formed under extreme conditions, such as those produced by high-energy electron irradiation. There is circumstantial experimental evidence for the presence of heptagonal rings within these spherical fullerenes.     

Comparison of the thermal behavior of three cellulose fibers mercerized or submitted to solar degradation

Comparison of Lyocell, modal and viscose fibers was performed by means of differential scanning calorimetry, thermogravimetry and scanning electron microscopy. Thermal analysis was performed in air atmosphere. Samples were mercerized (21.3 g 100 mL-1) or submitted to solar radiation (seven months). Solar degraded samples presents a higher thermal stability and are initially less degraded. Furthermore, Lyocell fiber is the most stable under thermal degradation conditions. Heating produces a reduction of the fiber diameter (about 50%). This revised version was published online in July 2006 with corrections to the Cover Date.