An adaptive pruning algorithm for the discrete L-curve criterion

We describe a robust and adaptive implementation of the L-curve criterion. The algorithm locates the corner of a discrete L-curve which is a log–log plot of corresponding residual norms and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations). Our algorithm needs no predefined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned L-curves that correspond to considering the curves at different scales. We compare our new algorithm to existing algorithms and demonstrate its robustness by numerical examples.     

An interior estimate for a nonlinear parabolic equation

In this paper the derivatives of the solution of an initial boundary value problem for a nonlinear uniformly parabolic equation in the interior with the total variation of the boundary data and the L^∞-norm of the initial condition are estimated.     

Photochromic reverse mode polymer dispersed liquid crystals

Control of light intensity and colour are two of the major features required in the realization of smart windows. We designed a bi-functional polymer dispersed liquid crystal (PDLC) film in order to satisfy such requirements, i.e. it is able both to modulate the optical transmission, if an external electric field is applied, and to change colour if exposed to sunlight. A monomer/liquid crystal mixture was doped with a small amount of photochromic material and homeotropically aligned by means of rough surfaces. A transparent and pale pink coloured film was achieved after photopolymerization. Such a film changes colour upon exposure for some seconds to sunlight or ultraviolet radiation in a persistent but reversible manner. In addition, the film appears transparent without the application of an electric field (OFF state) and becomes opaque on application of a driving voltage of about 75 V (ON state), and thus the film operates in reverse mode with respect to conventional PDLCs.     

Modification of surface properties of electrospun polyamide nanofibers by means of a perfluorinated acridine

Polyamide 6 (PA6) nanofibers were prepared from formic acid solutions by using electrospinning technique. The fibers were smooth, defects free and with diameters smaller than 200 nm. Small amounts of a perfluorinated acridine were added as dopant to the feed solution to modify the wettability of the fibers. The effect of doping on the contact angle values is well apparent. The contact angle values go from 50° of pure PA6 to 120° when 6% of acridine is added. A comparison between fibers and films of pure and doped polyamide 6 was carried out in order to determine the effect of morphology on wettability. Thermal annealing near the T_g of the polymer promoted the segregation of the molecules to the surface, reaching contact angles of 131° with smaller amounts (4%) of acridine. The surface segregation was also promoted by time aging.     

Continuous reaction system to investigate the dispersion polymerization of vinyl monomers in supercritical carbon dioxide

A laboratory‐scale continuous reaction system using a stirred tank reactor was assembled in our laboratory to study the dispersion polymerization of vinyl monomers in supercritical carbon dioxide (scCO₂). The apparatus was equipped with a suitable downstream separation section to collect solid particles entrained in the effluent stream from the reactor, whose monomer concentration could be measured online with a gas chromatograph. The dispersion polymerization of methyl methacrylate in scCO₂ was selected as a model process to be investigated in the apparatus. The experiments were performed at 65 °C and 25 MPa with 2,2′‐azobisisobutyronitrile as the initiator and a reactive polysiloxane macromonomer as a surfactant to investigate the effect of the mean residence time of the reaction mixture on the monomer conversion, polymerization rate, polymer molecular weight, and particle size distribution. The results were compared with those obtained in batch polymerizations carried out under similar operative conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4122–4135, 2006     

Components of the Hilbert scheme of smooth space curves with the expected number of moduli

For any d and g such that the Brill-Noether number (d,g,3) is negative, d20 and gf(d), where f(d)=d^3/2/(6·2^1/2) + lower order terms, there exists a regular component of H _d,g ³ (the closure in Hilb₃ of the open set parametrizing smooth, connected, non-degenerate curves in ₃) with the expected number of moduli. Moreover, examples of the fact that such components are not unique are given.