Mathematical Modeling of the Microstructure of Poly(propylene) Made with Ziegler‐Natta Catalysts in the Presence of Electron Donors

Two different modeling techniques, the method of moments and Monte Carlo simulation, were compared for propylene polymerization with coordination catalysts including a new mechanistic step, site transformation by electron donors. We used the models to show how the molecular weight and tacticity distributions of several poly(propylene) chain populations were affected by changing the concentration of hydrogen, electron donor, and propylene in the reactor, under steady‐state or dynamic operating conditions. The Monte Carlo simulation describes the molecular weight and tacticity distributions for the whole polymer and chain populations with distinct microstructural characteristics. We have also applied the Monte Carlo model to simulate the pentad sequence distributions and its equivalent ¹³C NMR spectra.

     

Fast synthesis employing a microwave assisted neat protocol of new monomers potentially useful for the preparation of PDLC films

It has been reported that the length of the molecular chain and the rigidity of molecules influence the structure of the polymer network in PDLC films and hence the electro-optical properties of the composites. Herein, a series of new aromatic monomeric monomethacrylates, bismethacrylates and monovinylbenzene derivatives with a mesogenic core were successfully synthesized under microwave irradiation. The microwave assisted synthesis resulted in decreased reaction times, reduced solvent requirement, increased operational simplicity, and in most cases, improved yields and selectivity.      

Intraspecific variation in the essential oils from Drimys brasiliensis leaves and stem barks

The essential oils from leaves and stem barks of Drimys brasiliensis Miers (Winteraceae), collected in July and December 2008, were analyzed by GC/FID and GC/MS. The stem bark oils were composed mainly of monoterpenes (July, 45 +/- 3%; December, 92 +/- 4%), while the oils from leaves showed the predominance of sesquiterpenes (July, 47 +/- 1%; December, 55 +/- 1%). The variation in the relative amount of constituents could be associated, at least in part, to several microclimatic parameters such as precipitation, temperature and/or phenological state, which were different for each collection of D. brasiliensis.     

Antioxidant capacity and larvicidal and antifungal activities of essential oils and extracts from Piper krukoffii

The leaves and twigs of Piper krukoffii, collected in the Carajás National Forest, north Brazil, yielded essential oils (2.0% and 0.8%), the main constituents of which were myristicin (40.3% and 26.7%), apiole (25.4% and 34.1%) and elemicin (2.8% and 3.0%). The antioxidant activities of the oils, methanol extract and its sub-fractions were evaluated. The DPPH EC50 values varied from the ethyl acetate sub-fraction (73.4 +/- 3.7 microg/mL) to the methanol extract (24.9 +/- 0.8 microg/mL), and the ABTS TEAC values ranged in the same order from 265.7 to 349.2 microMol TE/g. These results indicated a significant antioxidant activity for the plant. The lignans (-)-kusunokin, yatein, (-)-hinokin and cubebin were identified in the methanol extract. The hydro-methanolic sub-fraction showed a high value for total phenol content (106.5 +/- 0.7 mg GAE/g), as well as 1H NMR signals for sugar moieties. Crude extracts and sub-fractions were also able to inhibit beta-carotene bleaching, varying from 22.4 to 47.1%. The oils from the leaves and twigs showed strong larvicidal (21.4 and 3.6 microg/mL) and fungicide (0.5 and 0.1 microg/mL) activities.     

Modeling and simulation of the coupled mechanical-electrical response of soft solids

Dielectric elastomer (DE) is one type of electro-active polymers (EAP) that responds to electrical stimulation with a significant shape and size change. As EAPs, dielectric elastomers are lightweight, inexpensive, pliable and can be fabricated into various shapes, all of which are attractive properties to justify the intense research in the field. This paper presents a nonlinear, electrical and mechanical coupled, large deformation finite element formulation for DEAs. Maxwell’s equations for the electroquasistatic fields were solved simultaneously with equation of linear momentum. The hyperelastic Ogden model and total Maxwell stress method were combined to describe the material. The formulation was based on the weak forms of Maxwell’s equation and linear momentum expressed in the reference configuration. The closed form consistent tangent moduli for dielectric elastomers were derived. The results of the simulation compared with the experiments have demonstrated the validity of the method from the computational aspect.     

Statistical approach for a hyper-visco-plastic model for filled rubber: Experimental characterization and numerical modeling

This paper presents a campaign of experimental tests performed on a silicone elastomer filled with silica particles. These tests were conducted under controlled temperatures (ranging from ?55 °C to +70 °C) and under uniaxial tension and in shearing modes. In these two classes of tests, the specimens were subjected to cyclic loading at various deformation rates and amplitudes and relaxation tests at various levels of deformation. A statistical hyper-visco-elasto-plastic model is then presented, which covers a wide loading frequency spectrum and requires indentifying only a few characteristic parameters. The method used to identify these parameters consists in performing several successive partial identifications with a view to reducing the coupling effects between the parameters. Lastly, comparisons between modeling predictions and the experimental data recorded under harmonic loading, confirm the accuracy of the model in a relatively wide frequency range and a large range of deformations.     

Surface holonomy for non-abelian 2-bundles via double groupoids

In the context of non-abelian gerbes, we define a cubical version of categorical group 2-bundles with connection over a smooth manifold. We address their two-dimensional parallel transport, study its properties, and construct non-abelian Wilson surface functionals.     

Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications

We introduce a novel algorithm (JEA) to simulate exactly from a class of one-dimensional jump-diffusion processes with state-dependent intensity. The simulation of the continuous component builds on the recent Exact Algorithm (Beskos et al., Bernoulli 12(6):1077–1098, 2006a). The simulation of the jump component instead employs a thinning algorithm with stochastic acceptance probabilities in the spirit of Glasserman and Merener (Proc R Soc Lond Ser A Math Phys Eng Sci 460(2041):111–127, 2004). In turn JEA allows unbiased Monte Carlo simulation of a wide class of functionals of the process’ trajectory, including discrete averages, max/min, crossing events, hitting times. Our numerical experiments show that the method outperforms Monte Carlo methods based on the Euler discretization.     

Existence results for functional first‐order coupled systems and applications

This paper is concerned with the existence of solutions of the first‐order fully coupled system with coupled functional boundary conditions. These functional boundary conditions generalize the usual boundary assumptions and may be applied to most of the classical cases. The arguments used are based on the Arzela‐Ascoli theorem and Schauder's fixed‐point theorem. An application to a mathematical model of the thyroid‐pituitary interaction and their homeostatic mechanism is included.