An adaptive scheme for the approximation of dissipative systems

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, a regular explicit Euler scheme–with constant or decreasing step–may explode and implicit Euler schemes are CPU-time expensive. The algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. Several examples are presented including gradient dissipative systems and Hamiltonian dissipative systems.     

A combined mixed and discontinuous Galerkin method for compressible miscible displacement problem in porous media

In this paper, we present a numerical scheme for solving the coupled system of compressible miscible displacement problem in porous media. The flow equation is solved by the mixed finite element method, and the transport equation is approximated by a discontinuous Galerkin method. The scheme is continuous in time and a priori hp error estimates is presented.     

Poly(L‐lysine) and clay nanocomposite with desired matrix secondary structure: Effects of polypeptide molecular weight

Nanocomposites (NC) were formed using cationic poly(L ‐lysine) (PLL), a semicrystalline polypeptide, that was reinforced by sodium montmorillonite (MMT) clay via solution intercalation technique. By varying solution conditions such as pH, temperature, and polypeptide concentration in the presence of clay platelets, the secondary structure of PLL was controllably altered into α‐helical, β‐sheet, and random coil. The high molecular weight polypeptide shows a strong propensity to fold into the β‐sheet structure when cast as films, irrespective of the initial secondary structure in solution. Nanocomposite local morphology confirms intercalated MMT platelets with PLL over a wide range of compositions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 239–252, 2007.     

Influence of organic modifiers on morphology and crystallization of poly(ϵ‐caprolactone)/synthetic clay intercalated nanocomposites

ε‐caprolactone was polymerized in the presence of neat montmorillonite or organomontmorillonites to obtain a variety of poly(ε‐caprolactone) (PCL)‐based systems loaded with 10 wt % of the silicates. The materials were thoroughly investigated by different X‐ray scattering techniques to determine factors affecting structure of the systems. For one of the nanocomposites it was found that varying the temperature in the range corresponding to crystallization of PCL causes reversible changes in the interlayer distance of the organoclay. Extensive experimental and literature studies on this phenomenon provided clues indicating that this effect might be a result of two‐dimensional ordering of PCL chains inside the galleries of the silicate. Small angle X‐ray scattering and wide angle X‐ray scattering investigation of filaments oriented above melting point of PCL revealed that polymer lamellae were oriented perpendicularly to particles of unmodified silicate, while in PCL/organoclay systems they were found parallel to clay tactoids. Calorimetric and microscopic studies shown that clay particles are effective nucleating agents. In the nanocomposites, PCL crystallized 20‐fold faster than in the neat polymer. The crystallization rate in nanocomposites was also significantly higher than in microcomposite. Further research provided an insight how the presence of the filler affects crystalline fraction and spherulitic structure of the polymer matrix in the investigated systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2350–2367, 2007     

On the pivot structure for the weighing matrix W(12,11)

In the present article we concentrate our study on the growth problem for the weighing matrix W(12,11) and show that the unique W(12,11) has three pivot structures. An improved algorithm for extending a k × k (0,+,-) matrix to a W(n,n-1), if possible, has been developed to simplify the proof. For the implementation of the algorithm special emphasis is given to the notions of data structures and parallel processing.     

A nondifferentiable extension of a theorem of Pucci and Serrin and applications

We study the multiplicity of critical points for functionals which are only differentiable along some directions. We extend to this class of functionals the three critical point theorem of Pucci and Serrin and we apply it to a one-parameter family of functionals Jλ, λ∈I⊂R. Under suitable assumptions, we locate an open subinterval of values λ in I for which Jλ possesses at least three critical points. Applications to quasilinear boundary value problems are also given.     

Formation of functional groups on graphite during oxygen plasma treatment

Improved sample wettability was obtained by oxygen plasma functionalization of pyrolytic graphite. The samples were exposed to highly dissociated oxygen plasma with the density of 1 × 10¹⁶ m⁻³, the electron temperature of about 5.5 eV and the density of neutral oxygen atoms of 8 × 10²¹ m⁻³ for 20 s. The surface wettability was measured by a contact angle of water drop. The contact angle dropped from original 112° down to about 1°. The functional groups were detected by XPS analyses. The survey spectrum showed a substantial increase of oxygen concentration on the surface, while high-resolution analyses showed additional oxygen was bonded onto the graphite surface in the form of C-O polar functional group responsible for the increase of the surface energy.     

A Note on Log-Convexity of q-Catalan Numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q = 1, to the Catalan numbers: 1, 1, 2, 5, 14,…, a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted. Received January 2, 2007     

Many body effects and internal transitions of confined excitons in GaAs and CdTe quantum wells

Many body effects contribute significantly to the energy states of electron-hole pairs confined in quantum wells in the presence of excess electrons. We present results of optically detected resonance spectroscopy of the internal transitions of photo-excited electron-hole pairs in the presence of excess electrons for GaAs QWs and CdTe QWs. Compared to the case of isolated negatively charged excitons, excess electrons produce a large blue shift of the internal transitions in modulation-doped GaAs quantum wells (QWs) for filling factor <2, and similar effects are found in CdTe QWs. For filling factor >2 no internal transitions are observed. These measurements demonstrate the strong effects of electron-electron correlations on the internal transitions of charged excitons in these quasi-2D systems and the importance of magnetic translation invariance. In the presence of excess electrons, the observed internal transitions are those of a magnetoplasmon bound to a mobile valence band hole.     

Electrochemical characterization of poly(vinylidenefluoride)-zinc triflate gel polymer electrolyte and its application in solid-state zinc batteries

Gel polymer electrolyte (GPE) films comprising of poly(vinylidenefluoride), propylene carbonate, ethylene carbonate and zinc trifluoromethane sulfonate are prepared and characterized. The composition of GPE is optimized to contain minimum liquid components with a maximum specific conductivity of 3.94×10⁻³ S cm⁻¹ at (25±1) °C. A detailed investigation on the properties such as ionic conductivity, transport number, electrochemical stability window, reversibility of Zn/Zn²⁺ couple and Zn/gel electrolyte interfacial stability have been carried out. The ionic conductivity follows a VTF behaviour with an activation energy of about 0.0014 eV. Cationic transport number varies from 0.51 at 25 °C to 0.18 at 70 °C. Several cells have been assembled with GPE as the electrolyte, zinc as the anode, γ-MnO₂ as the cathode and their charge–discharge behaviour followed. Capacity values of 105, 82, 64 and 37 mAh/g of MnO₂ have been achieved at 10, 50, 100 and 200 μA/cm² discharge current densities, respectively. The discharge capacity values are almost constant for about 55 cycles for all values of current densities. Cyclic voltammetric study of MnO₂ electrode in Zn/GPE/MnO₂ cell clearly shows intercalation/deintercalation of Zn²⁺.