Molecular weight distribution in emulsion polymerization. II. The copolymer case

A model for evaluating instantaneous degree of polymerization distribution and the chain composition distribution of copolymers produced in emulsion is developed. The approach adopted is based on the mathematics of Markov processes and represents an extension of the one developed for homopolymers in Part I. As in the homopolymer case, the main aspect of the theoretical treatment is the definition of the proper one step transition probability matrix through the so called subprocess-main process procedure. The model accounts for monomolecular and bimolecular termination (both by combination and disproportionation) and, in principle, it can be applied to any number of reacting monomer species as well as to any number of active chains per particle. However, only the 0–1–2 and 0–1–2–3 emulsion copolymerization systems are discussed in detail. In the case of the chain composition distribution, the model allows the calculation of its moments only, through the method of the Generating Function associated with the probability density function. The expression obtained for the instantaneous probability density functions, as well as for the corresponding cumulative distributions, are all in explicit form and involve only algebraic operations among matrices. Efficient numerical procedure for their application are reported in the Appendix. Illustrative calculations are reported for a 0–1–2–3 copolymerization system, simulating the copolymer styrene–methylmethacrylate. The effect of the various termination mechanisms on the distribution of degrees of polymerization and on the first two moments of the chain composition distribution is discussed in detail. Finally, the three dimensional overall distribution function of both chain length and composition is shown under the assumption of Gaussian type chain composition distribution.     

A horizontal Chern–Gauss–Bonnet formula on totally geodesic foliations

Annals of Global Analysis and Geometry - Under suitable conditions, we show that the Euler characteristic of a foliated Riemannian manifold can be computed only from curvature invariants which are...     

Post processing of solution and flux for the nodal mimetic finite difference method

We develop and analyze a post processing technique for the family of low‐order mimetic discretizations based on vertex unknowns for the numerical treatment of diffusion problems on unstructured polygonal and polyhedral meshes. The post processing works in two steps. First, from the nodal degrees of freedom, we reconstruct an elemental‐based vector field that approximates the gradient of the exact solution. Second, we solve a local problem for each mesh vertex associated with a scheme degree of freedom to determine a post processed normal flux that is conservative and divergence preserving. Theoretical results and numerical experiments for two‐dimensional (2D) and 3D benchmark problems show optimal convergence rates. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 336–363, 2015     

Simple Synthetic Routes to Carbene-M-Amido (M=Cu,Ag, Au) Complexes for Luminescence and Photocatalysis Applications

The development of novel and operationally simple synthetic routes to carbene-metal-amido (CMA) complexes of copper, silver and gold relevant for photonic applications are reported. A mild base and sustainable solvents allow all reactions to be conducted in air and at room temperature, leading to high yields of the targeted compounds even on multigram scales. The effect of various mild bases on the N−H metallation was studied in silico and experimentally, while a mechanochemical, solvent-free synthetic approach was also developed. Our photophysical studies on [M(NHC)(Cbz)] (Cbz=carbazolyl) indicate that the occurrence of fluorescent or phosphorescent states is determined primarily by the metal, providing control over the excited state properties. Consequently, we demonstrate the potential of the new CMAs beyond luminescence applications by employing a selected CMA as a photocatalyst. The exemplified synthetic ease is expected to accelerate the applications of CMAs in photocatalysis and materials chemistry.     

Steric control of the donor/acceptor interface: implications in organic photovoltaic charge generation

The performance of organic photovoltaic (OPV) devices is currently limited by modest short-circuit current densities. Approaches toward improving this output parameter may provide new avenues to advance OPV technologies and the basic science of charge transfer in organic semiconductors. This work highlights how steric control of the charge separation interface can be effectively tuned in OPV devices. By introducing an octylphenyl substituent onto the investigated polymer backbones, the thermally relaxed charge-transfer state, and potentially excited charge-transfer states, can be raised in energy. This decreases the barrier to charge separation and results in increased photocurrent generation. This finding is of particular significance for nonfullerene OPVs, which have many potential advantages such as tunable energy levels and spectral breadth, but are prone to poor exciton separation efficiencies. Computational, spectroscopic, and synthetic methods were combined to develop a structure-property relationship that correlates polymer substituents with charge-transfer state energies and, ultimately, device efficiencies.     

Putative palytoxin and its new analogue,ovatoxin-a,in <Emphasis Type="Italic">Ostreopsis ovata</Emphasis> collected along the ligurian coasts during the 2006 toxic outbreak

In this article we report on the liquid chromatography tandem mass spectrometry (LC-MS) investigation of plankton samples collected in the summer of 2006 along the Ligurian coasts, coinciding with a massive bloom of the tropical microalga Ostreopsis ovata. LC-MS analyses indicated the occurrence of putative palytoxin along with a much more abundant palytoxin-like compound never reported so far, which we named ovatoxin-a. On the basis of molecular formula, fragmentation pattern, and chromatographic behavior, the structure of ovatoxin-a appeared to be strictly related to that of palytoxin. We report also on the analysis of cultured O. ovata, which was necessary to unequivocally demonstrate that putative palytoxin and ovatoxin-a contained in field samples were actually produced by O. ovata itself.     

An efficient and conservative hybrid method for solving multidimensional conservation laws

We have developed an efficient hybrid technique for solving nonlinear conservation laws. Previous hybrid techniques have been accurate but lacked the property of conservation, whereas our technique is both accurate and conservative. To achieve this, we superimposed all possible stencils for ENO polynomials and weighted the value from each cells in a way that depends on the numerical solution. Computational efficiency relies on switching from central data where the exact solution is smooth to noncentral data near discontinuities. We prove the theoretical consistency of the technique and discuss the connection with ENO and WENO methods. We introduce time dependency by combining our method with Runge‐Kutta schemes that are TVD preserving. We have verified our technique experimentally by solving a suite of test problems with convex and non‐convex flux functions taken from the literature. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009     

Spectrum Sensing Implemented with Improved Fluctuation-Based Dispersion Entropy and Machine Learning

Spectrum sensing is an important function in radio frequency spectrum management and cognitive radio networks. Spectrum sensing is used by one wireless system (e.g., a secondary user) to detect the presence of a wireless service with higher priority (e.g., a primary user) with which it has to coexist in the radio frequency spectrum. If the wireless signal is detected, the second user system releases the given frequency to maintain the principle of not interfering. This paper proposes a machine learning implementation of spectrum sensing using the entropy measure as a feature vector. In the training phase, the information about the activity of the wireless service with higher priority is gathered, and the model is formed. In the classification phase, the wireless system compares the current sensing report to the created model to calculate the posterior probability and classify the sensing report into either the presence or absence of wireless service with higher priority. This paper proposes the novel application of the Fluctuation Dispersion Entropy (FDE) measure recently introduced in the research community as a feature vector to build the model and implement the classification. An improved implementation of the FDE (IFDE) is used to enhance the robustness to noise. IFDE is further enhanced with an adaptive method (AIFDE) to automatically select the hyper-parameter introduced in IFDE. Then, this paper combines the machine learning approach with the entropy measure approach, which are both recent developments in spectrum sensing research. The approach is compared to similar approaches in literature and the classical energy detection method using a generated radar signal data set with different conditions of SNR(dB) and fading conditions. The results show that the proposed approach is able to outperform the approaches from literature based on other entropy measures or the Energy Detector (ED) in a consistent way across different levels of SNR and fading conditions.