TERAHERTZ QUALITY CONTROL OF POLYMERIC PRODUCTS

We report on experiments that evaluate the potential of terahertz (THz) time-domain spectroscopy (TDS) for quality control of polymeric compounds. We investigate specimens out of a polyethylene compound with silver-coated titanium dioxide nanospheres and a glass-fiber reinforced epoxy composite. We further examine an industrial polymer product produced by injection molding. Our data demonstrates that THz imaging is a powerful tool for contactless quality control in the polymer industry.     

Weighted Sobolev embedding with unbounded and decaying radial potentials

We prove embedding results of weighted W1,p(RN) spaces of radially symmetric functions. The results then are used to obtain ground and bound state solutions of quasilinear equations with unbounded or decaying radial potentials.     

Kinetics and mechanisms of chlorine transfer from chloramine to amines in aqueous medium

The kinetics and the equilibrium constant of the chlorine transfer reaction between monochloramine NH₂Cl and the amines: C₂H₅NH₂, (CH₃)₂CHNH₂, (CH₃)₂NH, and (C₂H₅)₂NH are investigated by spectrophotometry in aqueous medium at 25°C, in the pH range from 8 to 13 and for an ionic strength equal to 1.03 ± 0.05M. For a concentration of total ammonia equal to 1M, the observed rate constant is pH independent below 8 and above 12.8 and reaches a maximum located between the pK_as of NH₄⁺ and RR'NH₂⁺. From these results and those obtained earlier for NH₂Cl and CH₃NH₂, the reaction is shown to involve an interaction between neutral molecules NH₂Cl and RR'NH, subject to general acid catalysis. The ability of an interaction corresponding to a specific catalysis and involving NH₃Cl⁺ and RR'NH rather than NH₂Cl and RR'NH₂⁺ is also discussed. The activation parameters are given for each reaction.     

Global Optimal Image Reconstruction from Blurred Noisy Data by a Bayesian Approach

In this paper, a procedure is presented which allows the optimal reconstruction of images from blurred noisy data. The procedure relies on a general Bayesian approach, which makes proper use of all the available information. Special attention is devoted to the informative content of the edges; thus, a preprocessing phase is included, with the aim of estimating the jump sizes in the gray level. The optimization phase follows; existence and uniqueness of the solution is secured. The procedure is tested against simple simulated data and real data.     

Evolution equations for shapes and geometries

The first object of this paper is to introduce a new evolution equation for the characteristic function of the boundary Γ of a Lipschitzian domain Ω in the N-dimensional Euclidean space under the influence of a smooth time-dependent velocity field. The originality of this equation is that the evolution takes place in an L^p-space with respect to the (N − 1)-Hausdorff measure. A second more speculative objective is to discuss how that equation can be relaxed to rougher velocity fields via some weak formulation. A candidate is presented and some of the technical difficulties and open issues are discussed. Continuity results in several metric topologies are also presented. The paper also specializes the results on the evolution of the oriented distance function to initial sets with zero N-dimensional Lebesgue measure.     

A New Differential Method Applied to the Study of Arbitrary Cross Section Microstructured Optical Fibers

The present work adapts a recent grating theory called “Fast Fourier factorization” to cylindrical coordinates in order to study microstructured optical fibers (MOFs). Compared with the classical differential method, this new differential method takes into account the truncation of Fourier series and the discontinuities of the fields across the diffracting surface with the help of new factorization rules. The main advantage of this method is that the directrix of the diffracting cylindrical surface is arbitrary and permits anisotropic and inhomogeneous media although its numerical application needs longer computation time, compared with other well-known numerical methods. The S-propagation algorithm is used to avoid numerical contaminations. The numerical results are validated and compared with the well-established Multipole method in the case of a MOF with six circular cylinders. Further, a new cross-sectional profile (with sectorial inclusions) that the Multipole method cannot consider is studied.     

Free energy of the spherical mean field model

We compute at any temperature the free energy of the multi p-spin spherical model when only terms for p even are considered. Work partially supported by an NSF grant